Microwave Reflector Antenna Design Concepts and

MICROWAVE REFLECTOR ANTENNA DESIGN CONCEPTS AND TECHNIQUES

Roland Schwerdtfeger 2011

MICROWAVE REFLECTOR ANTENNA

DESIGN CONCEPTS AND TECHNIQUES

Roland Schwerdtfeger

March 2011

MICROWAVE REFLECTOR ANTENNA DESIGN CONCEPTS AND TECHNIQUES Roland Schwerdtfeger

MICROWAVE REFLECTOR ANTENNA

DESIGN CONCEPTS AND TECHNIQUES

Roland Schwerdtfeger

December 2010


Copyright (C) 2010 by Roland Schwerdtfeger.

All rights to this book are reserved. No part of this publication may be reproduced, copied, or distributed to anyone without written permission from the author. [email protected] While the author believes the information and guidance given in this work is correct, all parties must rely upon their own skill and judgment when making use of it. The author assumes no liability to anyone for any loss or damage caused by any error or omission in the work, whether such error or omission is the result of negligence or other cause. Any and all liability is disclaimed. First Edition: Printed in the United States of America. April 2010 Revision: December 2010 Second Revision: March 2011

Cover Photographs

Used with permission of General Dynamics SATCOM Technologies Inc.

Reflector Antenna Assemblies

7m L-band 1-port lp Rx only 8.5m S-band lp dual offset

9m Ka-band 4-port cp with monopulse

Feed Systems

S/X 8-port cp Rx/Tx with monopulse C/Ku/Ka 6-port cp/lp mono Rx only

X 2-port cp Rx/Tx

Introduction


i

Introduction Objective This collection of notes is intended to offer some insight into the subject of microwave antennas for satellite communications. Microwaves cannot be seen, heard, or even felt. And so, gaining an appropriate understanding of the nature and control of microwaves has its difficulties. World-wide, individuals and enterprises are involved in the business of operating one or more satellite links. Many have only a rudimentary understanding of how the microwave antenna segment of these links functions. Young engineers with a university training in microwave theory and associated mathematics lack the experience to recognize a particular design approach, or to understand specific and singular difficulties in performance once a design is complete. Technicians without the substantial physical and mathematical background to work through the intricacies of microwave antenna and feed system design, have their moments of frustration when asked to engage in assembling and testing components and systems designed by others. Many books and papers on the subject of antennas engage in complicated, and in some instances, abstruse mathematics and concepts. The present work offers some descriptive thoughts on the physical nature of microwaves, how they can be guided from a transmitter to an antenna, and discusses how the antenna radiates microwave energy toward a specific target with the least amount lost in the process. Low level signals received from a satellite are subject to interference, creating difficulties that require special design concepts to ensure the least amount is lost on its way to the station receiver. The principal thrust here is to offer an understanding of techniques with which an appropriate model of an antenna system can be laid out against a specific performance requirement. Then, with the minimum of complex mathematics, to set up a preliminary model which can form the basis for either empirical refinement in the lab, or with a variety of computational routines, to meet severe performance specifications often controlled by independent Government agencies. Short history Commercial satellite communications started in the early 1960s using the C-band 5.925-6.425 GHz uplink and 3.7-4.2 GHz downlink. The US, Canada, Britain, Germany, France and Spain contributed earth station antenna systems to communicate with the first LEO (low earth orbit) satellite called Relay. Interestingly, each of these antennas adopted a singular RF design approach.

▪ US - Andover Maine - Bell Telephone - a 67ft horn reflector ▪ Canada - Mill Village, Nova Scotia - Dept of Transport - a classic 85ft Cassegrain ▪ Britain - Goon Hilly - British Post Office - 25m prime focus ▪ Germany - Raisting - German Post Office - 25m two reflector quasi beam waveguide Cassegrain

Low satellite power prompted large antenna sizes and low feed losses. In 1965, the first of the GEO (Global Equatorial Orbit) stationary satellites became available. These satellite operations soon were placed under the control of an international organization called Intelsat. In the 1970s, Intelsat "Standard A" antenna sizes increased to 32m to accommodate lower antenna operation cost demands, yet maintain received signal quality. As the number of satellites increased, interference from neighbouring satellites forced antenna designs to possess low level sidelobes. Additionally, dual polarization techniques increased communication capacity, prompting low cross-pol characteristics to minimize same satellite interference. Deep space communication with spacecraft on long distance journeys to the fringes of the solar system, and radio telescopes operating anywhere from 100 MHz to 1 Terahertz, represent the continued use of very large fully steerable precision reflector antennas, in some instances up to 100m in size, and equipt with cryogenically cooled low noise amplifiers to suppress the system noise floor to the absolute minimum. The 1980s saw the introduction of the 11-13m C-band "Standard-B", and the 13m Ku-band "Standard C" using the 14.0-14.5 GHz uplink and 10.95-12.75 GHz downlink. Satellite power levels increased. For the low link capacity applications 4.5-6.1m Ku-band, small 2.4m to 4.5m Ku antennas for low capacity applications such as for banks, public TV broadcast, and direct satellite-to-home broadcast at C-band were next. Remote earth sensing satellites for scientific and meteorological purposes adopted the S-band and the upper X-band. Military interests came early, adopting the single polarized X-band 7.9-8.4 GHz uplink

Introduction


ii

and 7.25-7.75 GHz in 20ft, 38ft, and 60ft Cassegrain antennas. These designs were accompanied by special antennas for MILstar satellites working Ka/Q bands 20.2-21.2 GHz downlink and 43.5-45.5 GHz uplink. Other obscure frequency bands followed for very high gain surveillance applications at the Kt/Ka bands. The 1990s saw the advent of satellites simultaneously operating multiple frequency bands such as C and Ku, L and C, S and X, S and Kt, X and Ku, Ku and Ka, and even C+X+Ku and C+Ku+Ka bands, as well as multi-beam antennas to link with several satellites simultaneously. Because of the global aspects of earth station performance, independent regulatory agencies have been established by various International government agencies to ensure that satellite links do not interfere with each other. The FCC in the US and Eutelsat in Europe, as well as a number of regional organizations, dictate uplink flux densities, sidelobe envelope, and cross-pol performance. Communications owners dictate the G/T and uplink power handling based on link budgets calculated on specific satellites. Special antenna systems for TTC (Telemetry, Tracking and Control) and IOT (In Orbit Test) functions, demanding high precision calibrated antenna designs to establish the exact position of a target satellite and measuring its receive and transmit performance, are in continuous operation; in other words, monitoring the relative health of an orbiting satellite. In the beginning, costs of antenna instruments were secondary - performance was first. Today, costs are of paramount importance. Many owners are now faced with changing satellite links involving new frequency bands and functions, and for financial reasons want to convert existing antennas. However, there are many dangers with such moves, and antenna designers must be able to understand the difficulties associated with damaged antennas, constraints in reusing existing feeds, and polarization and frequency compatibility. Since 1962, satellite eirp has increased from less than 0dbm to >50dbW. In step, earth based reflector antennas have become smaller in size - from 32m at C-band to 50cm at Ku-band. This has sparked a need for vehicle mounted communications for SOTM (Satellite communications On The Move). These small multi-function antennas demand new RF and mechanical packaging design concepts and methods. For the future, reflector antenna precision will remain a requirement. And feed system design will need to offer increasingly wider frequency bandwidths and lower losses in ever more compact packages, involving new waveguide components. Life of the microwave antenna engineer Microwave antennas involve

▪ precision mechanical and structural engineering ▪ a comprehensive understanding of the nature of microwaves and the components used to control

them, and reflector optics ▪ interface engineering ▪ electrical and mechanical measurement techniques to establish proof-of-performance

To complicate the life of the microwave antenna design engineer – working on several antenna projects at the same time; project engineering pressuring him/her to finish the job on a predetermined estimate of the design-fabrication-test schedule – quite likely estimated by someone in marketing while being pressured by a customer who thinks he needs the antenna yesterday. So the necessary disciplines of an engineer working in commercial industry can be summed up with the following list:

▪ Evaluate the Customer’s request and understand the mission for the antenna system ▪ Propose a technical solution that is effective – in performance as well as cost ▪ Generate an effective plan that delineates details and delivery estimates of all actions needed to

complete the work. This to be used to unequivocally establish when the job can be completed. ▪ Educate the Customer, as well as those within the company contributing to the program, during

technical reviews. In particular, the engineer must be able to impart concepts, methods, and understanding to new members of the technical staff, so that the enterprise can continue to thrive and prosper. So it is hoped that this book can form a basis for continued education for all interested participants in the sport of microwave antenna engineering.

Introduction


iii

Biographical sketch As director of the RF Development Labs at Vertex Communications from 1988 to 2003, the need became clear early on that instructive material was needed for the engineering and technician staff in the labs. In the process, I also realized there were several aspects of feed system design about which I was not certain. It prompted detailed examination of the matter. The beginnings of this book were hand-written and used for many years as instructional material and even handed out to interested Customers. But when too many errors crept into the work, and corrections became increasingly difficult, the original notes were transcribed and reorganized into the present book. Born in Adelaide, Australia in 1941, the author attended the School of Engineering at McGill University in Montreal and graduated in 1963 with a BEng degree. An introduction to serious microwave engineering was acquired at RCA Victor Co. Ltd. under the leadership of Peter Foldes, while participating in a project for the first Canadian earth station in Mill Village Nova Scotia in 1965. Post graduate studies on reflector antennas were undertaken at the University of Southern California (USC) with Dr Willard Rusch in 1979. A brief sojourn in Switzerland with Huber + Suhner AG permitted some consultative time with the Swiss PTT on the subject of a new earth station at Leuk. A new RF Lab was set up at H+S while developing a transportable C and Ku band man-pack antenna for the Swiss Army. 1982 to 1983 gave a brief time to assist Spar Aerospace in Montreal in their short escapade into the business of large earth station antennas. Scientific Atlanta supported entry into the US. 1984 to 1988 was time to experience self employment as a technical consultant with company name Antenna Design and Consulting. Since 1988, the author has been with Vertex Communications Corporation (now General Dynamics SATCOM Technologies) in Kilgore, Texas - initially as Director of RF Development Labs, and since 2003 as Director of RF Concepts and Technical Advisor. He is a Life Member of the IEEE. Acknowledgements Initial introductions into the mysteries of microwaves were given me in 1962 by Professor Tom Pavlasek in an electromagnetics class at McGill University, Montreal, Canada. But the real practical aspects were only discovered in 1963 under the valuable and greatly appreciated guidance of Peter Foldes, the director of the antenna RF Labs at RCA. Great opportunities to assist in the development of new multimode components and feed systems for earth station antennas and methods of measurement were provided by Peter. This was at a time when much empirical work was performed, based on preliminary hunches and some fundamental arithmetic, and then, with an acquired finger-tip feel, refined without aid of computational equipment. Andreas Bosshard, manager of the RF Development Labs at Huber + Suhner in Herisau, Switzerland, was instrumental in supporting and contributing to inventive work on the cavity backed dipole feed for a Swiss Army requirement in 1977. Fred Maeder, Klaus Duespohl and staff at Krupp (later to become Vertex Antennentechnik), supported my life as a private consulting engineer with several major cutting edge multi frequency band antenna projects in Germany in 1984, thereby providing the opportunity to realize high efficiency C/Ku antenna systems. To all these gentlemen, many thanks for your very kind attentions. Heartfelt thanks must go to Rex Vardeman and Helmut Schwarz of Vertex Communications Corporation, who in 1988 invited me to join the Vertex RF Labs with design and development capabilities to create a large palette of special multiband and multi-function antennas large and small – many with selectable polarization and tracking functions. Warmest regards are accorded Dr. Robert Hoferer, Dr. Nader Farahat (both of General Dynamics SATCOM Technologies), and Dr. Christophe Granet (CSIRO – BAe Systems Australia), for kindly offering their valuable time for comment and criticism on the manuscript. In particular, special thanks to Neville Hesketh, a long time friend in Ballarat, Australia, for an intensive proof-reading effort and editing suggestions, prompting this revision. Also thanks to the many interested colleagues who have kindly stayed awake during frequent lectures, which formed the basis for much of the material included in this book.

Introduction


iv

In Memorium Good friend and close professional colleague Dr. Raj Chugh, who passed away 23 May 2005, is to be remembered as a very clever computational antenna designer. He contributed greatly to these notes by offering many hours of constructive technical discussion and criticism. In large part, the reflector designs put forward by Raj during his time as Principal Engineer are still currently offered by General Dynamics SATCOM Technologies. Dedication Since the bulk of this work was prepared at home, my wife Marilyn essentially suffered many years from an uncommunicative presence writing and studying at the kitchen table. She has travelled with me to various antenna sites, and has a measure of understanding of the issues. Therefore, it is fitting that this book be dedicated to her. Corrections During the past year, a number of items have been detected by readers that required correction, and these have been incorporated in to this 2011 revision of the book. Roland Schwerdtfeger March 2011 Kilgore, Texas 75662

The author at CSIRO’s impressive 64m Radio Telescope in Parkes, NSW, Australia - 2007

Table of Contents


v

Table of Contents Chapter 1 - Radiated Fields 1.1 What are Radio Waves ? 1 1.2 The Nature of Radiated Fields 6 1.3 Transmission Line 11 1.4 Types of Transmission Line 14 1.4.1 Coaxial Lines 14 1.4.2 Rectangular Waveguide 15 1.4.3 Complex Rectangular Waveguide Components 19 1.5 Circular Waveguide 28 1.5.1 Circular Waveguide Modes 28 1.5.2 Circular Waveguide Components 31 Chapter 2 - Reflector Design 2.1 Introduction 34 2.1.1 Concept of Gain 34 2.1.2 Determination of Gain 36 2.1.3 Concept of "Gain Relative to Isotropic" 37 2.2 Single Reflector Antenna 39 2.2.1 Prime-Focus Antenna Efficiency Components 41 2.2.2 General Performance Features 45 2.3 Two Reflector Design 46 2.3.1 Cassegrain and Gregory Configurations 46 2.3.2 Antenna Efficiency Components 49 2.3.3 Shaped Reflector Design Considerations 52 2.3.4 The Ring-Focus Antenna 59 2.4 Off-set Reflector Antennas 61 2.4.1 Single Offset Reflector Antenna 61 2.4.2 Horn Reflector 65 2.4.3 Dual Offset Antennas - Cassegrain and Gregorian 66 2.4.4 Dragonian Reflector System 69 2.5 Characteristics of Antenna Patterns 69 2.5.1 Concept of Antenna Pattern Gain 73 Chapter 3 - Feed Horn Design 3.1 Feed Horn Design Considerations 79 3.2 Phase Fronts and Phase Errors 82 3.3 Pyramidal and Conical Horn 84 3.4 The Diagonal Horn 89 3.5 Smooth-walled Multimode Horn 90 3.6 The Corrugated Horn 92 3.7 Multi-frequency Corrugated Horn 94 3.8 The Finned Horn 97 3.9 The Quad-ridge Horn 99

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3.10 Small Aperture Horn 99 3.10.1 Introduction 99 3.10.2 Prime Focus Horn 100 3.10.3 Cavity-backed Dipole 101 3.11 Concentric Aperture Horn 104 3.12 Rudimentary Design Considerations for a Feed Horn 105 Chapter 4 - Feed Systems Design 4.1 Introduction 109 4.2 Linearly Polarized Rx Feed Design and Configurations 110 4.2.1 Example Satellite Link 110 4.2.2 Single Linear Polarization - with Polarization Rotation 114 4.2.3 Dual Linear Polarization - Receive Only 116 4.2.4 Linearly Polarized Tx/Rx Feed Design and Configurations 116 4.2.5 Linear Polarization - Two Orthogonal Rx and One Tx 117 4.2.6 Dual Linear Polarized Rx and Tx 120 4.3 Circular Polarization - Receive Only Feed Configurations 122 4.3.1 OMT + 90 deg Power Divider 123 4.3.2 Differential Phase Shifter with OMT 124 4.3.3 Septum OMT 128 4.3.4 OMT with Rectangular Horn 130 4.4 2-port Circularly Polarized Rx/Tx Feed Systems 131 4.4.1 4-port CP Feed Network 133 4.5 Polarization Rotation and Switching 133 4.5.1 90 deg Differential Phase Shifter - CP/LP Selection 134 4.5.2 180 deg Differential Phase Shifter - LP Angle Adjust Only 135 4.5.3 CP/LP and LP Angle Adjust 137 4.5.4 90 deg Differential Phase Shifter - CP Adjust 138 4.5.5 CP/LP Selection - 2-port Rx/Tx Feed 138 4.6 Combined Dual Polarized Tx/Rx Feed Configuration 139 4.6.1 Single QJ and Magic Tee Feed System Network Layout 140 4.6.2 Twin QJ Feed System Layout 140 4.6.3 Combined CP and LP Tx/Rx Feed Configuration 141 4.7 Feed System Terminal Characteristics 143 4.7.1 VSWR - Effect of Multiple Contributions 144 4.7.2 Practical Matching Techniques 145 4.7.3 Polarization Discrimination - Axial Ratio and Cross-pol 146 4.7.4 Port-to-Port Isolation 146 4.7.5 Insertion Loss 146 4.7.6 Signal Delay Time 147 Chapter 5 - Antenna System Design Issues 5.1 Polarization 149 5.1.1 Linear and Circular Polarization 149 5.1.2 Aspects of Cross-polarization in Antennas 161 5.1.3 Polarization in Offset Antennas 166 5.1.4 Cross-pol Matched Feed System for Single Offset Reflector Applications 173

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5.2 Noise in Antennas 176 5.2.1 Noise Mechanisms 176 5.2.2 Signal-to-Noise Ratio 176 5.2.3 Noise Power 176 5.2.4 Equivalent Noise Temperature 177 5.2.5 Noise Figure 178 5.2.6 Antenna Noise Temperature 179 5.2.7 Noise in a Satellite – Earth Station Link 181 5.2.8 Antenna System G/T 182 5.2.9 Antenna Noise Temperature Components 182 5.2.10 Sky Noise Temperature Variation with Ambient Temperature and Humidity 189 5.3 Interference in Antennas 191 5.3.1 Introduction 191 5.3.2 Interference by the Transmitter 192 5.3.3 Interference by Tx Signal Power 194 5.3.4 Interference due to Tx Noise Power 196 5.4 Passive Intermodulation in Antennas 199 5.4.1 Brief History 199 5.4.2 Theory 199 5.4.3 Some Interesting Observations 203 5.5 Link Analysis 206 5.5.1 Uplink Analysis 206 5.5.2 Downlink Analysis 208 5.5.3 EIRP and Power Density 210 Chapter 6 - Tracking Feed Systems 6.1 Introduction 213 6.2 Maximum Signal “Search and Track” Methods 215 6.2.1 Step Track 215 6.2.2 Conical Scan 216 6.2.3 Electronic Conical Scan 217 6.3 Zero Signal Track Methods 219 6.3.1 Phase-amplitude Monopulse 219 6.3.2 TE21 mode Coupler Design Concepts 221 6.4 Array Monopulse Feeds 231 6.4.1 4-horn “cross” Array 231 6.4.2 4-horn “corner” Array 233 6.4.3 The Integrated 5-horn Array 233 6.4.4 Polarization Requirements for Monopulse Functions 237 6.4.5 Monopulse Detection Methods 237 6.5 Array Analysis and Design 241 Chapter 7 - Special Application Antennas 7.1 Antennas with Simultaneous Multi-band Feeds 250 7.1.1 Single Aperture Feed Horn 250 7.1.2 Wideband Feed Horn 254 7.1.3 Concentric Aperture Feed Horns 254 7.1.4 Dual Aperture Feeds with FSS 256

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7.2 Selectable Multi-feed Systems 256 7.3 Beam-waveguide 259 7.3.1 Introduction 259 7.3.2 Large Antenna Beam Waveguide 259 7.3.3 The Quasi Beam Waveguide 265 7.4 Multi-beam Antennas 267 7.4.1 Introduction 267 7.4.2 The Torus 270 Chapter 8 - Structural and Mechanical 8.1 Antenna Configurations 282 8.2 Antenna Axis Configurations 285 8.3 Reflector Support Structures 291 8.4 Reflector Geometries 295 8.5 Reflector Accuracy 297 8.6 Design of Reflector Panels 299 8.6.1 Main Reflector Fabrication 300 8.6.2 Subreflector Fabrication 306 8.7 Pointing Accuracy 306 8.8 Structural Alignment 315 8.9 Panel Alignment 316 8.10 Influences of Weather 318 8.11 Mechanical Layout Concepts for Complex Feed Systems 319 Chapter 9 - Proof-of-Performance 9.1 The Specification 322 9.2 Basic System Requirements 323 9.3 Factory Testing 324 9.3.1 Feed System and Performance Features 324 9.3.2 Feed System – Sample Measurements 328 9.3.3 Reflector System 331 9.3.4 Effects of Reflector Errors 335 9.3.5 Other Subsystems 336 9.3.6 Outdoor Test Range 337 9.4 Customer Site Preparations 345 9.4.1 Pedestal Alignment Check 345 9.4.2 Reflector and Feed System Mechanical Alignment Check 345 9.4.3 Ancillary Equipment Function Check - Control System, LNAs, HPAs 346 9.4.4 IFL Signal Path Integrity 346 9.4.5 Pretest Preparations 347 9.4.6 Test Equipment, Location, Setup, and Function Check 349 9.5 Preliminary RF Checks 349 9.5.1 Sum Patterns 350 9.5.2 Difference Patterns 354 9.5.3 Antenna Gain 358 9.5.4 Antenna Noise Temperature 358 9.5.5 Radio Star Track Check 358 9.5.6 IFL Signal Paths 359

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9.6 Formal On-site RF Antenna Tests 360 9.6.1 Antenna Patterns - Sum, Difference, Cross-pol 360 9.6.2 Monopulse Tracking Sensitivity 361 9.6.3 Antenna Noise Temperature 361 9.6.4 Antenna System G/T, Noise Temperature, and Gain 362 9.6.5 Transmit Uplink Gain and eirp Stability 365 9.7 Measurement Accuracy 365 Chapter 10 - Antenna Protection 10.1 Protecting the Feed against the Elements 366 10.1.1 Feed Horn Window Considerations 366 10.1.2 Feed Pressurization Principles 367 10.1.3 Waveguide System Dehydration 372 10.2 Feed Protection against Rain, Mist, Snow and Ice, and Birds 374 10.3 Radomes 377 10.3.1 Sandwich Radomes 381 10.3.2 Space Frame Radomes 382 10.3.3 Solid Laminate Radomes 387 10.3.4 Air Supported Radomes 388 10.3.5 Selection Criteria 389 10.3.6 Brief Summary of Radome Features 390 Chapter 11 - Site Considerations 11.1 Radiation Hazard 393 11.2 Earth Station Site Planning 397 11.2.1 Obstructions and Safety 397 11.3 Antenna Site Interference Issues 401 Chapter 12 - Appendices A. Critical Antenna Measurements A.1 Feed Insertion Loss Determination 406 A.2 Determination of Antenna Gain and G/T using Calibrated Radio Stars 411 B. Satellites and Radio Stars B.1 Pointing Angles to Geosynchronous Satellites 424 B.1.1 The case for the Elevation–over–Azimuth antenna 424 B.1.2 The case for the Declination–over–Hour Angle antenna 427 B.1.3 Polarization twist 428 B.1.4 Elevation-over-Azimuth pattern angle correction 429 B.2 Sun Outage 430 B.3 Pointing Angles to Radio Star Positions 431 B.3.1 Introduction 431 B.3.2 The coordinate system and time 431 B.3.3 Positional geometry of the sun over the earth 434

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B.4 Radio Star Information 435 B.4.1 Star flux densities 435 B.4.2 Star flux change with frequency - spectral index 437 B.4.3 Angular extent 437 B.4.4 Correction for atmospheric attenuation 440 B.4.5 Correction for star polarization 441 C. Waveguide C.1 Characteristics of Waveguide 442 C.1.1 Signal velocity in waveguide 442 C.1.2 Attenuation in waveguide 445 C.1.3 Rectangular waveguide attenuation 446 C.1.4 Circular waveguide attenuation 449 C.1.5 Power handling of waveguides 452 C.1.6 Standard waveguide features and characteristics 455 C.1.7 Ridged waveguide 460 C.2 Aperture Patterns 465 C.2.1 Rectangular or square aperture 465 C.2.2 Rectangular waveguide aperture with higher order modes 465 C.2.3 Circular waveguide aperture 467 C.2.4 Diagonal horn with square aperture 468 D. General Information D.1 Exponentials, Logarithms, and db 470 D.2 Bessel Function Polynomial Approximations 473 E. Reference Performance Documents E.1 Regulatory Specifications for Antenna Pattern Performance 474 E.2 Recommendation ITU-R S.580-6 474

E.3 Recommendation ITU-R S.465-5 477 E.4 Excerpt from FCC Document 47 CFR Ch. (10-1-97 Edition) containing para 25.209 and 25.134 479 E.5 Recommendation MIL Std 188-164 482

E.6 Electrical and Mechanical Characteristics of Earth Station Antennas EIA -411- A 483 Index 490

Glossary of Terms xi


Glossary of Terms

Item Meaning ACU Antenna Control Unit AIAA American Institute of Aeronautics and

Astronautics ANSI American National Standards Institute a.r. A.R. Axial ratio (in db) ATIS Automatic Terminal Information Service Az or az or Azim Azimuth b/a aspect ratio (of waveguide) BDF Beam Deviation Factor bw Bandwidth bw/g beam waveguide C Celsius (temperature scale) C-Band 5.85 – 8.2 GHz CCIR Comite Consulatif Internationale de la Radio

(fore runner to ITU-R) CCW or ccw Counter clock-wise CFR Code of Federal Regulations (USA) C/N Carrier to Noise ratio or Dynamic range (of

signal) Coax. or coax Coaxial line Ch. or ch. Channel con-scan Conical scan Co-pol or co-pol Co-polarized CP or cp Circular Polarization CP/LP or cp/lp Switch from circular to linear polarization cps cycles per second ( frequency unit) CSIRO Commonwealth Scientific and Industrial

Scientific Organisation (Australia) Cross-pol Cross-polarised CSU Colorado State University (USA) CW or cw Clock-wise D Diplexer db decibel dbc decibel relative to the carrier level dbi decibel relative to isotropic dbK decibel relative to 1 Kelvin dbm decibel relative to 1 milli-Watt db/m decibel per meter dbs direct broadcast satellite (service) dbW decibel relative to 1 Watt Dc direct current deg Degree (angular measurement) DNC or d/c Down Converter DPS or diff. ph. sh. Differential Phase Shift(er) DSF Dielectric Space Frame

E or E-Field Electric Field EHF Extremely High Frequency EIA Electronic Industries Association (USA)

Glossary of Terms xii


eirp or EIRP Effective Isotropic Radiated Power El or el or Elev Elevation e-m Electromagnetic E-Plane (bend) Waveguide component Eq Equation ET Earth Terminal e.s.or E.S. earth station F frequency (as Hertz or cps) FCC Federal Communications Commission (USA) F/D or f/d Focal length/reflector aperture diameter ratio FoV Field of View FSS Frequency Selective Surface G Antenna Gain GEO Geostationary Earth Orbit GEO Global Equatorial Orbit GHz Gigahertz GMT Greenwich Mean Time GSO Geostationary Satellite Orbit G/T Antenna Gain/NoiseTemperature ratio H Magnetic Field H Horizontal polarized signal component HA Hour Angle HLP Horizontal Linear Polarization HPA High Power Amplifier HPF High Pass Filter H-plane (bend) Waveguide component H-pol or Hor pol Horizontal polarization (of signal) H + S Huber and Suhner AG (Switzerland) ICSC International Satellite Communications

Commission IEEE Institute of Electrical and Electronic Engineers

(USA) IESS Intelsat Earth Station Standards IF Intermediate Frequency IFL Inter Facility Link IM Intermodulation IMP Intermodulation Products i/o input/output IOT In-orbit Test i/p Input IRE Institute of Radio Engineers (USA) ISRO Indian Space Research Organization ITU-R International Telecommunications Union -

Recommendations (USA) JPL Jet Propulsion Laboratory (USA) K Kelvin (temperature scale) k Beam deviation factor K – Band 18 – 26.5 GHz Ka – Band 26.5 – 40 GHz kHZ kilo Hertz Ku – Band 12 – 18 GHz Kt – Band 17.7 – 21.2 GHz

Glossary of Terms xiii


La or la Latitude L – Band 390 MHz – 1.5 GHz LCP Left hand Circular Polarization LEO Low Earth Orbit LHA Local Hour Angle (of star) LNA Low Noise Amplifier Lo or lo Longitude LP or lp Linear Polarization LPF Low Pass Filter MEO Medium Orth Orbit MHz Megahertz MOD Modulation (of slope performance) MIL Military Standard (USA) MIT Massachusetts Institute of Technology (USA) MSF Metal Space Frame MSL Mean Sea Level MSS Mobile Satellite Service MT Magic Tee MTT Microwave Theory and Techniques NBS National Bureau of Standards NF Noise Figure NIST National Institute Of Standards and

Technology (USA) NOAA National Oceanic and Atmospheric

Administration (Vermont, USA) OMT Orthomode Tranducer or Orthocoupler PA Power Amplifier PC Phase Center PD Polarization Discrimination PF Packet Filter pfd power flux density Ph Reference or “hot load” noise power ph. sh. phase shift PIM Passive Intermodulation PL Path Loss pol angle polarization rotation angle p – p port to port PR Power Ratio Pre-preg Pre – impregnated psf pounds per square foot (pressure) psig pounds force per square inch gauge PTFE Polytetrafluoroethylene (used in Teflon) PTT Post, Telegphone, Telegraph (Switzerland) Q –Band 33 – 60 GHz QJ Quadrature Junction R Ratio of one or more voltage axial ratios r Voltage axial ratio RA Right Ascension (of star) RAS Royal Astronomical Society (England) RBW Resolution Band Width RCA Radio Corporation of America RCP Right Hand Circular Polarization RF Radio Frequency RH Relative Humidity

Glossary of Terms xiv


RL Return Loss rms root mean square RRF Receiver frequency Rejection Filter Rx Receiver sat. Satellite S-Band 2.6 – 3.95 GHz SGH Standard Gain Horn SLE Sidelobe Envelope SMA Sub-miniature coax line Connector S/N Signal to Noise ratio SOTM Satellite Communication On The Move s-pol satellite polarization SSM Satellite System Monitor SSPA Solid State Power Amplifier subref sub-reflector Sw Switch T Temperature (in Celsius or Kelvin) Tc Cold load noise temperature TE Transverse Electric wave TEM Transverse Electromagnetic wave Th Hot load noise temperature THz Terahertz TM Transverse Magnetic wave TRF Transmit frequency Rejection Filter Ts System noise temperature TTC Telemetry Tracking and Control TWTA Travelling Wave Tube Amplifier Tx Transmitter UER Upper Equipment Room USC University of Southern California (USA) UTC Coordinated Universal Time V Vertical polarized signal component VAR or var Voltage Axial Ratio (of antenna) VBW Video Bandwidth VHF Very High Frequency VLP Vertical Linear Polarization VP Vertical Polarization V- pol Vertical(ly) polarized signal VSAT Very Small Aperture Terminal (network) VSWR or vswr Voltage Standing Wave Ratio w/g or W/G Waveguide X – Band 8 – 12 GHZ Xpol or xpol Cross polarization X-Y Elevation over Cross-Elevation (positioner) y-factor Noise power ratio Zee or Z Flexible stiffener (for antenna) Zf Feed axis Zm Main reflector axis Zs Sub-reflector axis

Chapter 1 – Radiated Fields


1

Chapter 1 - Radiated Fields 1.1 What are Radio Waves ? 1.2 The Nature of Radiated Fields 1.3 Transmission Line 1.4 Types of Transmission Line 1.4.1 Coaxial Lines 1.4.2 Rectangular Waveguide 1.4.3 Complex Rectangular Waveguide Components 1.5 Circular Waveguide 1.5.1 Circular Waveguide Modes 1.5.2 Circular Waveguide Components 1.1 What are Radio Waves ? Concept of charge Figure 1.1-1 represents a simple 2-wire transmission line with a battery connected to two terminals at one

end, with an open circuit at the other end aa . Excluding inherent losses in the transmission line, a

voltage V will be detectable at aa . The "charge" of the battery has been transferred from the battery

terminals to the end of the transmission line. Further, an electric field will be detectable between the

terminals a and a .

V Static Electric Field - E

a+

a_

Figure 1.1-1 Battery with two long open-ended wires Concept of moving charges

If now the terminals a and a are closed (or short circuited), current will flow from the battery, through the

transmission line and points aa , and back to the battery. Associated with this current is now an

electric field E and a magnetic field H . The current consists of moving +ve charges These charges will have a maximum velocity of c = speed of light ~ 3x108 meters per second. As a result of the voltage

polarity, the E field is shown as a vector (with a directional arrow). The magnetic field curls around the wire with direction as shown (according to the "left hand rule"). This is shown in Figure 1.1-2

Switch

VE

moving +ve charge = current

moving electrons

H a+

a_

Maximum speed of moving charges = speed of light c ~ 3 x 108 m/s Figure 1.1-2 Battery with two long short-circuited ends



2

Imagine now the dc voltage into the transmission line being switched on and off. Do this quickly enough, a

varying E and H field will result along the length of the transmission line. At aa , a short circuit

offers continuity for the current path. The electric and magnetic fields are orthogonal to each other E ┴H . The assumption is that the transmission line is long - and the switch is operated sufficiently quickly for the charges to have moved only a distance ΔL in the time t1 - to . See Figure 1.1-3.

t0 t1 t2 t3 t4 t5

TV

time

average

Figure 1.1-3(a) Switched voltage pulses traveling along the 2-wire line.

L

Length = LV

Switch

a+

a-

E

L = distance charge has moved in time t1 - to

Figure 1.1-3(b) Distance pulse has traveled in one time frame Concept of Moving Fields Using Figure 1.1-4 as a reference, as switch S is closed (at time to), +ve charges will begin to move

(current) from point 0 to point 1 in time 012/ ttT . E and H are generated as a result. At time t1 , the

switch S is reversed, and E and H are reversed in sense, and charge moves from point 1 to point 2. At

time t2, S is reversed again, E and H are positive, and new +ve charges move from point 2 to point 3. E

and H fields move with the moving charges with period T along the 2-wire system.

Double switch assembly

0 1 2

V E E E

a+

a-

t0 t1 t3

+V

-V

T = 1 period

1 Wavelength

time

[a]

[b]

t2

Figure 1.1-4 Double switched 2-wire transmission line showing moving field



3

Concept of Frequency Frequency refers to the number of switch changes per unit time. Therefore,

HertzsecondcyclesfttT

Frequency

/11

02

Concept of wavelength The length of wire traveled in period T is equal to one wavelength. Therefore the distance between points 0 and 1 is ½ wavelength, or ½ . Concept of Radiation

With reference to Figure 1.1-5, suppose aa is not short circuited. Charges associated with E and

H fields will arrive at a and a . What happens here ? Will the charges "pile up" ? Imagine the field increasing to a maximum at the end of the wire. Here the charges supporting the field E must turn around. In the process, the returning field will add to the approaching field as shown in Figure 1.1-5(b). The forward and backward moving fields are in phase, generating a stationary field of magnitude

E2 . So the "open circuit" will behave like a "short circuit," because now all the current elements will travel back the way they came.

a+

a-

E

H

Ea+

c*

1/4

E

End of wire

+

_

(a) (b)

Figure 1.1-5 Open-ended transmission line with moving field approaching the open end Now consider the ends of the wire pair bent at c-c* as shown in Figure 1.1-6. The field is zero at c-c*. The charges turn the corner at c-c*. The field line E continues to exist but is curved. The field increases in

magnitude as the supporting charges reach a . Because of the bent geometry of the line, the field line 1E

is curved to connect with the wire segment going to a . For the field E to reach maximum value at a ,

the length of the wire segment ac must be 1/4 . At a , the charges turn around to return to c ,

arriving there 21 later in time T/2. In the meantime, the field 1E has progressed to 2E to 3E to 4E . For

4E , the field line ends have returned to *cc .

Now the next 21 segment of the field E begins, but in the opposite phase. Field line 4E will close,

having moved to the right in Figure 1.1-6 as a kind of “packet” of energy, to make room for the next “packet” . Associated with this electric field “packet” is the magnetic field H oriented at right angles (orthogonally) to

E . In this way, an electromagnetic wave is radiated from the wire support structure *cc and aa .

Because the field lines are closed 21 “packets”, the wave can exist away from the dipole, and will travel at

the speed of light. All the energy associated with flow of charges (current) will be transferred to the radiated field. If the same wave encounters a second dipole, the E field (a voltage) will induce a corresponding flow of charges (current) in the dipole; i.e., a current will be generated in the 2-wire line connected to the dipole in an identical but reverse time sequence.



4

Note that if the total length of the dipole wings aa is not 21 long, an incomplete transition to a

radiated field results, and the difference will be seen in some of the field not leaving the dipole, and

returning to the signal source as a reflected field. The 21 dipole is the most efficient at transferring e-m

energy to a radiated field. In principle, the dipole as a passive conducting element cannot tell the difference which direction the field support currents are flowing. Therefore, a transmitting dipole is also good as a receiving dipole.

c*

c

a+

a_

E

time = t0 t0

c*

c

a+

a-

(a) (b)

Direction ofPropagation

E

L =

l/4

E

E

t1

1/2 wavelength

H

H

H

HE

E

Propagation time

E 1E 2 E 3 E 4

Figure 1.1-6 Electromagnetic wave emanating from dipole structure The features of the pattern associated with the electro-magnetic field will be as shown in Figure 1.1-7. To be noticed is that the vertically oriented E -field propagates equally 360 degrees around the y-axis, but along the y-axis is zero. Looking along the z-axis, the view of the field lines around the dipole shows a

quasi circular pattern. The E -field is generated by a voltage between two isolated terminals a and a , and the dipole is called an electric dipole.

y

xE

Null along y-axis

z

H H

View along z-axis

Figure 1.1-7 The electric dipole

Suppose now we join a and a in the form of a loop as shown in Figure 1.1-8. The current will radiate a magnetic field around the wire element. The magnetic field will curl around the wire carrying current, and radiate equally 360 degrees around the x-axis, but zero along the x-axis. The associated electric field now



5

has to lie along the wire and propagate along the z-axis. Observing the E -field from along the x-axis, it will be circular in form, and the electric field lines will all be parallel to the y-axis. Observing the E -field from along the z-axis, the field lines will be parallel to each other.

The E -field in this case is generated by a current between a and a , and the dipole is called a magnetic dipole.

y

x

z

H

E

Null along x-axis

View along z-axis

Figure 1.1-8 The magnetic dipole Based on these observations, if the electric and magnetic dipole could be combined and fired from the same signal source, then the combined electric field would look like that in Figure 1.1-9, and is known as a Huygen's dipole. Such a dipole is more an analytical concept, since it can only be approximated in practice.

x

z

y

Null at z-axis

View along z-axis

z

Figure 1.1-9 The field of the combination of the electric and magnetic dipoles making up the Huygen’s source. The differences between the electric and magnetic dipoles are used in Section 2 and 3 to suggest how electric and magnetic field modes can be used to advantage in optimizing reflector system performance. Points of interest: 1. A dipole represents the fundamental generator of electro-magnetic waves. 2. The dipole of /2 or half wave length, represents the most efficient generator of waves - efficiency meaning that all energy coming along the wires toward the bent portion, will be radiated, and none reflected back to the signal source.



6

1.2 The Nature of Radiated Fields Concept of Polarization - Linear Polarization

The wave depicted in Figure 1.2-1 is defined as being linearly polarized – as seen by the E -field existing in only one plane; in this case the y-z plane or the V (vertical) plane. If the dipole is rotated by 90o, waves will be H (horizontally) polarized.

y

x

z

E

H

H H

E

E

E

H

Direction of Propagation

Maximum along x and z axes

z

Figure 1.2-1 Radiating dipole and view of propagating electromagnetic wave Suppose two electric dipoles, V and H polarized, are each excited next to each other. These two orthogonal waves can propagate without interference. One does not "see" the other. Obviously to maintain independence between these two H and V components, the receiver antenna (dipole) must also consist of H and V dipoles, or the equivalent. Concept of Circular Polarization Consider two dipoles, H and V polarized. Further, the two dipoles are fed from the same source. See

Figure 1.2-2. With a V-polarized receiver, only 1E is received. with an H-polarized receiver, only 2E is

received. At some other orientation, the receiving dipole will receive signals from both 1E and 2E .

Maximum signal will come from RE with the plane of polarization rotated to y = 45o for 1E = 2E , and some

other angle if 1E ≠ 2E .

E1

E2

E2E2

E1

E1


EREV

EH

= 45o

ER

ER

ER

Figure 1.2-2 View of a linearly polarized wave generated by two orthogonally polarized dipoles excited in phase



7

Now consider the same two dipoles fed from the same source, but 90o (1/4 wavelength) time phase shifted with respect to each other. See Figure 1.2-3. Looking at the wave end-on, and in the direction of propagation:

If 1E = 2E and = 90o differential phase shift between 1E and 2E , then we have circular polarization.

That is, the resultant wave is rotating at frequency f . By definition, if the wave resultant rotates ccw

(counter-clockwise) into the direction of propagation, it is LCP (Left-hand Circularly Polarized). If rotation is cw (clockwise), the wave is RCP (Right-hand Circularly Polarized).

EREV

y

x

EH

Resultant ER rotating CCW field is left hand circular polarization - LCP

EV

Direction of propagation

z

EH

EV

On the other hand, EV leading EH

by 90o phase produces right hand circular poalrizartion - RCP

= 90o

Figure 1.2-3 View of a rotating wave generated by two orthogonally polarized dipoles differentially shifted by = 90 degrees phase. E2 leading E1 results in ER rotating ccw - an LCP wave. If E1 were to lead E2, this would result in ER rotating cw - an RCP wave. Concept of Elliptical Polarization

For the case 1E ≠ 2E and not exactly 90o differentially phase shifted, the resultant ER will trace an elliptical

path – the ellipse may even be rotated by an angle as shown in Figure 1.2-4.

E2

E1

a

a*

Figure 1.2-4 Condition for elliptical polarization Points of Interest 1. Orthogonal LP (linear polarized) fields can exist independently, and not interfere with each other. 2. Equal magnitude orthogonal LP fields with 90o differential phase shift will generate circular polarization. 3. Correspondingly, LCP and RCP components do not interfere with each other. 4. Any deviation from the conditions above will lead to interference, commonly referred to as "cross-polarization".



8

5. If an elliptically polarized wave is propagating toward a receiver, then the polarization ellipses of both transmitter Tx and receiver Rx must be oriented in such a manner that major axes a - a* match. Otherwise "polarization efficiency" will be degraded, and not all signal will be captured. More on this in Section 5. Reflection Case No.1 - Normal incidence by an LP wave.

The wave iE is intercepted by a plane (flat) conductive reflector. The iE field component induces a

supporting current in the reflector. The iE field cannot exist on a conductive surface, and must be zero. To

satisfy this condition, an equal opposite current must exist to cancel iE and generate rE . The sum of iE

and rE at the surface will be zero. See Figure 1.2-5. But rE will travel in the opposite direction. Because

the frequency is the same, iE and rE will interact to generate a standing wave which does not move. This

stationary standing wave will have the same wavelength

Ei

ER

Direction of incident wave

Direction of reflected wave

ES

EI

ER

Plane flat reflector

Standing Wave

Figure 1.2-5 Reflection of incident wave and resulting standing wave

Case No. 2 - Slanted incidence by an LP wave ( E field parallel to reflecting surface). In this case there is no standing wave. Figure 1.2-6



9

ER

HR

EI

EI

ER

HI

HR

HI

Incident wave

Reflected wave

Reflector

ER

EI

Figure 1.2-6 Slanted incidence of LP wave - E-field parallel to reflecting surface

Case No. 3. - Slanted incidence by an LP wave ( H field parallel to reflecting surface) Figure 1.2-7

Incident wave

Reflected wave

Reflector

HR

ER

HI

EI

EI

ER

HI

Figure 1.2-7 Slanted incidence of LP wave - H-field parallel to reflecting surface

1. Note the exchange in the configuration of the E and H field vectors at the reflector as shown in cases 2 and 3. The analogy is the exchange between "left" and "right" when you look at yourself in a mirror.

2. Note that the requirement for the E -field to be zero at the plane of the reflector is maintained, creating the mirror image.



10

Case No. 4 - Normal incidence of CP wave on a flat reflector - Figure 1.2-8

EiV

Direction of incident wave

Direction of reflected wave EIV

ERV

Plane flat reflector

RCP LCP

EiH

ERV

ERH

ERH

90 deg

90 deg

90 deg90 deg

Figure 1.2-8 Normal incidence of CP wave on a flat reflector Concept of VSWR or Return Loss Imagine a wave traveling along the waveguide (w/g). Figure 1.2-9(a) shows the progression of the wave with time along the line. The wave meets a short circuit: See Figure 1.2-9(b). Another way of looking at this situation: See Figure 1.2-9(c)

E

t1 t0

Time

Direction of propagation of the moving wave

E

Time

Position along waveguide

Electric field or voltage = 0at the reflecting short circuit

Standing wave which does not travel

Incident wave

Reflected wave Short circuit

V+

V-

V +

V -

t0 t1 t2 t3

V +

V -

V+

V -

V -

V +

V -

V+

or

time =

[c]

[b]

[a]

[a] Traveling wave in transmission line [b] Traveling wave reflected from a short circuit [c] Vector view of the time interaction between reflected and incident voltages

Figure 1.2-9 Generation of a constant "standing wave" when a wave is reflected



11

Voltage V at any point along the line will be

)1(1)(

V

V

VVVVEorV

where = Reflection Coefficient

11

)(00 Z

VVV

ZHorICurrent

oZZ

ZZorZ

I

VZImpedance

00 1

1

VSWR is defined as

1

1

min

max

VV

VV

V

VS

(1.2.1)

and 1

1

S

S

Terminology: VSWRS (voltage standing wave ratio)

Reflection Coefficient

Return Loss = 20log( ) db Points of Interest 1. We have discussed a mechanism for the generation of radio waves and their propagation. 2. We have seen what can happen when such a wave is intercepted by a conducting flat reflector -

the wave is redirected, with angle of incidence equal to angle of reflection. 3. Consider now a wave generated by a dipole. Consider a second dipole in the path of the

propagation. The wave will induce a current in the 2nd dipole. The 2nd dipole is then a receiver. The 1st dipole is a transmitter.

4. Since the dipole is a passive device, and bilateral, it cannot tell which way the waves/currents are traveling. This means that radiation properties of the dipole are the same for receive and transmit functions.

5. Sometimes it is convenient to analyze the behaviour of antennas in a "transmit" mode, sometimes in a "receive" mode.

1.3 Transmission Line The development of "waveguide" as transmission line The behaviour of waves in parallel-plate and waveguide transmission lines is slightly different from two- wire and coaxial lines. We will discuss waveguides here.



12

E

E

E

Parallel plate transmission line: e.g., microstrip or stripline.

2-wire open transmission line

(a) (b)

E

(c)Waveguide: Parallel-plate transmission line with side walls

E

Coaxial Transmission Line

(d)

Figure 1.3-1 The development of "waveguide" as transmission line for microwave frequencies Examples: 2-wire lines - used in the kHz to MHz range low power coaxial 2-wire lines - used in the MHz to GHz range coaxial 2-wire line - used up to ~ 50 GHz high power applications - modified 2-wire lines, as represented by waveguide structures. - used in GHz and THz feeds optical fiber - used in long land links at Angstrom wavelengths Definitions: Frequency (ƒ) = 1/T(secs) units = 1 cycle per second = 1 Hertz (Hz) 1000 Hz = 1 kHz 106 Hz = 1 MHz 1000 MHz = 1 Giga Hertz - GHz 1000 GHz = 1 Tera Hertz - THz Free-space propagation The magnetic and electric field vectors are connected by parameters that depend on the medium. In vacuum, there are two constants with values

121085.8 o Farad/m

7104 o Henry/m

In any other medium, we will have electric inductive capacity

magnetic inductive capacity

ro

known as relative dielectric constant

ro

known as relative magnetic permeability

For most normally encountered materials, 1r



13

The velocity of propagation of a wave in free space is given by

810997925.21

oo

c

meters/sec (1.3.1)

and the velocity of propagation in a material defined by r and r

11

oror

v meters/sec

The propagation phase constant

22

2 v

ffk (1.3.2)

where f 2 ; f frequency, and wavelength.

Propagation in transmission lines The solution to the wave equations results in the classification of waves in uniform guides into three fundamental types:

1. TEM-waves - transverse electromagnetic waves. Only xE and yH fields exist in the xy -plane transverse

to the direction of propagation along the z -axis; zE and 0zH .

2. TE-waves - transverse electric waves. Only xE and yH fields exist transverse to the direction of

propagation, and 0zE .

3. TM-waves - transverse magnetic waves. Only xH and yE fields exist transverse to the direction of

propagation, and 0zH .

TEM-mode waves The features of TEM waves Can propagate in free space Can propagate at any frequency Can only propagate on a two-conductor line Cannot propagate in hollow waveguide TE-mode waves

TE waves with a longitudinal magnetic field component zH will only exist in uniform hollow waveguide.

Solutions to the wave equation in waveguide involve complex characteristic propagation constants . To each characteristic constant we can assign a mode of propagation. Any one mode is specified by the field configuration over a section of the waveguide. The propagation constant is defined as

21

22 k (1.3.3)

If 22 k , then is imaginary, and the wave is propagated with no attenuation.

If 22 k , then is real, and the wave is attenuated.

The transition between forward propagation and no propagation is called the “cut-off” condition.

A wave of frequency f will propagate in free space with wavelength , and 2

k . In the waveguide, a

wave of frequency f will propagate freely in the guide with wavelength g only for

21

21 222

2 kfg

(1.3.4)



14

Defining the cutoff wavelength as c , we can write c 2

, and

222

111

cg (1.3.5)

from which 21

2

1

c

g

(1.3.6)

This says that the wavelength in uniform waveguide is always greater than in free space. When the

wavelength exceeds the cutoff wavelength mnc , the wave cannot propagate in that particular mode.

Hollow transmission line is therefore a high-pass filter.

When the waveguide is filled with a dielectric material with relative dielectric constant r the propagation

wavelength increases. This implies that the waveguide in its nominal cut-off condition at frequency cf can

propagation a signal at cff if adequately fitted with dielectric material 1r .

In terms of free-space wavelength o , we then can write

21

21

21

1

cr

r

o

g

(1.3.7)

TM-mode waves

TM waves with a longitudinal electric field component zE will only exist in uniform hollow waveguide.

The changed boundary conditions relative to that of TE waves leads to a new propagation constant , but

the corresponding guide wavelength g is given by (1.3.6)

1.4 Types of Transmission Line 1.4.1 Coaxial Lines Various forms of coax are available.

symmetric square and circular flexible

a

b

Figure 1.4-1 Geometry of coaxial transmission line



15

Positive aspects of coaxial lines coaxial lines form excellent low power interconnects and can be flexed to suitable shape

without impact on the propagation characteristics demonstrate bandwidths of several octaves in contrast to waveguide, attenuation increases with increasing frequency. The design of waveguide components such as wideband symmetric couplers and multiband

rotary joints rely on transformations in and out of the coax TEM mode. On the other hand, coaxial lines are of limited interest in the design of feed systems and components for microwave antennas for the following reasons:

cannot offer H and V polarization discrimination in the same line to a small extent, due to the presence of dielectric material of relatively small dimensions

needed for structural integrity of the line, power handling will be limited by the “loss tangent” [ tan ] of the material.

Cut-off wavelengths for the first higher mode bac (1.4.1)

where a diameter of outer conductor

b diameter of inner conductor

Attenuation for the first dominant mode tan (1.4.2)

where tan = loss tangent of the conductor material, as described in (1.4.10). 1.4.2 Rectangular Waveguides Various forms of waveguide

rectangular ridged flexible

b

a

b

a

Figure 1.4-2 (a) Rectangular waveguide; (b) Ridged rectangular waveguide for wide band applications Rectangular waveguides are used as transmission line interconnects and feed components, because of the following properties:

polarization discrimination low loss, and therefore good power handling for most applications, loss decreases with increasing frequency

On the other hand:

single mode (to be discussed below) bandwidth f is limited to 21 f .

practical frequency range is cc fff 95.125.1

waveguide symmetry critical for mode discrimination in square and circular waveguide configurations, but not a real difficulty in rectangular guide.

The principal characteristic of ridged waveguide is a special set of modes which offer frequency band extension of greater than 2:1. Ridged waveguide is discussed in part in Chapter 12 Section C.1.7.



16

Propagation modes "Modes" are forced by the fact that 0E at a conductor surface parallel to the direction of the E-field

vector. If frequency is chosen too low, (or wavelength too long), the field cannot go to zero at the "b" wall of the waveguide. Therefore, the wave cannot travel along the guide, and the waveguide will appear as a short circuit. More on this in Chapter 12 Section C.1.1. Terminology: TEmn means "transverse electric" mode. The electric field associated with this mode exists only in the plane transverse to the direction of propagation. m = no. of variations in the E field across the "a" dimension. n = no. of variations in the H field across the "b" dimension. TMmn means “transverse magnetic” mode. The magnetic field associated with this mode exists only in the plane transverse to the direction of propagation. m = no. of variations in the H field across the “a” dimension. n = no. of variations in the E field across the “b” dimension.

1st mode = TE10 3rd mode = TE20

5th mode = TM114th mode = TE11

2nd mode = TE01

= electric field lines = magnetic field lines

6th mode = TE21

Figure 1.4-3 The first six rectangular waveguide modes TE-modes in rectangular waveguide The solution to the wave equations permits either 0m or 0n .

For TE - modes in rectangular w/g, the characteristic propagation constant is

2222 2

cb

n

a

m

(1.4.3)

The lowest frequency is called "cut-off frequency" cf , and from (1.3.4)

21

22

2)(

b

n

a

mf

cwavelengthoffcut

cc (1.4.4)

For f larger than cf , the wavelength in the guide is given by

2

12

1

f

f c

og

(1.4.5)



17

where: f

co (1.4.6)

and c speed of light = 2.997925 x 108m/sec.

The first TE10 mode is the most important mode in rectangular waveguide components. (1.4.4) shows that for TE10 mode:

ac 2

and may be in the ranges aa 2 to ensure propagation.

The TE01 mode is identical to the TE10 mode, just rotated in polarization by 90 degrees. Note that for TE01

to exist in the rectangular waveguide, broadwall dimension a01 must be 2a10, or for the frequency 01f to be

two times 10f .

TM-modes in rectangular waveguide For the TM wave, if either 0m or 0n , all field components are zero, and the whole wave vanishes.

The cut-off wavelength is given by

21

22

2)(

b

n

a

mf

cwavelengthoffcut

cc (1.4.7)

For the first TM11 mode, 22

2

ba

abc

(1.4.8)

Surface current distributions Current distribution on the waveguide surface (inside): If current lines are not disturbed, the wave will travel along the guide. If current lines are disturbed, then standing waves (or reflections) will be set up. Figure 1.4-4 shows how current lines are distributed on the inside of the waveguide.

H

E

E=0 E=0

Field distribution in rectangular waveguide

Propagation characteristics determined by waveguide dimensions "a" and "b"

b

a

Figure 1.4-4 Rectangular waveguide first (fundamental) mode and corresponding current paths These suggest the following ideas: a. Cut a slot along the center line of the "a" wall, and no major disturbance is introduced. b. Cut a slot from top to bottom in the "b" wall, and no major disturbance is introduced. c. Cut a slot along the center line of the "b" wall, or a slot across the "a" wall, current lines will be cut, and the slot will radiate.



18

A number of useful waveguide components are based on cutting slots in appropriate places to make: directional couplers, power splitters, combiners, array antennas, filters, slotted lines. Points of Interest 1. Waves can propagate down or along waveguides. In reality, all waveguides exhibit loss or are “lossy”, i.e., absorb part of the signal as it goes along. This is because all conductive metals have resistivity, or finite conductivity. 2. Waveguides must be of high class manufacture - surface finish must be flat, optically flat if possible. Types of defects seen most often:

Waveguide wall

Waveguide wall

Non-ideal Inside surface rough

Ideal Inside surface flat and smooth

Current path

Current path

Note:Here, current has to travel a much longer distance in the rough surface

[a]

[b]

[c]

Figure 1.4-5 Common detrimental effects in waveguide structures Current is really a "surface current," and runs in the "skin" of the conducting material. The degree of penetration by the current is given by the "skin" depth, expressed by (3.5.1) as

)(1

1564

1materialsconductivemostforinches

f GHzs (1.4.9)

See also Section 12.10 for more details – (12.10 11). 3. The larger the available surface area in a waveguide, the "thinner" the current density, and therefore the higher the power that can be transmitted. 4. Flanges for connecting waveguides: Referring to Figure 1.4-6, flanges must ensure that w/g is aligned accurately. Flanges must ensure contact all around inside of w/g (a) If w/g flanges are optically finished (lapped), then small warping can create an RF gap that will also leak when w/g is pressurized (b) If flanges are slightly "roughed up", then the flange surfaces will tend to mechanically "mash-mate", and RF contact is maintained. (c) Most recent developments in flange design demand complete contact all around the waveguide joint.

Flat flanges will always tend to warp Grooved flanges have wide contacting lips in the flange When hardware is tightened, inside of w/g will open Grooved flanges with narrow contacting lips in the flange, in which the hardware is mildly

torqued, bending is reduced, and flange remains closed.



19

Flanges, connecting waveguides must ensure that waveguide halves align accurately. Flanges must ensure contact all around the insde of the waveguide.

a. If w/g flanges are optically finished (lapped), then small warping can create an RF gap that will also leak when the w/g is pressurized.

a

bb. If the flanges are slightly "roughed-up",then the flange surfaces will tend to "mash-mate" mechanically, and RFcontact is maintained

c (i)

c. Most recent developments in flange design, which demanded complete contact all around the waveguide joint.

(i) Flat flanges will always tend to warp.

(ii) Grooved, choke flanges have wide contacting lips in the flange joint.

(iii) When hardware is tightened, inside of waveguide will open.

(iv) Hardware mildly torqued in order to reduce bending. Contacting surface width ~ <0.050 inches

c (ii)

c (iii) [c] (iv)

Figure 1.4-6 Waveguide flange design considerations Table 1.4-1 Standard Waveguide Sizes

Theoretical Midband Attenuation for Standard

Copper Waveguide

Freq. GHz

W/G Section Size (inches)

Standard WR

Designation db/100 ft. db/m

L 1.0 – 1.7 6.500 x 3.250 WR-650 .3 0.009 S 1.7 – 2.6 4.300 x. 2.150 WR-430 .4 0.012 S 2.2 – 3.3 3.400 x 1.700 WR-340 .6 0.018 S 2.6 – 3.95 2.840 x 1.340 WR-284 .8 0.024 C 3.3 – 4.9 2.290 x 1.145 WR-229 1.0 0.031 C 3.95 – 5.85 1.872 x 0.872 WR-187 1.5 0.045 C 4.90 – 7.05 1.590 x 0.795 WR-159 1.8 0.055 C 5.85 – 8.20 1.372 x 0.622 WR-137 2.3 0.07 X 7.05 – 10.0 1.122 x 0.497 WR-112 3.2 0.10 X 8.20 – 12.4 0.900 x 0.400 WR-90 4.5 0.14 Ku 10.0 – 15.0 0.750 x 0.375 WR-75 6.5 0.20 Ku 12.4 – 18.0 0.622 x 0.311 WR-62 8.3 0.25 Kt 15 – 22 0.510 x 0.255 WR-51 11.5 0.35 Ka 18 – 26 0.420 x 0.170 WR-42 15 0.45 Ka 22 – 33 0.340 x 0.170 WR-34 19 0.56 Ka 26.5 – 40 0.280 x 0.140 WR-28 23 0.70 Q 33 – 50 0.224 x 0.112 WR-22 25 0.75 Q 40 – 60 0.188 x 0.094 WR-19 32 0.97

1.4.3 Complex Rectangular Waveguide Components Up until now, we have discussed the simple building blocks for guiding electromagnetic waves, much as wires guide electricity, and pipes contain and guide water and gas in a controllable manner. And just as in these disciplines, to ensure that the radio waves are directed and processed in the correct directions, extensive use is made of bends, “size transformers,” “reducers” (attenuators), power dividers and combiners, frequency “sorting devices” (filters), “delay lines” (phase shifters), and “switches.”



20

“Signal processing” is achieved by an appropriate combination of waveguide components which perform a selection of the above mentioned functions. To differentiate between “ordinary” waveguide and waveguide components used in “signal processing” networks, we will name the latter “complex waveguide components". This perhaps for no better reason than a reference to the difficulty many of these components present in their design. Types:

1. Bends - E-plane, H-plane 2. Transformers

- waveguide to waveguide - waveguide to free space (horn, any antenna)

3. Power Splitters – to divide or combine signals to or from several paths. - (dividers) - (combiners)

3. Attenuator - Fixed, variable 4. Phase Shifter - Fixed, variable 5. Differential Phase Shifter - Fixed, variable 6. Differential Attenuator - Fixed, variable 7. Filters - Pass Band, Stop Band Bends Change direction or orientation of the waveguide opening

E

H

E

H

[a] H-plane bend - bends in the H-plane

[b] E-plane bend - bends in the E-plane

[c] TwistE

H

Figure 1.4-7 Various waveguide bends in common use



21

Transformers This refers to transformation from one waveguide size/shape to another. Figure 1.4-8 shows some examples.

[a] Rectangular Waveguide >>> Rectangular Waveguide [b] Step Transformer

[c] Rectangular waveguide >> Circular waveguide [d] Rectangular Coupling >> Circular Waveguide

Figure 1.4-8 Various waveguide transformers Power Divider (Magic-T) As shown in Figure 1.4-9, input power is divided into two equal in-phase, or 180o out-of-phase, components.

1 watt in >>

1/2 watt out here

1/2 watt out here

Nothing out here IF : (1) Ports b and c are equally matched or : (2) Ports b and c equally short circuited

a

b

c

d

Note: Signals out of ports b and c are equi-phased.

a

b

c

d

1 watt in here

Nothing out here

1/2 watt out here

1/2 watt out here

Note: Signals out of ports b and c

are 180o out of phase

Figure 1.4-9 Magic Tee junction



22

Power Divider (Hybrid) Power division into two equal components with 90o phase difference as shown in Figure 1.4-10.

a

b

c

d

1 watt in here

1/2 Watt out with 0o relative phase

1/2 Watt out with -90o relative phase (relative to that at port "b")

The added path length to "c" here causes the time/phase delay in the signal relative to that travelling straight through to port "b".Nothing out here

a

b

c

d

1 watt in here

1 Watt out here = 2 times 1/2 Watt arriving in phase

The added path length from "b" to "d" here arrives in phase with that from "c" to "d", causing all signal from "a" to be available at "d". Any return from "c" to "a" is 180 deg out of phase with that at "a" and is therefore cancelled.

Reflecting short circuit

Figure 1.4-10 90o Hybrid power splitter. Adjusting the position of the short circuit provides a means of phase shifting the output signal with respect to the input. Important Aspects of Directional Couplers These devices generally find application in measurement or power monitoring setups. Figure 1.4-11 shows three typical arrangements.

To monitor power, frequency, by sampling a very small amount of signal from the straight-through path. The sampling process has negligible effect on the signal path because of small coupling levels and high directivity. These terms are defined below.

To measure any reflected power from the straight-through path. To combine two separate signals into a common path.



23

Uses of a directional coupler:

Signal Source

Coupler Straight through path

Sample out to measure power, frequency, etc., (monitor function)

~

Signal Source

CouplerStraight through path

Sample out to measure reflected power, (measurement application)

~

Signal Source 1

Coupler

Straight through path

Combining two signals into one port

~

Any reflected return signals

~

Signal source 2

1

2

Figure 1.4-11 Applications for multi-hole directional couplers The power dividers described in Figures 1.4-9 and 1.4-10 possess directivity. This means that the isolated 4th port is de-coupled from the path of power division. The magic tee and the 90o hybrid are relatively narrow band (10-20%) devices. If wide bandwidth (50%) is required, multi-hole coupling devices, broadwall (as shown in Figure 1.4-12) or sidewall couplers are typically used.



24

P3

P2

P1

P4

Signal in

P3

P2

P1

P4Termination

(a)

(b)

Coupling slots

Coupling slots

Residual is absorbed in termination

1/4 = 90

Signal out

Coupled signal out

Coupling phase = 90o

Coupled signal out here

Signal in here

180 90 90180 90 180 90180

Σ=0360

270

Main signal out here

90 180

270

180

360

180

360

3600Σ=0 Σ=0 Σ=0

90

Refers to the summation of two out-of-phase signals

moving towards P4

Figure 1.4-12 Important features about directional couplers. (a) shows the general construction of the directional coupler. (b) shows the directivity mechanism as a result of the series of slots; the addition of coupled components for the signal going to the right; the cancellation of coupled components going to the left. 1. The greater the number of slots, the greater the useful bandwidth; the longer the slots, the greater the coupling.

2. The ratio CouplingP

P

1

3 , the ratio IsolationorDecouplingP

P

1

4

3. Directivity │Isolation│- │Coupling│.

Note: On most commercial directional couplers, 4P is internally terminated, and1

4

P

Pis usually measured by

turning the coupler around, and measuring 2

3

P

P.

Typical Performance Long multi-hole couplers: 3 db to 40 db coupling 30 to 55 db directivity Full w/g bandwidth Short multi-hole couplers: 3 db to 10 db coupling 20 to 35 db directivity Full w/g bandwidth



25

Magic Tees/Hybrids: 3 db coupling 50 db + directivity 30% bandwidth Cross-guide couplers: 20 db to 60 db coupling 20 to 30 db directivity 30% bandwidth Cross-guide Coupler Given a high power transmit signal path, to measure the actual power level at some specific point in the line, a very small amount need only be coupled out; this primarily only to protect the power meter. Further, small physical size is usually important too. Figure 1.4-13 shows a view of a typical cross-guide coupler.

2 Coupling slots eachin the form of a crossin the in-between wallof the two guides

Coupling pathCoupled signal

Isolated port

Signal in

Signal out

Figure 1.4-13 Cross-guide coupler configuration Polarization Couplers Sometimes called “Orthomode Transducer” or more familiarly OMT, these are devices to support two orthogonally polarized signals simultaneously. When orthogonality is maintained, there will be no interference between the two signals of the same frequency. Figure 1.4-14(a) is a standard T-style OMT.

Side port Horizontal Polarization

Symmetrical output terminal

Plane of effective short circuit for Horizontally Polarized component

Straight through path for Vertical Polarization

Note: 1. In rectangular waveguide, only one polarization can exist. The orthogonal polarization is cut-off. 2. This type of OMT is a 0db coupler

[a] Figure 1.4-14(a) Polarization coupler - OMT (Orthomode Transducer) also known as an "Orthocoupler"



26

Note: 1) In rectangular w/g, only one polarization can exist. The orthogonal polarization is cut off. 2) This type of OMT is a 0 db coupler.

Question: The OMT shown in Figure 1.4-14(b) – will it work?

The OMT shown here will not work because of cross-coupling between horizontal and vertical components

[b]

Figure 1.4-14(b) Un-balanced OMT Figure 1.4-15 shows a configurational variation of the T-style OMT, useful for some feed network designs.

EH

EV

EV

EH

Figure 1.4-15 Y-junction OMT Applications: Coupling two signals to an antenna and maintaining orthogonal independence (polarization discrimination) between them. Return loss (VSWR), Port-to-port isolation and polarization discrimination (sometimes called isolation) are the key features characterizing the OMT. Point of interest : In years gone by, this device was more suitably called an “orthogonal (polarization) coupler”.



27

P2

P3

P1

Signal in, and measure how much is returned

P3

Terminated

[b] Port-to-Port Isolation

Measure P1

P2

Question: Is = P1

P2

P2

P1

P2

P3

P1

Horizontal and V ertical polarization signal in here

Horizontal polarization out here

Vertical polarization out here

Measure P1

to determine "Polarization Discrimination" or "Polarization Isolation"P2

[c] Polarization Discrimination

[a] Return Loss (VSWR)

Figure 1.4-16 Important features of an OMT and their measurement. (a) refers to how much signal is reflected from the device. Measurement at P1 and P2 will completely define the reflective properties of the OMT. (b) considers the case for a signal injected into P1 and measures how much is lost in coupling into P2. Nominally all power in at P1 should be available at P3. (c) examines signal of Vertical polarization in at P3; it should all be available at P1. If some is detected at P2, then the polarization discrimination PD is equal to the ratio of P1/P2. Similarly for the case of horizontal polarization in at P3. Return Loss

(a) For signal in at Port 1, measure how much is returned V

rP

1P

PRL

Vr with Port 3 terminated

(b) For signal in at Port 2, measure how much is returned H

rP

2P

PRL

Hr with Port 3 terminated

Isolation (a) For signal in at Port 1, measure how much is coupled to Port 2

1

2

P

PI with Port 3 terminated

Polarization discrimination or isolation (a) For vertical pol signal in at Port 3, measure how much is coupled to Port 2 and Port 1

VP

PPD

1

2

(b) For horizontal pol signal in at Port 3, measure how much is coupled to Port 1 and Port 2

HP

PPD

2

1

Rule: Incoming polarization orientation defines the sense of polarization



28

Frequency Selective Polarization Couplers – Single Polarization

Side port Horizontal Polarization

For example 4 GHz

Straight through path for Vertical Polarization

For example 6 GHz

6 GHz vertical polarization out here

4 GHz horizontal polarization in here

Blade to prevent 4GHz signal from traveling down the 6 GHz path

Figure 1.4-17 Frequency-selective OMT 1.5 Circular Waveguide

circular corrugated ridged finned elliptical

E

(a)

(d)(c)

(b)

(e)

Figure 1.5-1 Various circular waveguide structures. (a) Circular waveguide; (b) Corrugated waveguide; (c) Ridged waveguide; (d) Finned waveguide; (e) Elliptical waveguide 1.5.1 Circular Waveguide Modes The first five circular waveguide modes are shown Figure 1.5-2. The particular solution to the wave

equation for circular waveguide indicates a propagation constant c 2

for which c will have the

following expressions for the TE and TM modes.



29

TEmn - modes

Cut-off wavelength mn

c

a

2

(1.5.1)

where mn is the thn vanishing root of the thm order Bessel function )(mJ and a radius of the

circular waveguide

Guide wavelength 2

1

f

f

f

c

c

g (1.5.2)

nm, 0,1 1,1 2,1 3,1 0,2 1,2 2,2 3,2 0,3 1,3 2,3 3,3

mn 3.832 1.841 3.054 4.201 7.016 5.331 6.706 8.015 10.713 8.536 9.969 11.346

TMmn - modes


c

a

2

(1.5.3)

mn is the thn vanishing root of the thm order Bessel function )(mJ .

Guide wavelength 2

1

f

f

f

c

c

g

nm, 0,1 1,1 2,1 3,1 0,2 1,2 2,2 3,2 0,3 1,3 2,3 3,3

mn 2.405 3.832 5.136 6.380 5.250 7.016 8.417 9.761 8.654 10.173 11.620 13.015

E

(1) TE11 Mode (2) TM01 Mode

(5) TM11 Mode(3) TE21 Mode (4) TE01 Mode

f cGHz =

6.92

2a inches f cGHz =

9.03

2a inches

f cGHz =

11.47

2a inches f cGHz =

14.39

2a inches f cGHz =

14.39

2a inches

Cutoff frequency forfundamental mode

2a

Figure 1.5-2 The first five circular waveguide modes



30

Terminology: TEmn means “transverse electric” mode. The electric field associated with this mode exists only in the plane transverse to the direction of propagation. m = no. of variations in the E-field across the diameter. n = no. of variations in the H-field around the circumference. TMmn means “transverse magnetic” mode. The magnetic field associated with this mode exists only in the plane transverse to the direction of propagation. m = no. of variations in the H-field across the diameter. n = no. of variations in the E-field around the circumference. TM- modes in circular waveguide The guide wavelength is given by

21

2

1

c

g

(1.5.4)

When the wavelength exceeds the cutoff wavelength c , the wave cannot propagate in that particular

mode. Hollow transmission line is therefore a high-pass filter. In terms of free-space wavelength o , then

we can write

21

21

21

1

c

o

g

(1.5.5)

Points of interest 1. The lowest order TE11 mode has the longest cutoff wavelength, and the most important in the design of components and antennas. 2. Waveguide symmetry critical for mode discrimination 3. Circular waveguide modes are affected by rotational symmetry of the guide. Any deformations in the guide will lead to instabilities and the creation of higher order modes.

These horizontal components willcancel if equal in magnitude.This only if w/g is round and symmetrical.

These horizontal components are NOT equal.The lowest mode will break up into next possible mode(s).

[a] [b]

Figure 1.5-3 The TE11 mode, as all other circular waveguide modes depend on rotational symmetry in the guide. Any deformations will prompt cross-polarization components as shown in (b) 4. As a result, complex components are much more difficult to design.



31

1.5.2 Circular Waveguide Components The principal characteristic of circular waveguide is that it is very difficult to design the equivalents to magic tees and hybrids and E- and H-plane bends so commonly found in rectangular waveguide format. However, circular waveguide is useful for applications requiring dual (orthogonal) polarization. Because of the impracticality of bends, components are typically connected in series. This frequently results in serious packaging problems – the feed can become untenably long. Therefore, the most important component has become the transition from circular to rectangular waveguide. Figures 1.5-4 to 1.5-8 show several designs that allow separation of polarizations, to be recombined into circular waveguide again, and possibly lying on a different axis. Circular waveguide OMT

Short circuit end plate

g/4

g/4

Figure 1.5-4 An OMT. The horizontal and vertical pol ports are offset from the same circular waveguide body. The OMT functions because of the presence of the short circuit presented by the end plate. However, if the end plate were replaced with a circular waveguide in cutoff at Lf , and working at a higher

frequency Hf , then a second and similar OMT could be connected in series.

Symmetrical circular waveguide to rectangular waveguide transition – style 1. Many feed packaging problems demand a change in direction of the basic RF axis defined by the horn. This requires a separation in H and V signal components with equal phase and amplitude in a symmetrical junction. The coupling of H and V components may occur longitudinally along the circular waveguide body as shown here in Figure 1.5-5; or the coupling may be accomplished with the coupling junction occuring radially as shown in Figure 1.5-6. This transition is used in configurations demanding a shift in the RF axis a – a’ to another b – b’ which may be parallel or orthogonal to a – a’, or even at some other arbitrary angle for the benefit of mechanical fit.

H


g/4


a

a*

b

b*

Figure 1.5-5 Symmetrical coupler with longitudinal coupling slots. Relatively narrow band performance features – 30 percent bandwidth



32

Symmetrical circular waveguide to rectangular waveguide transition – style 2

g/4

Figure 1.5-6 Symmetrical coupler with radial coupling slots. Relatively narrow band performance features – 30 percent bandwidth Symmetrical OMT

g/4


Endfire coax lineto generate TE21

coax mode for broadband coupling intosidewall rectangular waveguide slots

Figure 1.5-7 Symmetrical OMT with radial coupling slots. Relatively wide band performance features – nearly 48 percent bandwidth.



33

Quadrature Junction

High frequencysignal

High frequency

signal

Low frequency

signal

Low frequencysignal

Common aperture for low and high

frequencies

Low frequencysignal

Low frequencysignal

Figure 1.5-8 The quadrature junction is a symmetrical frequency selective coupler, for use in multi-frequency feeds. Usually, H and V components of the high frequency signals are fed back along the straight axial path. The H and V components of the low frequency signals are coupled out to the side. The design is such that high frequency signals do not couple significantly to the low frequency ports. The advantage of this device is polarization symmetry, as well as a means to couple widely separated frequency bands into one horn aperture. Suggested reading [1] Kraus, J.D., "Antennas", McGraw Hill Book Company, 1950, 1988 [2] Kraus, J.D., "Radio Astronomy", Cygnus-Quasar Books, 1966, 1982, 1986 [3] Marcuwitz, N., “Waveguide Handbook”, Radiation Laboratory Series, MIT. [4] Silver, Samuel, “Microwave Antenna Theory and Design”, Boston Technical Lithographers, Inc., 1963

Chapter 2 – Reflector Design


34

Chapter 2 - Reflector Design 2.1 Introduction 2.1.1 Concept of Gain 2.1.2 Determination of Gain 2.1.3 Concept of "Gain Relative to Isotropic" 2.2 Single Reflector Antenna 2.2.1 Prime-Focus Antenna Efficiency Components 2.2.2 General Performance Features 2.3 Two Reflector Design 2.3.1 Cassegrain and Gregory Configurations 2.3.2 Antenna Efficiency Components 2.3.3 Shaped Reflector Design Considerations 2.3.4 The Ring-Focus Antenna 2.4 Off-set Reflector Antennas 2.4.1 Single Offset Reflector Antenna 2.4.2 Horn reflector 2.4.3 Dual Offset Antennas - Cassegrain and Gregorian 2.4.4 Dragonian Reflector System 2.5 Characteristics of Antenna Patterns 2.5.1 Concept of Antenna Pattern Gain 2.1 Introduction What is the real purpose of an antenna? Communication appears to be an instinctive requirement for the human animal. In early days, when two parties were separated by some considerable distance, the coded smoke signal, flashes of light, and much later the telegraph and telephone using a solid wire connection, offered the essential medium for contact. But circumstances have arisen that make it impractical or even impossible to string a wire. The discovery that radio waves can be forced to leave a 2-wire system has bridged this problem. Now the problem is to examine how to launch the wave in the most efficient manner from point "A" towards point "B." That is, we would like for all the energy from "A" to be captured at "B." 2.1.1 Concept of Gain Consider the following situation: See Figure 2.1-1. The apertures of two open-ended waveguides, separated by a distance of 1 mile, are pointed toward each other. A representation of the radiation pattern for each aperture is shown.



35

-180o +180o0o

Elevation plane pattern of open ended waveguide

elevation

azimuthOpen ended WR-229 rectangular waveguide

Open ended WR-229 rectangular waveguide

Pattern of open ended waveguide

Aperture "B"

Aperture "A"

3db

-180o +180o0o

Azimuth plane pattern of open ended waveguide

3db

Half power beamwidth

Rel

ativ

e P

ower

- d

b

Rel

ativ

e P

ower

- d

b

(a)

(b) (c)

-45o 45o

90o80o

-40o 40o

Figure 2.1-1 (a) Two open-ended waveguide apertures with patterns pointing toward each other. Approximate waveguide aperture pattern (b) in the elevation plane, (c) in the azimuth plane. Examining the 3-dimensional pattern in detail, and plotting it in rectangular coordinates, we see a main beam and some sidelobes. The noteworthy aspect of this pattern is that the area under the complete power pattern is equal to the area under the rectangle containing the half-power points on the main beam, as shown in Figure 2.1-1. The area under the complete pattern is to be interpreted as equaling the total radiated energy. Therefore, the half power beamwidth represents the angle into which all the energy is ideally concentrated. In fact, for the open rectangular waveguide,

903 degrees and 803 degrees

This means that all of the effective energy is radiated over an angular spread of 90 x 80 = 7200 deg2. The amount of energy actually impinging on the aperture at point "B" is 0.001 x 0.002 = 2 x 10-6 deg2 or about 3 x 10-8 per cent of the total radiated from "A" as seen in Figure 2.1-2.

= 0.001 deg

1 mile = 5280 ft = 63360 inches

= 0.002 deg

"A" "B"

"A" "B"

1.145 inches

2.290 inches

Elevation plane

Azimuth plane

Narrow side of waveguide

Wide side of waveguide

Figure 2.1-2 Capture angles for open-ended waveguide apertures "A" and "B" If we increase the size of the antenna at "B" to subtend an angle of 80 x 90 deg2 as seen from "A", then all of the transmitted energy could be received. The dimensions of the aperture at "B" would have to be as in Figure 2.1-3.

99525180

905280123 rA inches (1.57 miles)



36

88467180

805280123 rB inches (1.40 miles)

where r distance separating the waveguide apertures

and 3 and 3 angles are expressed in degrees

a

bB

A

"A"

"B"

Figure 2.1-3 View of change in size of aperture "B" needed to capture pattern from "A" Since an antenna doesn't care in which direction the wave is travelling, it can be seen that if the wave were to emanate from "B" toward "A," it will be "bundled" or collimated, to be completely received by the waveguide aperture at "A." We see here that the "degree of bundling" of radio waves is directly proportional to the area of the aperture. The "degree of bundling" is termed "antenna gain." The antenna at "B" is of course unrealizeably large. But taken to the extreme: an antenna with infinite aperture would collimate its energy into one direction – an approximation best exemplified by a laser beam. Interestingly, if such an antenna could be built, then the single ray of energy would be transmitted completely from "A" to "B," regardless of the distance. Practically, however, a diverging cone of RF energy will limit the distance over which a communication link can exist. Further, since radio waves travel through space at the speed of light, the greater the distance, the more time it takes to reach its target. An example: The deep space probe to the outer fringes of the solar system requires several hours for a communication link. Additionally, an extraordinarily large and sensitive antenna is required to support this event. 2.1.2 Determination of Gain Coming back to the 4 GHz WR-229 waveguide – when allowed to radiate, the open waveguide represents a discontinuity which, we have seen, causes reflections and hence loss of useful energy. Flaring the waveguide to a larger aperture creates a horn-like structure, and reduces the effects of the discontinuity. Let us look at a horn with 120 inch x 120 inch aperture at point "A." Relative to the WR-229 w/g, the bundling or gain can be determined as follows: 2.29" x 1.145" aperture produces a beam of 80 x 90 deg2 120" x 120" aperture produces a beam deg2 From which we can say

9080

1145.1290.2 k

and

2

1120120

k



37

Therefore

3110.1120120

)9080(145.1290.22

And deg145.1

By definition,

9.5491145.1145.1

9080)229(

waveguideopenWRtorelativeGain

and expressed in decibels as: dbG 4.37)9.5491(log10

2.1.3 Concept of "Gain Relative to Isotropic" Since waveguide apertures are frequency sensitive and badly matched, a more general and useful basis for assignment of gain is the so-called "isotropic source" - an imaginary antenna which radiates equally in all directions, regardless of frequency. Note: when determining gain, we compare the "degree of bundling" of one aperture with some sort of reference. In the previous section, the so-called reference was the open waveguide. The isotropic source, radiating spherically from a point will have a beam equal to

24 rad or 222

96.41252180

4 degdeg

The open waveguide gain compared to an isotropic source is

73.59080

96.41252

Gain

and dbiGain 6.7)73.5log(10

The "dbi" to show it has been calculated "relative to isotropic." Therefore, any open ended waveguide, operated within its fundamental frequency range will have a gain of about 6 to 8 dbi. Generalized, the foregoing discussion can be written as:

The surface of a sphere of radius R is 24 R containing all of the radiated energy. The surface area

S contained within the half power points 3 and 3 of the rectangular horn is RR 33 where 3 and 3

are expressed in radians.

22

33 180RS

where 3 and 3 are expressed in degrees.

33

2

233

2 96.412521804

R

RGain (2.1.1)

Since we have determined that 33 is inversely proportional to the aperture area ba , we can write



38

2

44

ab

k

ba

kGain

(2.1.2)

where the aperture dimensions have been expressed in wavelengths. Interestingly, for open waveguide, 6.0k ; for a flared horn 8.0k ; and for an elliptical aperture,

0.1k

The expression in equation (2.1.2) can be generalized as:

)()(4

2efficiencyapertureofareaActualGain

)(4

2apertureofareaEffectiveGain

For the circular aperture, this then results in:

)()(4

422

2efficiency

Defficiency

DGain

(2.1.3)

This is commonly written as

efficiencyGGGain os

where

2

D

Go for an ideal lossless circular aperture (2.1.4)

Now, from (2.1.1)

33

296.41252

DGo

and for the case 33

DD

65.6496.41252

3 (2.1.5)

This represents the beamwidth associated with a 100% efficient antenna. That is, if it were possible to

design an antenna with all sidelobes suppressed, then the 3db beamwidth will equal 3 .

Typically, for well designed reflector antennas, the overall illumination efficiency is about 75%. Hence the basis for the EIA-411A standard procedure for determining gain, which says measure the 3db beamwidth, and apply the formula

33

000,31

GainPattern (2.1.6)

Note: Total antenna gain = Pattern gain - Feed and reflector accuracy losses



39

2.2 Single Reflector Antenna So far we have spoken of radiating devices - dipoles and waveguides, and the control of guided waves. The intent of "control" is to organize guided waves toward an appropriate radiating device. The choice of device is driven by requirements. In our case, the requirement is to direct RF energy from earth to a spacecraft in a communication link. In order for as much of this energy to reach the spacecraft, it will be necessary to concentrate, spotlight, or bundle it into a specific direction. RF energy is bundled by increasing the radiating aperture dimensions. Another way of realizing a radiating aperture is to borrow from optics – the analogy of a flashlight. A single light bulb feeds energy toward a parabolic reflector, whose geometrical properties bundle (or collimate) this energy into a narrow angular beam. The light source is one which radiates more or less uniformly into all directions, and therefore can be considered as emanating spherical wavefronts from a point. A review of analytic geometry shows conic sections to contain a collection of curves which possess the feature called a focus. The parabola is generated when a line is drawn connecting all points which are equidistant from a fixed point and a fixed straight line. This can also be viewed as the transformation of a series of concentric spheres centered on the fixed point (the focus) to the aperture plane of the reflector (the straight line). Figure 2.2-1 shows the generation of a parabola by a series of circles drawn with a center at the focus F, radiating toward the left.

F = Focus

Reflector axis

P1

P2

P3

A2

A1

Reflector axis

Ap

ert

ure

dia

me

ter

D

F1

F2

Ap

ert

ure

dia

me

ter

D

F = Focus

R

Figure 2.2-1 (a) Construction of a parabola with intersections of circles and straight lines - or spheres and planes to produce a paraboloid. (b) Similar constructions showing two parabolas with long F1 and short

F2 focal lengths. The corresponding aperture angles 1 and 2 are also shown. Here one can see that a

shallow reflector will have a long focal length, a deep reflector has a short focal length. Straight lines, representing planar surfaces, intercept the circles at points P1, P2, ... P3. The line connecting these points gives the parabolic shape. The condition given above for the parabola requires the distances F to P1 to A1 = F to P2 to A2 = F to P3. A1 to A2 to P3 represents the aperture plane of the reflector with radius R. Rotating this figure around the axis gives the three dimensional surface of revolution called a



40

paraboloid with an opening of diameter 2R = D. F = the focus of the reflector. The distance F to P1 equals the focal length of the reflector. The ratio F/D provides a view to the depth of the reflector; the smaller the F/D, the greater the depth of the reflector. Notice also that, as the depth of the reflector increases, the larger the angular field of view from the focus to the edge of the reflector.

Important analytical expressions describing the parabolic reflector:

Fz

x

R

S

D

Figure 2.2-2 The parameters describing the parabola

Reflector depth F

xz

4

2

(2.2.1)

Maximum depth of the reflector F

Dz

16

2

max

Aperture angle 22 4

4arcsin

zx

xz

(2.2.2)

Maximum aperture angle

F

D

4arctan2

Focus to reflector distance cos1

2

4

4 22

F

z

zxR (2.2.3)

Reflector curve length = 2222 4ln44

1xFxFxFx

FL (2.2.4)

Aperture circle area = 24 xAp (2.2.5)

For most applications, D

F is chosen to be in the range 5.030.0

D

F.

The corresponding look angles from the focus to the edge of the reflector are 8055 degrees.

Effective magnification is the ratio of feed half power beamwidth to antenna half power beamwidth. This will be equivalent to the ratio of antenna aperture to feed aperture.



41

Figure 2.2-3 shows the application of the parabolic reflector with a light bulb (a), a dipole (b), and a horn feed (c), and the associated radiated pattern.

F

(a)Flashlight configuration

Mirror

Light bulb on focus of mirror

Parabolic reflector

Dipole on focus of reflector

(b)Reflector and dipole

FReflector

Feed assembly

= angle off-axis.

Intensity

Direction of collimated rays of light

Direction of collimated microwave signal

Antenna Pattern

Figure 2.2-3 Application of the parabolic reflector with (a) a light bulb), (b) a dipole, and (c) a horn feed, and the associated radiated pattern. The radiation from the light bulb can be considered as a series of spherical wavefronts emanating from the focus. The parabolic reflector transforms the spherical wavefronts to planar wavefronts. Because plane wavefronts do not converge or diverge, they represent the most (100%) efficient form for the transmission of energy. For microwave applications, the light bulb is replaced by a suitable equivalent such as a dipole. 2.2.1 Prime-Focus Antenna Efficiency Components The general features of the dipole feed are shown in Figure 2.2-3. The angular view of the reflector - the aperture angle - as seen from the focus where the feed is placed - is typically in the order of 60 to 80

degrees. Therefore, not all the energy available from the feed pattern is captured by the reflector. The idea in all such applications is to direct all the RF energy toward the reflector, with minimal loss in gain. What are these losses? Figure 2.2-4 reveals some of the more evident loss components commonly encountered in reflector systems. The following describes some of these loss mechanisms.



42

FReflector

Feed assembly

1. This illumination difference represents an error or loss in efficiency.

2. Spillover losses

3. Losses due to scatter and phase errors from an inaccurate reflector surface.

4. Shadow blockage loss

5. Feed insertion (ohmic) loss

Actual feed patternIdeal pattern to completely illuminate the reflector

FReflector

Feed assembly

Feed blockage shadow area

Losses from an inaccurate reflector surface

Reflector spillover

Figure 2.2-4 Errors in illumination of a reflector with a non-ideal feed pattern Phase error loss (a) The main beam of the feed pattern is not completely spherical, meaning that the electrical distances - phase - between the focus and the aperture plane will not be constant for all radials. This means that the reflector is now not quite parabolic, and the outgoing wave will not be planar. A non-planar distribution, possessing phase errors across the aperture, when compared to the ideal uniform distribution, will represent phase efficiency of the antenna. (b) Similarly, if fabrication errors in the reflector lead to imperfections in the parabolic profile, path length differences between the focus and the aperture plane will exist. Therefore reflector surface accuracy contributes to phase efficiency. This is frequently referred to as reflector rms loss. More on this in Chapter 8. Illumination loss The main beam of the feed pattern does not have constant signal amplitude, but decreases with off-axis angle, and is not axi-symmetric. Because it is not constant, that means the aperture of the reflector is not completely illuminated. The ratio of the signal distribution across the aperture to the ideal uniform signal distribution will represent the illumination efficiency of the antenna. An optimum will be seen when the illumination level from the feed seen at the edge (called edge taper) of the reflector is between 10 and 12db below the on-axis maximum. It also becomes evident that illumination efficiency will be increased if the circular aperture of the reflector is illuminated with a circular feed pattern. Additionally, referring to Figure 2.2-1, the nominally spherical wave travelling to the parabolic reflector, does not intercept the reflector all at the same time. The distance FP1 < FP2 < FP3. As will be identified in Section 5.5.1, signal level is reduced as the square of the distance travelled. This means that the illumination across the parabolic aperture must be modified with an additional path loss as reflector edge taper = edge taper of the feed pattern + path loss for distance R.



43

Spillover loss Since the amplitude of the feed pattern does not abruptly reduce to zero at the aperture angle , the

energy which is not captured by the reflector will be lost. The ratio of energy captured by the reflector to the total energy supplied by the feed will represent spillover efficiency. For the dipole, we could improve spillover efficiency by increasing the aperture angle of the reflector. However, if we do this, the illumination efficiency will decrease. But, as shown in Figure 2.2-5, there will be a configuration in which illumination and spillover efficiencies together will lead to an optimum aperture efficiency.

Effi

cien

cy

1.0

0.5

Aperture illumination

efficiency illum Spillover efficiency s

Resultant aperture efficiency a

Aperture angle - Psi

40 9050 60 70 80

Optimum efficiency occurs for edge taper = 10 to 12db

Figure 2.2-5 For the prime focus reflector feed configuration, as the illumination across the aperture increases (to become more uniform), more energy will escape the aperture as spillover. The resultant antenna efficiency will be represented by the dotted line. The optimum efficiency will be represented by an edge illumination between 10 and 12 db below maximum illumination level. Blockage Since the feed occupies space in the reflector focus, some signal from the reflector will be intercepted and returned to the feed terminal. This reflected signal is lost. The presence of the feed partially blocks the reflector aperture. In many instances, the feed requires mechanical support, which also partially blocks the aperture. The ratio of the total blockage area compared to the area of the reflector aperture represents the blockage efficiency. Polarization loss In Chapter 1, two different feed elements were discussed - the electric dipole, and the magnetic dipole. The polarization pattern of the electric dipole is characterized by straight lines on and near the axis, and curved field lines away from the axis; the curvature increases with increasing angular distance from the axis. Using this feed to illuminate the parabolic reflector, the field lines captured by the reflector will include a portion of those lines which are curved. See Figure 1.1-7 reproduced here.



44

y

xE

Null along y-axis

z

H H

View along z-axis

Figure 1.1-7 The electric dipole The curvature in the field lines implies vertical and horizontal polarization components - horizontal components here are called "cross polarization" components, and represent lost power from the vertically polarized signal path. Cross-polar components represent loss of signal, leading to polarization efficiency. Combining the electric dipole with the influences of a magnetic dipole (Figure 1.1-8) to get an illumination of the reflector to be as shown in Figure 1.1-9, the impact of cross-polarization can be minimized. If the viewing angle from the feed (focus) is kept reasonably small, the amount of cross-pol can be reduced. This is one of the design considerations for the choice of reflector F/D - the larger the F/D, the smaller the cross-pol for the antenna.

y

x

z

H

E

Null along x-axis

View along z-axis

Figure 1.1-8 The magnetic dipole

x

z

y

Null at z-axis

View along z-axis

z

Figure 1.1-9 The field of the combination of the electric and magnetic dipoles making up the Huygens source.



45

Feeds displaying such polarization matching characteristics can be designed, and will be discussed in Chapter 3. Note: When operating in circular polarization mode: In the presence of the single reflector, for an incoming RCP signal, the feed must be configured for LCP, as intimated in Figure 1.2-8 see page 10. Reflector panel loss So far we have assumed the reflector surface to be continuous, made of one piece. The illumination by fields with spherical wavefronts from the feed induces currents in the reflector surface that support new reflected fields with planar wavefronts. Large reflectors are assembled from symmetrical pie-shaped panels. There are gaps between the panels. This means that the currents in the reflector surface will be disturbed by the discontinuities represented by the panel edges. The disturbance in current lines will cause polarization changes, contributing to polarization losses. Further, panel-gap edge-currents represent a new and different radiating element superimposed on the basic reflector. This new antenna possesses radiation features that will disturb the reflector pattern. The larger the area of the panel gap, in terms of width and length, the greater the disturbance in the overall antenna pattern. This represents a loss in signal from the antenna system. Reflection loss A portion of the signal from the feed illuminating the reflector is intercepted again by the feed, and seen as an increase in VSWR at the feed terminal(s). The contributing VSWR is given by

F

G dbf 1

410 20

where 1

1

VSWR

VSWR

Feed terminal losses Signal in the feed will encounter absorptive (ohmic) or attenuation loss in the waveguide. Further, as seen at the feed terminals, reflections (expressible as VSWR from internal waveguide structures) cause a fraction of the desired signal to be unavailable. And lastly, if any coupled ports are present in the feed design, coupling loss contributes to the unavailability of signal in the overall link. Summary The dipole can be used as a feed, but is not always an appropriate element for the reasons just described, and because of inherent losses and low power limitations. Since most high efficiency feeds also involve high power, a w/g feed is typically used. The waveguide feed will also provide the vehicle for combining electric and magnetic dipole features to minimize polarization loss. The total antenna system efficiency is given by the product of all efficiency values. 2.2.2 General Performance Features Conditional parameters 1. Reflector

reflector F/D chosen to suit - feed capabilities - mechanical practicalities (structural, feed support)

reflector diameter > 20 wavelengths



46

2. Circular symmetric feed pattern is matched to reflector geometry edge taper (for optimum aperture efficiency) about 10 to 12 db path loss, about 2.5db, to be added to edge taper, is given as

2

log10

F

RPathLoss (2.2.6)

overall efficiency factors (excluding feed loss) approx 60 to 65% 3. Nominal realizable performance - range of values, depending on choice of design parameter

reflected power back into the feed from the reflector is

F

GLossturnRe f

4log20 db (2.2.7)

where fG = feed horn gain (db)

= wavelength F = focal length

1st sidelobe - approx. 18 to 28db below main beam peak 2nd sidelobe - approx. 23 to 32db below main beam peak sidelobe envelope beyond 1 deg approx. 25 to 29dbi

- Typically, the higher the frequency, the lower the sidelobe envelope 2.3 Two Reflector Design 2.3.1 Cassegrain and Gregory Configurations The disadvantages of the single reflector system (feed in the prime focus) are low efficiency (typically about 55%), and an impractical feed location. For large antennas, the feed may not be accessible at all. To solve these problems, we can adopt other tricks from the world of optics and telescope configurations, in particular two reflector systems, as shown in Figure 2.3-1.

FReflector

Feed assembly

F1

Reflector

Feed assembly

F1Reflector

Feed assemblyF2

(a) Prime focus Configuration (b) Cassegrain Configuration (c) Gregorian Configuration

Hyperbolic subreflector

Ellipsoidalsubreflector

F2

Figure 2.3-1 Development of a 2-reflector system. (a) the single parabolic prime focus, (b) the Cassegrain, and (c) the Gregorian configuration. These reflector systems are based on the features of the family of conic sections shown in Figure 2.3-2.



47

F

R

X

Z

c c

a

b

R R

Z

X

OOc c

a

b

R R

Z

X

O

a

(a) Parabola (b) Hyperbola (c) Ellipse

a

F F 2

F 1 F 1

F 2

Figure 2.3-2 Conic sections (a) parabola, (b) hyperbola, (c) ellipse Important expressions for each are given here: Parabola: Focal length = F

F

xz

4

2

and cos1

2

FR (2.3.1)

Hyperbola

Focal length = 21

22 bac

12

2

2

2

b

x

a

z and

cos

2

ca

bR

(2.3.2)

Ellipse

Focal length = 21

22 bac

12

2

2

2

b

x

a

z and

cos

2

ca

bR

(2.3.3)

F1F2

Xm

Zm

Parabola

Hyperbola

DsDm

Xs

ZmZs

Fs

Fm

L2

F1F2

Xm

Zm

Parabola

Ellipse

DsDm

Xs

ZmZs

Fs

Fm

L2

RR

r

r

(xm,zm)

(xs,zs)

(xm,zm)

(xs,zs)

L1L1

(a) (b)

Figure 2.3-3 (a) The Cassegrain, and (b) the Gregory reflector geometry.



48

Fundamental equations describing the Cassegrain and Gregorian reflector geometries are: The main parabolic reflector

m

m

F

xz

4

2

(2.3.4)

The subreflector

11

2

b

xaz s

s (2.3.5)

where the parameters are a = half major axis

b = half minor axis e = eccentricity

21

1;2

2 eabe

Fa s (2.3.6)

and

)(sin

)(sin

21

21

e (2.3.7)

The linking expressions for the two reflector system are given as

m

m

F

D41

21tan (2.3.8)

s

s

D

F2

tan

1

tan

1

(2.3.9)

s

s

F

L2

)(sin

)(sin1

21

21

(2.3.10)

The "+" sign in (2.3.5) is used for the Cassegrain reflector system The "-" sign in (2.3.5) is used for the Gregorian reflector system Borrowing from optics of curved lenses and reflectors, the ratio of dimensions of image to actual size of an object is termed optical magnification. For the Cassegrain/Gregorian reflector system, this is defined by

21

21

2

1

tan

tan

1

1

e

e

L

LM (2.3.11)

Optical magnification is not to be confused with "Gain". Points of interest:

In comparing the Cassegrain and the Gregorian reflector systems with equal main reflector focal length mF ;

and equal subreflector focal length sF :

1. The feed horn required to illuminate the Cassegrain subreflector is larger than that needed for the single parabolic reflector prime focus system - the 'look angle' toward the subreflector is smaller. 2. The feed horn required to illuminate the Gregorian subreflector is slightly larger than that needed for the Cassegrain subreflector, since the subreflector is located further away and will appear smaller.

3. For a given mF , any convenient value for sF can be chosen.



49

Figure 2.3-1 illustrates these points. It also shows that subreflectors can be hyperbolic, flat, or elliptical.

For a fixed value mF , the illumination angle from the feed will vary. If the feed illumination angle is kept

constant, then the main reflector focal length mF will have to vary as shown in Figure 2.3-1. The

connection between these reflector elements, members of the family of conic sections, is shown in Figure 2.3-4. They can all be expressed with one equation containing the eccentricity e . "Eccentricity" can be thought of as a measure of deformation of the circle - squash it one way, e becomes negative; pull it inside out, and it goes positive until e = infinity.

cos1

1

e

e

F

R

(2.3.12)

Ellipse e < 0Focal points inside Circle e = 0

Parabola e = 1

Hyperbola e > 0Focal points outside

Straight Line e = infinite

R R R

R

F

F1

F2

F1 F2

psi

F

Figure 2.3-4 The family of conic sections - all represented by the common equation (2.3.12). [1] 2.3.2 Antenna Efficiency Components For both the Cassegrain and the Gregorian, the reflector system loss components are more complicated. But because the feed is conveniently located in the vertex of the main reflector, and always reachable from behind, this antenna configuration is preferred by many users. Pattern performance is practically identical. Figure 2.3-5 shows diagrammatically the various loss elements. Antenna efficiency for the parabolic prime focus case (Section 2.2) must be modified with the inclusion of the phase error, illumination, and spillover errors associated with the subreflector. The understanding of these quantities is identical to that listed in Section 2.2.1. To be noted for this reflector configuration - the aperture angle presented by the subreflector at the feed in F2 is much smaller than for the prime focus single reflector case. This means the gain of the feed must be increased.



50

F1

MainReflector

Feed assembly

F2

Subreflector spillover

Subreflector edge diffraction

Antenna axis

Main reflector spillover

Reflector profileerror loss

Feed blockage and scatter

Subreflector support structure

Scatter from subref. support

Shadowing onto the main reflector aperture by the feed.Usually smaller than subreflector shadow

Scatter due to subreflector blockage

(a) (b)

Subreflector support blockage shadow

Subreflector blockage

Figure 2.3.5 Cassegrain reflector loss components, all contributing to a degradation in gain. The red arrows refer to the traces that contribute to the useful collimation of energy. The blue arrows show the traces that contribute to reflector losses. (a) Loss components due to the presence of the subreflector. (b) The view of the blockage caused by the subreflector support structure. Subreflector blockage The subreflector will occupy a central spot in the antenna aperture. How large can the subreflector be ?? Providing that the subreflector is at least about 10 wavelengths, edge currents and associated diffraction effects will be acceptably small. This then defines the smallest size of the subreflector. Nominally acceptable blockage is achieved when the ratio of subreflector diameter to main reflector diameter is less than 0.15. Gain will be impacted by the ratio of main reflector aperture area to subreflector aperture area

2

m

s

D

D. For the case Ds = 0.15Dm, the blockage efficiency = 0.978 or 0.1 db. An additional aspect for

wanting to constrain the subreflector size is the impact on the antenna pattern. The larger the subreflector blockage, the more the antenna pattern sidelobe envelope is disturbed. Subreflector support structure blockage The subreflector needs to be structurally supported in a manner which keeps the subreflector in position, regardless of which direction the antenna is pointing. This structure will contribute to blocking the main reflector aperture. So the idea is to keep the blocking area as small as possible. Further, the geometry of the supporting structure must be such that diffraction currents and associated radiation pattern is minimized. Figure 2.3-4(b) shows the various blockage elements generated by the subreflector and its supporting quadrupod. The currents generated in the quad-legs by fields intercepted from the main reflector aperture as well as fields intercepted from the subreflector will all contribute to disturbing diffraction patterns. Feed blockage The feed will be relatively large - a horn aperture or even an array of small radiating elements. The axial rays from the feed will be returned to the feed aperture as reflected signal from the subreflector. Any support structure for the feed system will also intercept reflections from the subreflector, and contribute to blockage. Surface currents induced in the illuminated portions of the support structure, will possess a relatively low gain radiation pattern that will be superimposed on the main reflector pattern.



51

Diffraction loss If the subreflector diameter becomes significantly less than 10 wavelengths, edge currents may become large and radiate a second pattern that will be super-imposed on the expected normal antenna pattern. This phenomenon will occur when surface currents wrap around the edge and continue to exist on the rear side of the subreflector. The magnitude will be dependent on the illumination from the feed. Low frequency high edge illumination levels will induce large edge currents. The results of the simulation of small aperture effects is shown in Figure 2.3.6 - the case of a Gregorian reflector system.

Figure 2.3-6 Computational simulation of the unseen radiation mechanism in a Gregorian antenna. General performance features Conditional parameters 1. Subreflector

subreflector diameter < 15% of main reflector subreflector diameter > 10 wavelengths focal length of subreflector chosen so that:

- F2 is in front of main reflector vertex - aperture angle of subreflector is in the range 15 to 25 degrees

feed horn aperture dimensions, when projected onto the main reflector, do not exceed the subreflector diameter. See Figure 2.3-7.

Main Reflector

Feed system and horn

Diffraction from edge currents on the main reflector

F1 F2

Diffraction from surface currents on the back of the subreflector

Subreflector



52

F2

F1

B Feed Assembly

DDs

Figure 2.3-7 Feed dimensions D are constrained to not contribute to reflector system blockage B < Ds 2. Feed system

circular symmetric feed pattern is matched to reflector geometry edge taper (for best antenna gain and lowest sidelobe) about 15 to 18 db

3. Main reflector

reflector F/D chosen to suit - dimensional requirements of the feed system network

▫ to fit hub, and permit horn focus to be located at F2 - mechanical practicalities

▫ hub depth, determined by size of feed structural requirements for the reflector

▫ hub diameter appropriate reflector structure, subreflector support 4. Nominal realizable performance - range of values, depending on choice of design parameters

overall efficiency factors (no feed losses) approx 75-80% 1st sidelobe - approx. 14 to 18db below main beam peak 2nd sidelobe - approx. 23 to 27db below main beam peak sidelobe envelope beyond 1 deg off-axis - approx 30 to 35dbi

- Typically, the higher the frequency, the lower the sidelobe envelope 2.3.3 Shaped Reflector Design Considerations In Section 2.3.2, we discussed some of the deficiencies of two reflector type antennas. Are there any ways of reducing these losses? Let us look at the pure parabolic/hyperbolic reflector system - the Cassegrain configuration - shown in Figure 2.3-8(a) and (b). The feed pattern can be narrowed down to reduce the lost subreflector spillover energy. Now, however, less energy will be directed to the edge of the reflector system, and this will mean less efficient use of the aperture, and therefore less gain. Can this loss in gain be recovered? Answer = yes.



53

[a]

F2

F1

Parabolic reflector convertsspherical waves into planar waves

Subreflector (Hyberboloid) convertsspherical waves from horn intospherical waves with focus or center F1

Spherical waves emanating through horn aperture seemingly emanating from focus F2, commonly referred to as the "phase center" - the center point from which the spherical waves emanate.

Captured by Subreflector

-15o 0o15o

Primary Feed Horn Pattern

-67o 0o 67o

lost as mainreflector spillover

Captured by feed horn blockage

Ideal shape of subreflector pattern

Represents distribution of energy across main reflector

Subreflector pattern which illuminates parabolic (main) reflector

Edge angle of main reflector

[b] [c]

67o 0o 67o

lost as mainreflector spillover

Subreflector pattern which illuminates parabolic (main) reflector

Edge angle of main reflector

[d]

(c) result of shaping in the reflector system

(a) Ideal illumination of main reflector aperture

Actual illumination from hyperbolic subreflector

180o

Reduced reflectionfrom subreflectorback into the feed Wideangle pattern

of subreflector

Figure 2.3-8 Aspects of the illumination of a Cassegrain reflector system



54

Let us consider what can be done with the subreflector. In the classical Cassegrain, the feed pattern - solid line in (b) - is transformed to the solid line in (c), with the associated spillover and blockage problems. The ideal illumination of the main reflector is represented by the dashed line in (d), including a “hole” in the central region to reduce the reflections from the subreflector back into the feed. If we rearrange the subreflector shape to direct the energy in the central region to be spread into the central region of the main reflector – into the useful unblocked segment of the aperture – then we could reach the distribution shown by the solid line in (d). This would also represent an increase in illumination efficiency. The nature of the new shaping of the subreflector is seen in Figure 2.3-9.

F1

X s

ZsF2

S3

S2

S1

M1

M2

M3

A3

A2

Z m

[a] Pure Cassegrain Reflector Layout

X m

Focal point

F1

Xs

Z sF2

S3

S2

S1

M1

M2

M3A3

A2

Z m

Shaped subreflector

Unshaped paraboloidal profile

Shaped reflector profile

[b] Shaped Cassegrain Reflector Layout

X m

A3

Focal line

Projected aperture plane

Figure 2.3-9 (a) Ray diagram in the pure Cassegrain; (b) ray diagram in the shaped Cassegrain that will accommodate for a maximum gain condition. The shaping function can be chosen to achieve a specific performance requirement. The features of (b) are:

reduced reflection of waves back into the feed horn steeper slope at the edge angle of the main reflector, and as a consequence, lower spillover

losses. F1 is no longer a point, but rather a line focus. Similarly so with F2.

The sensitivity of the feed location in F2 is determined by the ratio of main reflector mD and feed fd

apertures. The subreflector must be located in an F1 which offers the best focussed condition.

The positional bounds will be 20

. The feed may be located with an accuracy of

20

f

m

d

D, meaning

a small positional error will not have a significant impact on performance. Typically, f

m

d

D will have a value

> 20, suggesting the feed positional error may be in the order of 1 . The primary condition for any reflector system to produce planar waves at the aperture is that the path length from the focus to any point in the aperture be constant. Since the feed will be located in a fixed position along the focal line, F1 must be considered fixed. Therefore, in the ray diagrams of Figure 2.3-9, the path lengths F2 to S1 to M1 to A1 must be equal to the total length F2 to S2 to M2 to A2 and F2 to S3 to M3 to A3. What is the right shape? Well, that depends on what the desired end result is to be. For our purposes, the desired end result is to obtain the lowest possible sidelobe envelope. As it turns out, this is achieved by



55

choosing a distribution in the main reflector aperture as shown in Figure 2.3-10. The ideal shape is when the solid line (b) has a sine-curve shape. .

Note:The effect of the subreflector blockage does not go away, but any reflection effects of the subreflector back into the feed are very effectively reduced.

Note:This choice of illumination is only good for "blocked" circular apertures. Illumination (b) is the ideal, and (a) that which is most easily realized.

(a)

(b)

Antenna Axis5 - 10db

12 - 25 db

F2

F1

Figure 2.3-10 Main reflector illumination requirement for lowest sidelobe envelope The antenna sidelobe behaviour associated with the shaped reflector system is seen in the diagram of Figure 2.3-11.

Raised sidelobes due to blockage by subreflector

10 to 15 db sidelobe envelope suppression

Subreflector spillover

Lower envelope due to "shaping":

Lower envelope here because horn pattern narrowed to reduce spillover loss

Main reflector spillover

"Shaping" reduces level here

Back lobe

0o 20 100 180Angle Off-Axis - degrees

Rel

ativ

e Po

wer

- d

b

0db

10

20

30

40

Figure 2.3-11 Sidelobe envelope behaviour of Cassegrain and shaped Cassegrain reflector systems This does not represent a maximum gain condition. If the requirement is to offer not only a low sidelobe envelope, but also an optimized gain, then a slightly different shaping for the reflector system, as shown in Figure 2.3-12 will do the trick.



56

F1

X s

Z sF2

S3

S2

S1

M1

M2

M3A3

A2

Z m

Shaped subreflector

Unshaped paraboloidal profile

Shaped reflector profile

X m

A3

Focal line

Projected aperture plane

Figure 2.3-12 Ray diagram of a shaped Cassegrain reflector system to accommodate for an optimized gain and a low sidelobe envelope that will comply with 29-25log(t). Notice that the outer region of both sub and main reflector curl back, this permitting a steep edge taper in the illumination to be incorporated in the illumination across the aperture. The less power at the edge of the reflector, the lower the first few sidelobes and the lower the spillover. The distribution will not be sinusoidal in shape as was intimated in the shaping shown Figure 2.3-9, but rather that shown in Figure 2.3-13.

(a)

(b)

Antenna Axis5 - 10db

12 - 25 db

F2

F1

Figure 2.3-13 Illumination distribution across the reflector aperture to offer an optimized gain and low sidelobe envelope. Several approaches to reflector shaping have been discussed in the literature [4], [5]. Two major components in the sidelobe envelope (SLE) are evident.

Subreflector blockage Subreflector spillover

Can these effects be removed, or reduced? Let us consider subreflector blockage first. How is subreflector blockage evidenced? Consider the components as described in Figure 2.3-14(a). Subreflector blockage is seen as an interference pattern between the unblocked aperture, and the pattern associated with the subreflector shadow by itself. Every alternate sidelobe in the antenna pattern is raised in level, every sidelobe in between is lowered.



57

Aperture Plane

Subreflector

Main reflector

Pattern of the unblocked main reflector

Pattern of the blockage by the subreflector

diameter = "a"

Diameter = "A"

From the previous discussion, beamwidth of aperture "A" will be a/A smaller. For a/A = 1/10, antenna gain difference between apertures is 20db.

G = 10log(a/A)2

Therefore, when combining these pattern components, we have:

Pattern due to subreflector blockage

Pattern due to un-blocked aperture "A"

Resultant sidelobe pattern due to blocked aperture a/A.

Re

lativ

e P

ower

-

db

3db

0db

10

20

30

40

3db

3db

Angle off-axis

50

Figure 2.3-14 Effect of subreflector blockage on the antenna sidelobe envelope Now the subreflector spillover: Case 1: In Figure 2.3-15, the angle from the feed phase center (focus) to the edge of the subreflector is 15 degrees. This causes the spillover lobe to occur in the region 13 to 20 degrees off-axis. Current designs use this configuration, since it was good enough to meet FCC sidelobe envelope of 29-25log(t) dbi for < 7o and 32-25log(t) dbi for 9o < < 48o.

F2 F1F2 F1 F2 F1

Case 2: Subreflector Spillover at > 20 deg



15o25o 5o

Figure 2.3-15 Three cases for spillover sidelobe control. Case 1 for approximately 15 to 20 deg off-axis sidelobes due to subreflector spillover; case 2 for 25 to 35 deg off-axis sidelobes; case 3 for spillover sidelobes at 5 to 10 deg off-axis. Case 2: Suppose we now consider a configuration in which the subreflector half angle is 25 degrees. Now the spillover region in the pattern will occur from about 22 to 35 degrees. This is good when viewed from the SLE specification. However, it means

moving the feed on a long cantilever toward the subreflector. the shape of the sub and main reflectors will change

– that means tooling changes and therefore money.



58

And all we will have accomplished is to move the spillover lobe to another place. Unfortunately, the further away the spillover lobe is moved from the axis, the greater the loss in gain. More on this later in Section 2.5.1. Case 3: What about trying to move the spillover region closer to the antenna axis? Note from earlier discussion, that in order to increase the bundling of rays for a small angular spread (here +/- 5 degrees), the feed horn aperture will need to be very large. This also implies that the feed needs to be far away from the subreflector. This will cause the aperture of the horn to become comparable in size if not larger than the subreflector, an untenable situation in the antenna. The only real way of reducing spillover is by changing the shape of the feed horn pattern illuminating the subreflector. For the symmetrical reflector configuration, this can only be accomplished by shaping the beam of the primary feed pattern. One possible solution is with a multi-mode horn, to be discussed in Chapter 3. For more design details of the axi-symmetric two reflector system, see [2],[3]. General performance features of the shaped system Conditional parameters 1. Same as for the classical Cassegrain mentioned in Section 2.3.2 2. Subreflector and main reflector profiles matched for best illumination efficiency and lowest sidelobe performance features

o Nominal realizable performance - range of values, depending on choice of design parameters o overall efficiency factors (no feed losses) approx 80 to 90% o 1st sidelobe - approx. 15 to 17db below main beam peak o 2nd sidelobe - approx. 23 to 27db below main beam peak o sidelobe envelope beyond 1 deg off-axis - approx 27 to 32dbi

- Typically, the higher the frequency, the lower the sidelobe envelope 3. The shaped Cassegrain/Gregorian main reflector cannot be used as a prime focus reflector, since its shape is no longer parabolic. However, if the design frequency is low enough, or the wavelength long enough, then the reflector profile error compared with the wavelength may offer a sufficiently small error to offer negligible error in gain and distortion of the pattern. More on the effects of reflector surface errors on antenna performance in Chapters 8 and 9.



59

2.3.4 The Ring Focus Antenna The ring focus antenna is shown in Figure 2.3-16. This is an axi-symmetric reflector which is derived from a dual offset Gregorian which has been rotated around a shifted axis parallel to the reflector axis.

F1

F2

F1

F2Subreflector Subreflector

Axi-symmetricparabolicmain reflector

Feed Feed

Offsetparabolic sectionmain reflector

(a) Cassegrain Reflector Geometry (b) Ring Focus Reflector Geometry

High amplitude feed pattern rays

High amplitude pattern rays

Ring FocusPrimary focus

Se

con

dary

focu

s

Sec

ond

ary

Fo

cus

Offsetparabolic sectionmain reflector

Axis of Main Reflector

Axis of Offset Main Reflector

Low amplitude pattern rays

Low amplitude pattern rays

Axis of rotation of offset reflector

a

b

Figure 2.3-16 A comparison of geometrical features between (a) the Cassegrain and (b) the Ring Focus antennas. The Ring Focus offers a smaller blockage of the aperture and the use of a smaller feed However, the point on the center of the reflector represents a discontinuity. Positive features of the Ring Focus: 1. Small blockage of the main reflector aperture - about 50% smaller than for the same sized Cassegrain. 2. Smaller feed - small number of grooves, wideband performance - able to view a wider look angle toward the subreflector. Feed is therefore generally less expensive than that required for the Cassegrain. 3. The subreflector may, in some instances involving low frequencies, be supported from the feed with dielectric material, thereby precluding use of a quadrupod subreflector support assembly. 4. The Ring Focus can be shaped for improvement in efficiency. Negative features of the Ring Focus 1. The smaller subreflector does not lend itself to applications involving low frequencies. The longer wavelength waves will tend to demonstrate larger diffraction currents that will wrap around the edge of the subreflector, leading to higher sidelobe envelope. 2. The point in the middle of the subreflector profile generates an additional diffractive discontinuity, leading to higher near-in sidelobe peaks. 3. The main reflector is not a continuous parabolic surface of revolution, since the parabolic profile starts at "a" and ends at "b" shown in Figure 2.3-16. This means that the reflector cannot be used separately as a prime focus. 4. Only relatively simple feeds can be designed, since the small subreflector will be a major dimensional constraint. 5. More complex feeds demanding a larger horn - multiband, monopulse function, or both - cannot be accommodated without the horn becoming a major factor in causing blockage, or the feed assembly becoming so large as to contribute to blockage.



60

General performance features Conditional parameters 1. Subreflector

subreflector diameter < 10% of main reflector subreflector diameter > 7 wavelengths

o focal length of subreflector chosen so that: - F1 is in front of main reflector vertex and is evidenced as a ring around the axis, and not a

point. - aperture angle of subreflector is in the range 35 to 55 degrees

feed support dimensions the subreflector diameter. 2. Feed system

circular symmetric feed pattern is matched to reflector polarization edge taper (for best antenna gain) about 15 to 18 db horn design with phase center located close to or in the aperture

3. Main reflector

reflector F/D chosen to suit, generally < 0.4 as seen on half the aperture diameter. o dimensional requirements of the feed system network to fit hub, and permit horn focus to be

located at F2 o mechanical practicalities

- hub depth, determined by size of feed structural requirements for the reflector - hub diameter, determined by appropriate reflector structure subreflector support

4. Nominal realizable performance - range of values, depending on choice of design parameter

overall efficiency factors (no feed losses) approx 65 to 70% o 1st sidelobe - approx. 12 to 15db below main beam peak o 2nd sidelobe - approx. 23 to 27db below main beam peak o 4th sidelobe may reach 24 to 25 db below main beam peak o sidelobe envelope beyond 1 deg off-axis - can meet ITU Recommendation

Typically, the higher the frequency, the lower the sidelobe envelope For more design details of the ring focus reflector system, see [6],[7].



61

2.4 Off-set Reflector Antennas 2.4.1 Single Offset Reflector Antenna The principal difficulty with circularly symmetric antennas is central blockage by the feed in prime focus applications, or the subreflector in the 2-reflector configurations. See Figure 2.4-1. In an effort to reduce the blockage caused by the feed/subreflector support structures (a), (b), and (c), feeds and subreflectors were configured to be self-supporting or reduced in dimension (d) and (e) respectively. Figure 2.4-1(e) shows the effects of central feed/subreflector and strut blockage.

F

F2

F1 F1F2

F1

F2

F1

(a)Prime Focus

(b)Prime Focus

(c)Gregorian

(d)Cassegrain

(e) "Ring Focus" or "Compact Cassegrain"

Note:The ring focus is generatedby rotating anoffset Gregorianreflector systemwith RF axis "A" around the axis "B"

A

B

Subreflector support structure

Feed support structure

Figure 2.4-1 Various axi-symmetric reflector configurations, all showing central blockage of the main reflector by either (a) and (b) the feed; (c),(d), or (e) the subreflector However, the blockage issue can only go away if the aperture is cleared completely of all obstacles. This leads to considering the use of an off-axis segment of a reflector. See Figure 2.4-2(a). On the surface, these optical configurations are an excellent solution to the pattern problem. Unfortunately some not so desirable features characterize the off-set antenna.



62

Circular projected aperture

Mechanical center of aperture

NominalRF center

Feed horn

(a)Offset Prime Focus

F

F1

F2

Large unusable reflector segment

(b)Dual Offset Cassegrain

Parabola

Parabola

Hyperbola

Feed horn

Slightly tilted RF axisto compensate for mechanical asymmetry

F1

F2

Parabola

Ellipse

Feed horn

Parabolicmain reflector


F1

F2

(c)Dual Offset Gregorian

Feed Horn

Sm

all u

nus

ed

refle

ctor

se

gmen

t

Feed axis

Antenna axis

(d)Dual offset Dragonian antenna

Figure 2.4-2 Offset reflector configurations to reduce main reflector aperture blockage. (a) prime focus; (b) dual offset Cassegrain (with hyperbolic subreflector); (c) dual offset Gregory (with elliptical subreflector); (d) Dragonian antenna with concave hyperbolic subreflector Positive features: 1. Completely clear aperture, meaning all blockage induced sidelobes nonexistent. 2. The first sidelobe typically is suppressed to about 25 to 30 db below the main beam maximum.

Blockage sidelobes

Angle off-axis

Re

lativ

e P

ower

- d

b

Reflector surface error pedestal

Figure 2.4-3 Sidelobe suppression of the offset reflector system 3. The overall sidelobe envelope is lower, and therefore the antenna efficiency is higher than for axi-symmetric reflector systems. Note: For this reason, the "short cut" antenna gain formula, relying on a measurement of half power beamwidth, must use a higher K-value - see Section 2.8.1. If made carefully, the offset antenna efficiency can be improved by up to +1db relative to the same sized symmetrical antenna - meaning an antenna efficiency of 85 to 90 per cent.



63

4. Cross polarization errors, inherent in single offset reflectors, is to a large extent compensated in the dual offset Gregorian configuration, but not in the dual offset Cassegrain. 5. There is no great restriction in the size of the subreflector as there is in the axi-symmetric Cassegrain and Gregorian antenna, thereby reducing diffraction sidelobes from the subreflector perimeter, and permitting smaller feeds. Negative features: 1. Off-axis polarization discrimination suffers in the single off-set reflector antenna. The mechanism for this can be seen in Figure 2.4-4.

Azim

Elev

Azim

Elev

[a]Axi-symmetric Aperture

[b]Single Offset Aperture

Mechanical center of aperture

Feed horn F

Parabola

Focal Length "F"

Dia

me

ter

"D"

F/D small:

For F/D = 0.5, ~ 50 degreesNote: Equivalent to F/D = 0.25 for symmetrical reflector

Feed horn

F

Parabola

Focal Length "F"

Dia

me

ter

"D"

F/D Large:

For F/D = 1.2, ~ 30 degreesNote:The cross-polar fields in the reflector can be reduced by decreasing the angle of the feed toward the reflector.

18db

3db

0db

Cross-pol peaks in azimuth plane (plane of symmetry)

Cross-pol in elevation plane = 0

3db

0db

Cross-pol peaks in azimuth plane (plane of symmetry)

Cross-pol in elevation plane = 0

Co-pol pattern

Cross-polpattern

Co-pol pattern

Cross-pol pattern

[c] [d]

[e] [f]

RF center of reflector

c

c

c

c

30db

Figure 2.4-4 Cross-pol field components in the single offset prime focus reflector



64

Note: A special feed can be constructed possessing modes that compensate for cross-polar components in the single offset reflector, by purposefully generating equal and opposite cross-polar components. A design is discussed in Section 5.1.3 2. The elevation pattern has a small measure of asymmetry due to the tilted illumination by the offset feed. 3. When using a circularly polarized feed system, the main beam will be squinted (or tilted) slightly in the azimuth plane relative to the nominal or linearly polarized RF axis. For RCP outgoing waves tilt will be ccw, and for LCP outgoing waves the tilt will be cw in the azimuth plane, as seen from the front of the antenna. A good approximation to the beam squint angle is given by

reesF

os deg

4

sinarcsin

(2.4.1)

where wavelength

o aperture angle from the feed phase center

F Focal length

The squinting mechanism for CP signals is shown in Figure 2.4-5.

Azim axis

RCP

LCP

Cross-pol-ve phase

Cross-pol +ve phase

RCP

LCP

RCP

Incident RCP from feed

Reflected LCP

Squint angle

θ s

CP Feed

V

H

V

H

V

H

Curved co-pol field distribution in the reflector aperture

Antenna RF axis

Figure 2.4-5 Beam squint mechanism in offset reflector operating in circular polarization mode The following Table 2.4.1 gives a guide line to cross-pol values that can be anticipated in a single offset reflector system defined by F/D, depending on edge taper and alignment of the feed. Table 2.4.1 Approximate cross-pol values associated with F/D of single offset reflector systems

F/D 0.6 0.7 0.8 0.9 1.0 1.1 1.2 1.3 1.4 Xpol db 19 24 28 31 33 35 37 39 40



65

Seen from a slightly different perspective, Figure 2.4-6 shows how the cross-pol rapidly increases with

increasing angle of entry o of the illumination from the feed into the aperture of the main reflector.

Aperture Angle vs Offset F/D

10

12

14

16

18

20

22

24

26

28

30

0.5 0.6 0.7 0.8 0.9 1 1.1 1.2 1.3F/D

Ape

rtur

e A

ngle

- deg

o

o

o

Focus

X

Z

Pa

rab

olic

re

flect

or

0,0

Dm

(a) (b)

Cross-pol vs Aperture Angle for offset parabolic reflectors

0

5

10

15

20

25

30

35

40

45

15 20 25 30 35 40 45 50 55 60 65 70 75 80 85 90

Aperture Angle - degrees

Cro

ss P

olar

izat

ion

- db

o

= 15o

= 20o

= 30o

= 45o

o

= Illumination Angle

(c) Figure 2.4-6 Cross-pol characteristics of single offset parabolic reflector

(a) Relationship between F/D and aperture angle o ; (b) the offset reflector geometry;

(c) cross-pol levels as a function of o and feed pattern beamwidth = 2 . The more narrow the feed

pattern beam, the smaller the range of asymmetry in the aperture, and therefore the lower the resulting cross-pol. 2.4.2 Horn Reflector The simplest form of the offset reflector antenna is the "horn reflector". This is shown in Figure 2.4-7. One of the interesting features of this antenna is that the reflector edge is shielded, offering an antenna with an unsurpassed low sidelobe envelope performance. In order to achieve a reasonable 35db cross-pol characteristic, the reflector needs to be designed with an F/D > 1.1. For larger antenna sizes, the horn becomes a mechanical design and construction problem.



66

Feed Network

Ph

ase

cent

er

Focus of reflector

Circular aperture "D"

Horn

Parabolic reflector

"F"

Figure 2.4-7 (a) The horn reflector, sometimes named after its first proponent the Hogg horn. (b) First US earth station antenna – a 67 ft aperture horn under a 200 ft inflatable dacron radome, built in 1962. The largest antenna of this type, designed and built by Bell Labs in 1962, was located at Andover, Maine for use with the first of the US communication satellites Early Bird and Telstar. The principle attractive feature of this design is the achievable very low sidelobe envelope and consequent low noise temperature. 2.4.3 Dual Offset Antennas - Cassegrain and Gregorian The dual offset reflector systems as shown in Figure 2.4-8(c) and (d) have a number of redeeming features:

an unblocked aperture, with approximately 80% efficiency a suitably large (in wavelength) subreflector can be designed without causing any significant

blockage a relatively large feed system can be fitted without causing any significant blockage cross-pol associated with asymmetrical single offset reflector, caused principally by the

asymmetry and depth, can be compensated or even cancelled with the Gregorian subreflector.

F1

F2

2θe

θe

θU

θo

θL

X sr

Z sr

Z mr

X mr

2f

F

Ls

Dsx

Lm

Lt

Dm

Ht

h

Figure 2.4-8 Geometry of the dual offset Gregory reflector system.



67

Fundamental equations describing the dual offset Cassegrain and Gregorian reflector systems are given below.

FF

yxZ mrmr

mr

4

22

(2.4.2)

faf

yxaZ srsr

sr

22

22

1 (2.4.3)

144

2

2

2

2

mm D

y

D

hx (2.4.4)

F

ho 2

arctan2 (2.4.5)

F

Dh mU 4

2arctan2 (2.4.6)

2

tan1

1arctan2 e

U e

e (2.4.7)

Gregorianafor

Cassegrainafor

1

1

F

Dh mL 4

2arctan2 (2.4.8)

2tan

2tan

1

2tan

2tan

1

o

o

e

(2.4.9)

2

tan1

1arctan2

e

ea (2.4.10)

2

tan1

1arctan2 U

e e

e (2.4.11)

1cos

12

2

os e

eaL

(2.4.12)



68

F

F

Dh

e

ea

e

eaL m

U

U

L

Lt

16

2

1cos

sin1

2

1

1cos

sin1

2

1 222

(2.4.13)

F

Dh

e

ea

e

ea

DhH m

U

U

L

Lmt 16

2

1cos

sin1

2

1

1cos

sin1

2

1

2

222

(2.4.14)

aef (2.4.15)

The condition, called the Mizugutch condition [9], to cancel the cross-polarized component is

ee

e

2cos1

sin1tan

2

2

(2.4.16)

where = angle between horn axis and rotation axis of the subreflector

= angle between the rotation axis of the subreflector and that of the parabolic main reflector

To be noticed in this design - the feed axis can never be parallel to the antenna axis without upsetting the minimum cross-pol condition. For an antenna design incorporating a physically large feed system that will induce a large blockage into the main reflector, a new design can be made which provides for the feed axis to be parallel to the antenna axis. Now, in order to compensate for the resulting cross-pol errors, the trick is to shape the main and subreflectors. See Figure 2.4-9.

F1

F2

Parabola

Feed horn Feed axis

Shaped main reflector

Shaped subreflector

Xsr

Xf

Zf

Zm,Zxs

Figure 2.4-9 The convenient feed axis parallel to the antenna axis is only possible with a shaped system, while maintaining good cross-pol performance. For more design details of the dual offset reflector system, see [9]



69

2.4.4 Dragonian Reflector System The Dragone reflector configuration shown in Figure 2.4-10 has the attractive feature of offering a compact antenna with smallest dimensional extent. When appropriately hinged, a version of this antenna can be packaged for easy transport.

Parabolicmain reflector


F1

F2

Feed Horn

Figure 2.4-10 The layout of the Dragonian reflector system. The attractive features here are reflectors with large radii of curvature, resulting in low cross-pol performance For more design details of the Dragonian reflector system, see [8] 2.5 Characteristics of Antenna Patterns The general features of patterns associated with reflector antennas are shown in Figure 2.5-1. Here we see the influences of a variety of "efficiency" effects – blockage, spillover, over or under-illumination of the reflector system by the feed, and surface errors. Figure 2.5-1(a) represents wishful thinking - an ideal pattern with no sidelobes. The pattern in (b) displays a best theoretical realization of (a) - a single on-axis beam with decreasing sidelobes to either side. Patterns in (c) to (h), show the influence of spillover, subreflector blockage, reflector surface errors, and subreflector support. Every increase in sidelobe level prompts the antenna gain to decrease.



70

0 18090

[a] [b]

[d]

0 18090

[e]

Angle off-axis - deg

Angle off-axis - degrees

0 18090

[c]

Angle-off axis - degrees

-180 -90 +90 +180


Subreflector spillover region

Main reflector spillover region

Main beam

sidelobe envelope

1st sidelobe

180 90

Ideal Radiation Pattern Physically Realizable Approximation

Pattern Characteristics due to Spillover

Ideal Pattern

Actual

Pattern Characteristics due to Subreflector Blockage

Ideal Pattern

Actual Pattern

"sabretooth" sidelobes may occurdue to severe reflector panel damage

Pattern Characteristics due to Reflector Deformations or Disturbances

r1

1

= peak to peak deviation

Surface error "rms" = standard deviation of all s in the aperture.

1 and r1 can be correllated

Reflector

Figure 2.5-1 Mechanisms that affect the sidelobe characteristics of antenna patterns



71

0 18090

[f ]


Ideal Pattern

Actual Pattern

0 18090

Ideal Pattern

Actual Pattern

45o plane

Elevation plane

Azimuth plane

Off-axis scatter due to subreflector support strutsto be expected near 45 deg plane patterns

Pattern as seen in 45o plane of subreflector support strut

Typical subreflector support structure

[g]

Angle off-axis

[h]

Figure 2.5-1 cont. Mechanisms that affect the sidelobe characteristics of antenna patterns The quality of an antenna is expressed by two main features:

Cross-polarization discrimination or isolation. The largest contributor to cross-polarization is the feed. Details will be discussed later in Chapter 4.

Sidelobe Envelope



72

Sidelobe envelope specifications are set by various regulatory agencies. The angular spacing of satellites in the geostationary orbital arc, and in other orbital positions is 2o or less, which is small when compared with the angular extent of the main beam and first few sidelobes. There are basically two sidelobe envelope specifications with required compliance for earth station antennas in the transmit (uplink) mode. These are shown in Figure 2.5-2

0 1809048

-10dbi32-25log(t) dbi

29-25log(t) dbi

1 20 26 0 1809048


[ j ]

29-25log(t) dbi

1 20 26


7 9

[ i ]Angle off-axis

ITU 580 Specification FCC specification

+8dbi

-3dbi

Figure 2.5-2 Some noteworthy features of reflector sidelobe patterns Some noteworthy features of the resultant performance of the parabolic reflector/feed assembly are easily calculated: 1. Ideal lossless gain for a circular aperture is given by (2.1.4)

2

D

GGain o

Actual Gain is

efficiencyGG os

where efficiency = η = η illumination · η spillover · η blockage · η reflector surface errors · η feed loss 2. Beamwidth characteristics are given by the following good approximations. Using Figure 2.5-3 for reference:

Ddb

703

3. Based on the observation that the main beam has a nearly parabolic shape, beam width at any other

level - dbP10 and

dbnP - is given by

DP

Pdb

db

db

120~3

10310

db

dbn

nP

P

3

3 (2.5.1)

4. Off-axis angle to the null between main beam and 1st sidelobe ~ D

80

5. Off-axis angle to the peak of the 1st sidelobe ~ D

105



73

0db

3db = P3

10db = P10

Pndb

First sidelobe

3

10

n

mb

SL peak

0o

3 = 70λ/D

10 = 120λ/D

n = Pndb/P3

db

mb = 105λ/D

SL peak = 80λ/D

Re

lativ

e P

ow

er

- db

Figure 2.5-3 Antenna pattern main beam features and useful relationships 2.5.1 Concept of Antenna Pattern Gain In Section 2.1.3, we discovered the concept of gain as related to an isotropic, or spherical radiation pattern. In spherical coordinates, the surface integral around a unit sphere is

4)(sin4)(sin0

2/

0

2

0

2/

2/

dddd

where θ represents off axis pattern angles in the principal plane, and represents the angle of the pattern

cut from a reference principal plane around the antenna axis plane. For any other pattern, if we integrate the surface of the pattern, and include all the sidelobes in the angular ranges shown in the expression above, then an expression for gain of the antenna under consideration, compared to an isotropic source is

ddP

GGain pattern

)(sin)(

4

0

2/

0

(2.5.2)

where P represents the relative power pattern as a function of angle in a principal azimuth plane,

and represents the polarization angle of the pattern cut through the antenna axis. See Figure 2.5-4.

Isotropic patternP() = 1

Antenna pattern with gain

Elevation plane

Azimuth plane

Figure 2.5-4 Three dimensional pattern representation in two orthogonal planes



74

Note: This routine assumes axial symmetry in the pattern. For asymmetrical patterns, several patterns in different planes will need to be considered in the integration, and the end result averaged.

For example, in axi-symmetric antennas, the antenna patterns are usually circularly symmetric. Therefore integration of azimuth and elevation pattern cuts is sufficiently accurate. For antennas displaying markedly different patterns in elevation and azimuth, then the = ±45o planes and possibly = ± 22o and ± 67o

plane patterns will need to be recorded to maintain accuracy. As we have seen, for any antenna, the main beam is easily identified and measured in terms of beamwidth. In particular, if we consider the pattern shown in Figure 2.5-5, the dotted circular cylinder pattern nominally has the same gain as the solid line pattern.

3db

0db

or angle off-axis0 deg Figure 2.5-5

33

3

KG pattern (2.5.3)

As the beamwidth gets smaller, gain becomes larger, consistent with increasing aperture diameter. This of course suggests an easy method to determine antenna gain, providing K3 is determined with sufficient accuracy. The EIA-411 standard cites a value for K3 to be approximately 31,000. This was determined by integrating many antenna patterns submitted by a number of antenna manufacturers with an estimated accuracy of about ± 0.35db, and forming the product

333 patternGK

As it turned out, for axially symmetric Cassegrain type antennas, K3 = 31,000 when 3db beamwidths were measured, and as a backup measurement, K10 = 91,000 when 10db beamwidths were measured. The use of this formula is predicated upon knowledge of the antenna pattern in as much detail as practically possible - meaning detail about the sidelobe structure everywhere. This formula cannot be accurately and reliably applied for antennas of unknown wide angle patterns, or asymmetrical antenna patterns. It is further restricted to antennas with a sidelobe envelope approximated by the 32-25log(θ) and -10dbi envelope. Some examples are shown in Figure 2.5-6.



75

01809048

-10dbi

32-25log(t) dbi

0db

3db

10db

[a]

0 1809048

-10dbi

32-25log(t) dbi

0db

3db

10db

[b]

0 1809048


0db

3db

10db

[c]

29-25log(t) dbi

1 20 26


1 1

0 1809048


0db

3db

10db

[d]

29-25log(t) dbi

1 20 26


Note: All sidelobe peaks under the envelope

0 1809048


0db

3db

10db

[e]

29-25log(t) dbi

1 20 26


Note:All these gain values must be modified by subtracting feed loss values, as well as the loss associated with reflector errors. Knowing the reflector surface accuracy, reflector losses are given by:

where ε = rms surface accuracy expressed in cm = wavelength expressed in cm

Total gain is then given by

degrees off-axis degrees off-axis

000,31

log10~Gain dbi

000,31

log10~Gain dbi

5.0000,31

log10~Gain

dbi

5.0000,31

log10~Gain

dbi

8.0000,31

log10~Gain

dbi

000,37log10

dbdb

db

db Kp

33

lossreflectorlossfeedlog10Gain

24

log10

edbp

Figure 2.5-6 Antenna gain variation with different sidelobe envelopes In practice, the beamwidth constants are dependent on whether the reflector is “blocked” as in axi-symmetric 2-reflector systems, or “unblocked” as in offset antennas and axi-symmetric antennas with small sized feeds which represent negligible blockage.



76

Table 2.5-1 Antenna beamwidth constants for various antenna configurations Antenna Configuration Beamwidth Constant A. ▪ Axi-symmetric Prime Focus with large

feed blockage ▪ 2 (or more) reflector assemblies with

blocked aperture, e.g. Cassegrain, Gregorian

▪ Other forms of significant blockage

3K = 31,000; 10K = 91,000

B. ▪ Prime Focus with small feed

▪ Offset reflector assemblies with clear apertures

3K = 37,000; 10K = 107,000

Furthermore, in practice, ),( 33 and ),( 1010 are both measured and the values are averaged, in part to

minimize measurement errors, and in part to take into account any real pattern asymmetries.

1010

10

33

3

2

1

KK

G pattern (2.5.4)

Note: All these gain values must be modified by feed loss values, as well as the on-axis gain loss associated with reflector errors. Knowing the reflector surface accuracy, reflector losses are given by

24

log10

ep (2.5.5)

where = rms surface accuracy

= wavelength Now the total gain of the antenna being tested is given by

dbp

dbdbipatternG lossreflectorlossfeedGaindbi log10 (2.5.6)

In the extreme, consider the antenna pattern with all sidelobes suppressed as shown here. Such a pattern has never been achieved, but some pretty good approximations have been made and measured. The inference here is that the efficiency has increased, since now the energy that had been associated with the sidelobes must now reside in the main lobe. This will be synonymous with more gain. Higher gain means a greater "degree of bundling," therefore a more narrow beamwidth. As we found in (2.1.5), the optimum half-power beamwidth for a 100% efficient antenna will be given by

DD

65.64/

96.412523

If the half-power beamwidth θ3 associated with a real antenna is measured, then a good estimate of the antenna pattern (or illumination) efficiency can be derived from the ratio (θ3*/ θ3)

2. "Pattern efficiency" means only contributions related to illumination (phase and amplitude), spill-over, diffraction, and blockage. External effects of reflector errors, feed system insertion loss, VSWR, and internal coupling coefficients are not included. For example, for a well-designed 2-reflector system,



77

D

703 , and

2

3

*3

(θ3*/ θ3)2 = (64.65/70.0)2 = 0.85 (or 85% efficiency) which corresponds to

0.71db pattern efficiency. Considering now a feed insertion loss = 0.3db, VSWR (1.2:1) = 0.04db, reflector errors = 0.2db, the total antenna efficiency becomes 1.25db or 75%, which is a reasonable value to expect. Most good antenna designs display 65% to 75% efficiency, the spread depending on the frequency and complexity of the feed system. The relationship in (2.5.3) must be used with great care and understanding as to the real performance features of the antenna under consideration. More on this in Chapter 9. References: [1] A. W. Love "Reflector Antennas" IEEE Press Selected Reprint Series 1978 [2] Christophe Granet "Designing Axially Symmetric Cassegrain or Gregorian Dual-Reflector Antennas from Combinations of Prescribed Geometric Parameters" IEEE Antennas and Propagation Magazine, vol 40, No.2, April 1998. [3] Christophe Granet "Designing axially symmetric Cassegrain or Gregorian dual-reflector antennas from combinations of prescribed geometric parameters - Part 2: Minimum blockage condition while taking into account the phase center of the feed" IEEE Antennas and Propagation Magazine, Vol 40, No.3, June 1998. [4] William F. Williams “High efficiency Antenna Reflector”, Microwave Journal, vol 8, pp. 79-82, July 1965. [5] Victor Galindo “Design of reflector antennas with arbitrary phase and amplitude distributions”, IEEE Trans Antennas and Propagation, vol AP-12, pp 403-408, July 1964. [6] Christophe Granet "A simple procedure for the design of classical displaced-axis dual reflector antennas using a set of geometric parameters" IEEE Antennas and Propagation Magazine, Vol 41, No.6, December 1999. [7] Christophe Granet "Designing classical Dragonian offset dual-reflector antennas from combinations of prescribed geometric parameters" IEEE Antennas and Propagation Magazine, Vol 43, No.6, December 2001. [8] Christophe Granet "Designing classical offset inverse-Cassegrain dual reflector antennas from combinations of prescribed geometric parameters" IEEE Antennas and Propagation Magazine, Vol 45, No.3, June 2003. [9] Christophe Granet "Designing classical offset Cassegrain or Gregorian dual-reflector antennas from combinations of prescribed geometric parameters - Part 2: Feed horn blockage conditions" IEEE Antennas and Propagation Magazine , Vol 45, No.6, December 2003. [10] Mizugutch, Y., Akagawa, M., and Yokoi, H., “Offset dual reflector antenna” IEEE AP-S Session 1 Proceedings 1976 pg 2 - 5



78

Figure 2.5-7 A variety of antennas on display at the Yamaguchi Earth Station in Japan Left to right - two 32m beam-waveguide, 7m Cassegrain, (in the foreground) 2m Hogg horn.

Chapter 3 – Feed Horn Design


79

Chapter 3 - Feed Horn Design 3.1 Feed Horn Design Considerations 3.2 Phase Fronts and Phase Errors 3.3 Pyramidal and Conical Horn 3.4 The Diagonal Horn 3.5 Smooth-walled Multimode Horn 3.6 The Corrugated Horn 3.7 Multi-frequency Corrugated Horn 3.8 The Finned Horn 3.9 The Quad-ridge Horn 3.10 Small Aperture Horn 3.10.1 Introduction 3.10.2 Prime Focus Horn 3.10.3 Cavity-backed Dipole 3.11 Concentric Aperture Horn 3.12 Rudimentary Design Considerations for a Feed Horn 3.1 Feed Horn Design Considerations Transmission lines are used to bring the signal from the transmitter to the antenna, and/or from the antenna to the receiver. The problem of extracting the signal from the transmission line to illuminate the reflector in an efficient manner will be considered here. Coaxial lines are limited in power handling at microwave frequencies. Section 2 alluded to the relatively poor illumination efficiency associated with a coaxially fed dipole as a feed for a reflector aperture. Dominant or first mode rectangular and circular waveguides are the most important approach for this purpose. Let us concentrate on some features of feed horn design as shown in Figure 3.1-1.

Feed requirements for reflector illumination Waveguide modes Patterns associated with waveguide modes



80

Concept of pattern polarization planes

F2F1

H-plane

E-p

lan

e

TE10 - rectangular guideField distribution in rectangular waveguide

TE11 circular guideFundamental or lowest mode

(a)

H-plane pattern

E-plane pattern

E

H

H-plane

E-p

lane

H-plane

E-p

lane

45o plane

(b)

(c)(d)

Reflector illumination considerations Waveguide modes

Patterns associated with waveguide modes Concept of polarization planes

Figure 3.1-1 Requirements for a feed system in a reflector system Since most antenna systems possess dimensional symmetry, and, as we will see later, dual polarization requirements, square or circular feed apertures are particularly important. Let us examine the properties of square and circular waveguides as radiating structures. Figure 3.1-2 shows the waveguide modes and corresponding radiation patterns for square and circular waveguide apertures. Notice that E-plane patterns of single mode apertures all have relatively high sidelobe patterns. An undesirable feature of open ended waveguide apertures is that the sudden end into free-space causes a large reflection to be generated. In order to reduce this reflection, some matching mechanism must be implemented such as a corrugated flange, or a flare to a larger aperture. The larger aperture will prompt a narrowing of the pattern useful for illuminating subreflector elements of a larger reflector system.[2].



81

15db

0db

E

H45o

TE11 - mode

H-plane

E-p

lane

No cross-pol in E and H "principal" planes

EH

Cross-pol in

45o plane

E, H - circular symmetry

No cross-pol

E(vertical pol), H(horizontal pol)

No cross-pol

E-p

lane

H-plane

45o plane

E-p

lane

H-plane

45o

TM11 - mode

TE01 - mode

TE21 - mode

E

H

45o plane

H-plane

E-p

lane

E, H - circular symmetry

No cross-pol

(a)

(b)

(c)

(d)

(e)

TM01 - mode

TE10

TE20

TM11

TE30

15db

0db

E

H

EH

EH

E

H

(a)

(c)

(d)

Rel

ativ

e P

ower

- d

bR

elat

ive

Pow

er -

db

Rel

ativ

e P

ower

- d

bR

elat

ive

Pow

er -

db

Angle Off-axis

Angle Off-axis

Angle Off-axis

Angle Off-axis

Rel

ativ

e P

ower

- d

bR

elat

ive

Pow

er -

db

Rel

ativ

e P

ower

- d

bR

elat

ive

Pow

er -

db45o plane

H-plane

E-p

lane

H

E

(b)

No cross-pol

Cross-pol in

45o plane

No cross-pol in E and H "principal" planes

Angle Off-axis

Angle Off-axis

Angle Off-axis

Angle Off-axis

Cross-pol in 45 deg plane

Cross-pol in

45o plane

TE12

(e)

E

Rel

ativ

e P

ower

- d

b

Angle Off-axisNo cross-pol

Cross-pol in

45o plane

Figure 3.1-2 Waveguide modes and associated pattern forms Question: How to reduce these sidelobes, and achieve circular symmetry to illuminate a circular reflector system with the greatest efficiency ?? Answer: Use a method of combining several modes with appropriate phase and amplitude.



82

TE10 TM11 TE10+TE11+ TM11

Curvature of field lines reduced, and cross-pol pattern reduced.

E

H

Cross-pol

TE11 - mode TM11 - mode

+ =

TE11 + TM11

+ =

H

E

Pattern for the dual mode horn aperture

Angle Off-axis

Rel

ativ

e P

ower

- d

b

TE12

+

Figure 3.1-3 TE11 and TM11 modes to gain beam symmetry and consequent reduction of cross polarization components Section 3.3 and 3.4 discuss various methods of accomplishing this. 3.2 Phase Fronts and Phase Errors One aspect of these horn transformers – from w/g to free space – not discussed yet, is the fact that the wave launched into free space nominally appears to emanate from the point represented by the apex of the cone of the horn.

Equi-phase wavefrontsWaveguide

Fh

P P1 P2 P3 P4

Part of wave still inside the horn

Wavefronts with equal radius from the focus Fh

represent surfaces of equal phase with respect to the reference phase of point P on the axis.

Figure 3.2-1 The progression of spherical wavefronts emanating from the nominal vertex of the horn. But the wave at the center of the horn will leave the horn aperture before the same front has left the edge of the horn. Since the wave travels more quickly in free space than in the confines of the horn cone, the radius of curvature will appear to be smaller, forcing the “phase center” of the horn closer to the aperture. Therefore,



83

the point Fh – “focus” or “phase center” – does not occur at the apex of the horn. This results in a slightly distorted wavefront expressed by phase error = p as shown in Figure 3.2-3. The distortion becomes less prominent as the flare angle approaches 90o. The proper location of the horn requires Fh to be coincident with the reflector system focus. Therefore it is important to determine where Fh is with respect to the aperture plane.

F1

Pe

Distortion = Po

Pe~ 1.5

Small flare horn

Non-spherical shape representative of phase error

Po

Distortion = Po

Pe~ 1.2

Fh

F1

Pe

Po

Large flare horn

Fh and F1

Po

Pe~ 1.0Distortion =

Open ended waveguide 90o corrugated horn

Fh

P

P = aperture phase error

Figure 3.2-2 Behaviour of the wavefront as it leaves the horn aperture for horns with different horn flare angles. P is defined as the difference between the on-axis phase and the phase measured off-axis, in particular that measured at the reflector look-angle. The distortion values give an idea of the change in propagation velocity between in and out of the horn. Note also that in the case of the 90o corrugated horn/flange, the axi-symmetric pattern in this case provides for small off-axis phase errors. Just as the amplitude pattern of a horn can be recorded, the behaviour of the phase can be recorded in a similar fashion. However, if the phase error at the reflector edge is <60o, then reduction in gain is a tolerable 0 to 0.25 db. Larger phase errors lead to significant inefficiencies in reflector illumination, and therefore lower gain. For a wide bandwidth application, the horn must be located in the reflector geometry so that the phase centers for low and high frequencies lie on either side of the reflector system primary focus – as a best compromise. Choosing this condition, the phase pattern of the horn illuminating the reflector system will be as shown in Figure 3.2-3.

Amplitude - db

Ideal

Reflector Aperture

Ideal

15db to 20db typical

Fhi Flo

Fhi

Flo Ideal 0o

phase pattern

-ve phase error

+ve phase error

Phase - degrees

Feed patterns

Reflector Aperture

0o

Amplitude pattern for low and high frequencies Phase error patterns for low and high frequencies, taken around the chosen phase center of the feed horn

Figure 3.2-3 Phase and amplitude patterns for low and high frequencies around a fixed phase center



84

As the flare angle → 0, the horn approaches open w/g conditions. If the amplitude pattern of the horn is axially symmetric, then the location of F1 is fixed at one frequency. However, as frequency increases, F1 will shift axially toward the apex. The smaller the flare angle, the larger the phase center shift. This leads to the condition for multi-frequency horns as shown in Figure 3.2-4.

fH fL

1

fH fL

2

[a] [b]

Figure 3.2-4 Shift in the effective focus (phase center) of the horn with change in frequency If this horn is used in a Cassegrain reflector system, we notice that a measure of defocusing between frequency bands will occur. In order to keep the phase center variation not too far out of the bounds indicated by the subreflector shaping -F2 – the horn is shaped as shown in Figure 3.2-4(b). This will reduce phase errors in the illumination of the subreflector. 3.3 Pyramidal and Conical Horn The pyramidal horn refers to a horn with a square aperture, fed by a square waveguide. The conical horn possesses a circular aperture, fed by a square or circular waveguide. The general idea of the horn is to be able to direct all of the fields from the waveguide to a reflector, and not have any of them miss the reflector. The fields must all appear to be emerging from a point represented by a focus of the reflector. What geometry or physical shape is required for the horn to do this ?? The simplest approach is to flare the waveguide to the horn aperture. But how long, and to what aperture size ?? The answers to these questions were determined empirically in the 1930s, and then analytically substantiated later. In summary, it all depends on the application. For our purposes, there are essentially three fundamental cases: 1. Cassegrain/Gregorian reflector systems requiring a feed look-angle toward the subreflector ranging from 15 to 25 degrees. This corresponds to a feed horn pattern gain ~ 23 to 18dbi. 2. Prime focus (single reflector systems) requiring a feed look angle toward the paraboloid ranging from 60 to 80 degrees. This corresponds to a feed horn pattern gain ~ 11 to 8.5 dbi. 3. For beam-waveguide applications (see Section 7.3) requiring a 5 to 8 deg look-angle. This corresponds to a feed horn pattern gain ~ 32 to 28dbi. The term "look-angle" refers to the optical view from the feed axis toward the reflector edge. Since the horn pattern is not uniformly equal in amplitude across the look-angle, there will be an optimum amplitude taper for best illumination of the reflector. "Best illumination" refers to highest directivity for the pattern radiated from the reflector. As discussed in Section 3.2, there is also the matter of phase error across the beam radiated from the horn. As the horn pattern amplitude decreases toward the null and the first sidelobe, the phase will change from 0 deg to 180 deg (meaning the first sidelobe is out of phase with respect to the on-axis main beam maximum). If the phase error of the horn pattern captured by the reflector is less than about 45 deg, the affect on directivity will be small. Larger phase error will rapidly cause the directivity to decrease even further - this because the illumination at the reflector edge is now effectively defocussed.



85

The investigative work by Barrow and King (presented in [1]) showed that as the horn length was increased, the aperture size became larger and as a consequence, the gain increases. On the other hand, as the flare angle increased, the beam width of the main beam became smaller, but with continuing increase, the beam became wider. See Figure 3.3-1.

Constant horn length

Dh

Dh

dDhL L

L

0db

Re

lativ

e p

ow

er

- d

b

10db

10db beamwidth

20db

10db beamwidth 10db beamwidth

Constant flare angle

d

Dh

0db

(a) (b) Figure 3.3-1 A brief summary of the behaviour of the pyramidal horn as reported in [1]. The conical horn behaves in a similar manner. (a) shows the variable beamwidth of the horn as the flare angle is increased while maintaining the radial length of the horn constant. (b) shows a gradual decrease in beamwidth as the aperture of the horn increases with increasing radial length. This suggests that for an optimized gain, there is one particular horn geometry. Optimized gain means 3db beamwidths in both E and H-planes are nearly equal. However, sidelobes in both planes will not be equal. The one thing that remained unexplained until the paper by Hamid (presented in [1]) - why did the gain decrease so rapidly after the horn aperture diameter was increased beyond the optimum gain point ?? As the horn aperture becomes larger, the edge currents at the mouth of the horn have adequate length to set up an array of current loops, the sum total of which can now generate a new pattern. The new pattern will add to the aperture pattern as well as contribute sidelobes into unwanted directions. The result is a pattern that has a wider main beam, and higher sidelobes. Therefore, as the size of the horn increases, the gain will increase to the point where the aperture edge currents start to become dominant, and the gain rapidly starts to decrease. These edge currents can also lead to asymmetrical patterns. See Figure 3.3-2.

Figure 3.3-2 The progression of pattern deterioration as the size of the horn increases beyond the "optimum" design. The disparity between E and H-plane patterns of these "simple" horns was for many years the subject of much investigation. The objective was to reduce the influence of the edge currents with the use of higher order modes, multiple apertures, modified aperture and edge geometries, and variable horn flare angles. See Figure 3.3-3. But all these efforts were expensive, and of limited bandwidth.



86

Tapered flare flange Simple grooved flange Corrugated flange

Finned aperture9 horn feedSide horns with patterns when added to the aperture, convert aperture into a multimode radiator with sidelobe reduction effects.

Figure 3.3-3 Several approaches to multimode horn designs that have been attempted in the effort to suppress sidelobes and generate equal beam width patterns for feed system applications. In particular, the 9-horn feed was designed by Hughes Aircraft Co. in 1971 to optimize large antenna performance. At the time, Intelsat presented the formidable problem of accommodating 4 and 6 GHz bands - namely 3.7-4.2 and 5.925-6.425 GHz into the feed horn, a bandwidth of 1.74:1 or 56%, far beyond the capabilities of the unembellished pyramidal or conical horn. It was only the addition of higher order modes that permitted good sidelobe suppression and axi-symmetric horn patterns in the 4 and 6 GHz bands. At 5 GHz however, the horn patterns were badly disrupted with the presence of unacceptable sidelobes and asymmetries. Evaluation of feed horn patterns To determine how useful a particular horn design is to illuminate a reflector, two parameters are measured - amplitude and phase patterns. Horn patterns generally show a main beam and a series of sidelobes of lower amplitude. The main beam will also show a small phase variation (either decreasing or increasing with angle) across the beam peak until the first sidelobe is reached, whereupon the phase will change from nominal positive to negative. The objective of the horn design is to ensure that just the main beam illuminates the reflector. Significant sidelobe power not captured by the reflector represents loss of efficiency. Significant variation in phase across the main beam represents a form of defocussing of the feed/reflector system, and therefore represents an inefficiency in illumination. Spillover efficiency For the useful application of a horn design to illuminate a reflector, it becomes important to appreciate how the presence of sidelobes in the horn pattern can be quite detrimental to antenna system gain. The inset to Figure 3.3-4 shows two horn patterns, one with 14db first sidelobe, the second with 22db sidelobes. Are these acceptable feed patterns to efficiently illuminate a reflector ?? The spillover efficiency relationship is defined as

90

0

0

sin)(

sin)(

P

Pefficiencyoverspill

e

s (3.3.1)

where )(P feed horn power pattern as a function of angle off-axis

and e look angle from the feed phase center to the reflector edge



87

A very good view of the real effect of sidelobes in feed patterns can be seen graphically in Figure 3.3-4. The horn pattern )(P is replotted into a new coordinate system with the relative power scale modified by

the sin function. The area B under the curve represents that part of the power e

P

0

sin)(

captured by the reflector. The area (A + B) under the curve of this converted pattern represents the total

radiated power 90

0

sin)( P . The ratio of B to (A + B) represents the spillover efficiency.

Note: the angular range for can be set to that smallest value which most nearly represents the total power radiated by the feed aperture. may be 0< < 90. The assumption is that the feed pattern is axi-symmetric.

Psin(t) vs Angle (t)

0

0.01

0.02

0.03

0.04

0.05

0.06

0.07

0.08

0.09

0.1

0 5 10 15 20 25 30 35 40 45

Angle (t) - deg

0 db

1 db

2db

3db

4 db

5 db

6 db

7 db

8 db

9 db

10 db

11 db

12 db

13 db

14 db

15 db

16 db

17 db

18 db

19 db

20 db

21 db

Horn patterns

0

5

10

15

20

25

30

35

40

0 10 20 30 40Angle - deg

Rel

ativ

e Po

wer

- db

Ed

ge

of

Re

flect

or

Area "B"Captured by reflector

Area "A" Missing the reflector

Figure 3.3-4 The graphical view of a feed pattern and the graphical interpretation for spillover efficiency. The inset shows a pattern with 14db first sidelobe. The pattern is also shown replotted into a sin coordinate system as indicated by equation (3.3.1), showing the relative power content of the sidelobe to be approximately 50% which is missing the reflector as spillover. For comparison, the pattern with 22db sidelobe represents only about 5% lost power. The point to notice here is the magnitude of the sidelobe energy that can significantly reduce the overall efficiency. A horn pattern with 14db first sidelobe will mean about 50% spillover efficiency. A 22db first sidelobe will offer about 90% spillover overall efficiency. Aperture efficiency Aperture illumination efficiency can be determined with the same technique, using the expression

e

e

r

a

P

E

efficiencyaperture

0

2

0

sin)(

sin),(

(3.3.2)

where 222 )](sin)([)](cos)([),( EEEr (3.3.3)

and )(E the pattern voltage at angle , and )( phase of the pattern at angle

Aperture efficiency is calculated for the range = 0 to the reflector edge e .



88

The level at which the horn pattern intercepts the reflector edge is called "edge taper". The smaller the level here, the greater the "edge taper". The greater the edge taper, the lower the aperture efficiency. Typically, for an edge taper of 15db, aperture efficiency is 90%; an edge taper = 20db offers an aperture efficiency of about 85%; 25db gives about 80%. High edge taper implies an under-illumination of the reflector, meaning that in effect the reflector is smaller than the physical dimensions would suggest. This means a loss in gain. As a natural consequence, coupled with a higher edge taper is a greater variation in phase across the illuminated aperture. A 15db edge taper will possess a phase variation of only about 10 deg. A 25db edge taper may show a phase variation >80 deg. This would suggest a slightly defocused under-illuminated reflector. Further, in Figure 3.3-1, the patterns are not axi-symmetric. That means the reflector is not symmetrically illuminated, introducing yet another element of inefficiency. General requirements for a feed system Basic requirements for a feed system to satisfactorily illuminate a reflector - either a subreflector in a multi-reflector system, or as a prime focus feed 1. Feed pattern must have no or only very low sidelobes (25 to 30db or lower below main beam peak level) 2. Beam symmetry 3. Small phase variation (less than +/- 30 deg) across the main beam 4. Best cross-pol discrimination both on- and off-axis (>30 to 35 db or greater). It was the invention of the corrugated horn that finally solved the illumination and spillover efficiency problem (to be discussed in Section 3.4). The corrugated horn offered practically no sidelobes, axi-symmetric patterns with the consequent reduction in cross-pol, and a practically 2:1 bandwidth. An important comparison between the various horn solutions is shown in Figure 3.3-5.

0

10

20

30

40

50

E

E

H

H

Basic shape of the E and H-plane patterns forTE11 conical horn TE10 pyramidal horn.

Note: * High E-plane sidelobes, and asymmetric main beam* 1.5:1 bandwidth with variable sidelobe and beamwidthfeatures

Basic shape of the E and H-plane patterns formultimode horn design, as exemplified by TE11 + TM 11 apertures.

Note:* Nearly equal main beam widths, and lower sidelobes* Practically 2:1 bandwidth, but only in narrow band segments* Efficiency can be greater than that of corrugated horn

Basic shape of E and H plane patterns for the corrugated and finned horn. Horn dimensionscan be tailored to suit specific requirements.Note: * Filled sidelobe envelope skirts and equal beamwidths* Continuous practically 2:1 band width and higher multi-frequenecy functions

Re

lativ

e P

ow

er

- db

Reflector capture angle Reflector capture angle Reflector capture angle

Edge taper= 15db

Spillover

Edge taper= 12db

Edge taper = 18db

Spillover

Spillover

Angle - deg Angle - deg Angle - deg

H

E

Figure 3.3-5 A comparison of basic E and H-plane pattern shapes for (a) the conical and pyramidal horn, (b) the multimode horn, and (c) the corrugated and finned horn.



89

3.4 The Diagonal Horn The conventional square pyramidal smooth-walled horn will, when excited by rectangular waveguide, have a field distribution in the aperture as shown in Figure 3.4-1(a). The radiated pattern of this horn will be as seen in Figure 3.4-1(b). Note the variable beamwidth between the E, 45, and H-planes, the high sidelobes in the E-plane, and the high level of cross-pol.

10

20

30

(b)

Rel

taiv

eP

ower

- d

b

0db

y H-plane

xE

-pla

ne

z

(a)Pyramidal Horn

d

d

E-planeH-plane

Xpol 45o plane

b

a

Figure 3.4-1 The square aperture pyramidal horn (a) and its asymmetrical pattern with high E-plane sidelobes However, if the horn excitation is rotated into the 45-deg plane as in Figure 3.4-2(a), the field lines are transformed into the addition of two orthogonal components. The pattern associated with this distribution is now as seen Figure 3.4-2(b). Here, the E and H-plane pattern beamwidths are practically equal, and the first sidelobe is significantly lower. The net result is that within the main beam, the cross-pol pattern will be lower. However, note also that in the 45o plane, the cross-pol will be quite high, but it is high in a region which is essentially outside of the main beam used to illuminate a reflector system. The excitation of the diagonal horn is accomplished with the twisted field from a square or round waveguide as shown in Figure 3.4-2(a).

x

y

z

10

20

30

(a)

H-plane

E-p

lane

Rel

taiv

e P

ower

- d

b

0db

Diagonal Horn d

d

b

a

(b)

E-planeH-plane

Xpol 45o plane

10

20

30

Rel

taiv

e P

ower

- d

b

0db

E-planeH-plane

Xpol 45o plane

Diagonal horn pattern

Figure 3.4-2 (a) The diagonal horn and (b) its associated pattern. The nearly equal E and H plane patterns show good symmetry, and therefore low on-axis cross-pol. Off-axis cross-pol is high because of curved field lines close to the axis



90

A cautionary note: The diagonal horn looks simple, but fraught with manufacturing difficulties. In contrast with the corrugated horn, the diagonal horn cannot be machined. If relatively small, it can be electroformed; but if dimensionally large, only assembled from parts. The assembly of flat sheets means that there are discontinuities in the current flow in the joints, typically the corners of the horn, leading to the generation of new unwanted modes that will cause cross-pol, and if large, even upset the basic co-polar pattern. If solidifying the gaps with solder, thermal issues will upset the symmetry (flatness) of the horn walls. To escape these difficulties, the horn must be soldered or brazed in an oven to ensure thermal uniformity in the assembly, with a minimum of mechanical distortion. Historically, this horn design was first reported by Tingye Li in 1959, and examined by Alan Love[1] in 1962. Since then, the design has been used extensively, in particular in large low frequency antennas, in which the use of corrugated horns becomes prohibitive because of dimensional size and weight issues. 3.5 Smooth-walled Multimode Horn The idea of combining various modes to reduce cross-pol and sidelobes in the horn pattern has been mentioned in Chapter 1. Example 1: Combining TE10, TE11 and TM11 modes in square waveguide aperture. See Figure 3.1-3. The phase and amplitude of these two modes must be accurately matched in order for this pattern to result. This makes the horn design length dependent, since phase is accomplished with control of path length. Remember, guide wavelengths of TE10 and TE11 and TM11 modes are different.

Example 2: Similarly for circular waveguide, the TE11 and TM11 modes can be added. The straightened field lines in the aperture indicates the fields are "self-supporting," and currents in the wall are "reactive." Further, cross-polarized components are reduced to a minimum. Since the field structure is practically the same for E and H planes, the pattern beamwidth will be circularly symmetric. Nominally, this will only be true for a limited bandwidth; however if the horn length is chosen carefully, then several discrete bands can be found at which this zero cross-pol condition can be made to exist. For example: for the satellite C-band 4 GHz band (3.625 - 4.200) = 14% bandwidth 6 GHz band (5.85-6.425) = 9% bandwidth Figure 3.5-1 shows the progression of 4 and 6 GHz waves along the length of the horn. If the bandwidth is over-extended, then the mode phasing at the aperture breaks down, and the pattern loses symmetry.



91

Multimode Horn

TM11TE11

TM11

TE11

6 GHz

4 GHz

Figure 3.5-1 Multimode horn design philosophy for simultaneous 4 and 6 GHz functions. Multi-modes of this type are set up by controlled discontinuities in the horn throat with multi-flared sections - one to generate TM11 at the appropriate horn section, and a second further into the horn, to match the first. A long flared section follows to ensure the two modes arrive at the aperture in phase. Such a horn design, known as the Potter horn [3], is shown in Figure 3.5-2. The amount of TM11 mode generated depends on the size of the first discontinuity - either a step, or a flared section. The amplitude ratio of TM11 to TE11 modes to obtain a circularly symmetric pattern is approximately 0.15. Adding more modes can offer the mechanism to generate a feed horn pattern with characteristics shown in Figure 3.5-2(c). The result approaches the ideal uniform illumination for the subreflector.

10

20

30

Rel

taiv

e P

ower

- d

b

0db

E-planeH-plane

Xpol 45o plane

10

20

30

Rel

taiv

e P

ower

- db

E-planeH-plane

Xpol 45o plane

TE11 Input

Standard waveguide

TM11 generator

Matching discontinuity

Phasing sectionOptional higher order mode TE30

generator for additional sidelobe control

Horn aperture

(b) (c)

(a)

Figure 3.5-2 (a) Multimode horn design. (b) shows an achievable pattern using just the TM11 generator and the phasing section. (c) Patterns expected from a mutimode horn augmented by additional modes in the outer horn flare to generate the “flat top” main beam



92

3.6 The Corrugated Horn A simplified picture of the corrugated horn and its operation is given in Figure 3.6-1 and its pattern in Figure 3.6-2. Included is a comparison with the pattern of multi-mode (TE11 + TM11) mode horn.

Teeth surfaces support currents for TE11

Troughs support currents for TM11

dt

S

Horn for TM11 mode

Horn for TE11 mode

Field distribution in any section of the horn

Since this condition exists all along the horn, the surface currents in effect maintain modal phase with respect to each other, ensuring pattern integrity across the band of interest. Generally, the corrugatedhorn can achieve a 2:1 frequency bandwidth

HE11 - mode

(a) (b)

(c) Figure 3.6-1 The corrugated horn in its simplest conical form; sectional form (a), field distribution (b); and (c) photo of a machined horn. (Photo used with permission of General Dynamics SATCOM Technologies Inc.) The resulting mode is called HE11 mode, and is, to a large extent, independent of the length of the horn.

Further, only when the corrugation depth approaches /2 will the corrugated horn pattern break down. This

suggests further that the depth 4

nd for ...,5,3,1n will represent frequencies at which the chosen

horn will work.



93

Pattern of HE11

corrugated horn

Fall-off in mainlobe pattern with off-axis angle for the multimode horn, compared with corrugated horn - this can be significant for reflector illumination in Cassegrain applications to reduce subreflector spillover.

Remember: the objective is to achievethe ideal pattern shown here in red.

0o Off-axis Angle - deg

Pattern of TE11+TM11

multimode horn

Figure 3.6-2 Corrugated horn pattern An unusual feature of corrugated horns is that there is a nearly one-for-one correspondence between flare angle and beamwidth for a given aperture size. See Figure 3.6-3.

10db

0db

10db

0db 0db

10db

a A a A a A

Figure 3.6-3 Corrugated horn patterns for various horn flare angles As the flare angle increases, the aperture as defined by "a" becomes more and more prominent in its influence on the pattern. In the extreme, for flare angles reaching 60o or even 90o, "a" becomes the effective aperture size. In this last case, the horn becomes an open-ended waveguide with a corrugated flange. The flat flange design frequently seen in simple horn designs contributes to excessive unwanted sidelobes. The corrugated flange in effect kills the currents which support these unwanted sidelobes, leading to the pattern behaviour seen in Figure 3.6-3.

a A a A a A

Figure 3.6-4 Corrugated horn design features To be noticed in Figure 3.6-4, the mechanical realization of grooves becomes problematical with increasing flare angle, forcing them to become longitudinal rather than radial. The principal difficulties with the corrugated horn are related to the generation of the correct modes. The first few grooves in the horn are critical, to ensure that the modal voltages generated are not reinforced to contribute to the generation of undesirable modes – in particular those that are orthogonally polarized. At the same time, the VSWR of the transition from smooth wall to groove wall must be controlled. All this to



94

say that dimensionally the input to the corrugated horn must be designed carefully. There are several approaches to doing this, see Figure 3.6-5.

a b

g/4o/4

Figure 3.6-5 Corrugated horn groove design for the horn throat Notice that the first few grooves in the throat are deeper than those near the aperture. In the throat of the horn, the guide wavelength is the key dimension; at the aperture, the (smaller) free space wavelength dominates. As indicated earlier in this section, a feature of horns in general is the fact that the phase center or focus moves with respect to the aperture – near the aperture for low frequencies, deeper inside for high frequencies. If the frequency spread is large, then the separation in focal positions can become intolerable. One way of reducing this phenomenon is by profiling the length of the horn, as in Figure 3.6-6.

fH fL

1

fH fL

2

a b

Figure 3.6-6 Corrugated horn flare design 3.7 Multi-frequency Corrugated Horn The design for multifrequency single aperture feeds has relied extensively on the principles of horn design discussed here. Looking at the conical or tapered form of the horn in Figure 3.7-1, we can see that here is a natural frequency filter. Just ahead of the point for the low frequency cutoff, a coupling junction as in an OMT can allow low frequency signals to be coupled out. Similarly, mid and high frequency coupling junctions can be installed sequentially down the length of the horn.

Diameter representing cut-off conditions for low frequency signals

Mid frequency cut-off

high frequency cut-off

highest frequency out

Figure 3.7-1 Corrugated horn and the concept of diplexing multiple frequencies at the throat of the horn



95

Based on the nλ/4 rules for corrugation depths and diagrammed in Figure 3.7-2, only certain frequency bands can be accommodated for a given corrugation design. For example, the 4/6 GHz standard satellite downlink can be accommodated in a corrugated horn with groove depths of about 0.84 inches (which represents λo/4 – where λo equals free-space wavelength). But, if we tried to extend the frequency band to include 7/8 GHz or 3 GHz, the operation of the horn extends into the exclusion zones (1) and (2), in which the HE11 mode, and therefore, the pattern, falls apart. However, looking between zones (2) and (3) the groove structure will support the 11/14 GHz band. In fact, the groove depth must be readjusted slightly to 0.805 inches so that no exclusion zones are penetrated at either end of the C and Ku bands (3600, 14500 MHz). These ideas form the basis for the 4/6 – 11/14 (C/Ku – 8 port) feed design. As a first step in the realization of this design, the receive-only 4/12 GHz system was tried. From the groove – depth graph, to satisfy 3.4 – 4.2 GHz and 10.7 – 12.75 GHz bands, the groove depth needs to be about 1.350 inches. Notice also that the lower end of the Ku band projects slightly into exclusion zone 2. Projections into the high frequency side of exclusion zones are permissible, however, intrusions into exclusion zones from the low frequency side will prompt higher order modes, and the pattern collapses. As can be seen from the groove graph, various interesting frequency band combinations are possible.

Corrugated Horn Groove Depth vs Frequency

0.0

0.2

0.4

0.6

0.8

1.0

1.2

1.4

1.6

1.8

2.0

2.2

2.4

2.6

2.8

3.0

1.5 2.5 3.5 4.5 5.5 6.5 7.5 8.5 9.5 10.5 11.5 12.5 13.5 14.5 15.5 16.5 17.5 18.5 19.5 20.5 21.5

Frequency - GHz

Gro

ove

dept

hs -

inc

hes

Exclusion zone 1

Exclusion zone 2Exclusion zone 3

Exclusion zone 4

Exclusion zone 5

Exclusion zone 6

Figure 3.7-2 To determine the groove depth for a corrugated horn operating 4 and 12 GHz



96

From a tolerance point of view, the manufacture of the standard corrugated horn is quite forgiving. However, when the groove geometry must handle frequency bands separated by a factor 3 or more, manufacturing tolerances can have dramatic cumulative effects – contributing to undesirable modes in long corrugated horns. Typically, two methods present themselves in the fabrication of such horns:

machining of a conical casting or solid billet electroforming onto a machined mandrel

Various forms of corrugation teeth design have been examined. To fabricate the flared bottom of the groove is difficult.

d1

d2

flare angle

flared tooth d1 < d2

flared groove alternate flat toothd e f

Figure 3.7-3 Corrugated horn groove designs For obvious reasons, the corrugated horn has become the accepted horn design for symmetrical illumination requirements, as in circular aperture reflector designs. But, it is not necessarily the optimum – for reasons seen in Figure 3.6-2, the multimode horn has superior reflector illumination features for narrow band applications. The corrugated horn can be designed to have a “flat top” beam to increase the illumination efficiency of the subreflector, similar to that outlined in Figure 3.5-2. And for non-circular reflector requirements, the rectangular or elliptical aperture may be the only choice. For example, for a wide-angle pattern in azimuth and narrow angle beam in elevation, the configuration of Figure 3.7-4 is a possible design approach:

Azimuth

B

a

b

A

Elevation

1. Wide horn aperture in the plane containing the narrow reflector dimension.2. The narrow horn aperture in the plane containing the large reflector dimension

Azimuth (H-plane)

Elevation (E-plane)

0 deg Angle off-axis

Figure 3.7-4 Rectangular reflector characteristics In order to reduce cross-pol components, the rectangular horn could be corrugated in the E-plane, since in the H-plane we already have low sidelobes.



97

3.8 The Finned Horn A corresponding corrugational geometry is that represented by the finned horn, a circumferentially periodic structure shown in Figure 3.8-1. The closely spaced surfaces of the teeth will support the TE11 mode, and the spaces between the teeth will support the TM11 mode. Here the special hybrid mode is designated as the EH11 mode. The horn patterns are very similar in form and bandwidth features as the corrugated horn discussed in Section 3.3. A sample predicted pattern for this horn design is shown in Figure 3.8-2. The groove (or fin) depth must be ¼ < d < ½ wavelength, and fin separation at least 1/5 to 1/10 wavelength, for the horn patterns to show good axial symmetry, with low cross-pol and sidelobes.

Number of teeth = 60; tooth thickness = 1.5mm

600 mm

approx. 35mm dia

250mm dia

9mm

(a)

(b) Figure 3.8-1 (a) Estimated dimensions of the actual finned horn (b) Computational model of the horn The fabrication of this horn is more difficult compared to the corrugated horn, since it is impossible to machine. Electroforming seems to be the method required to achieve the greatest precision. There appear to be no references to this horn design in the literature. This horn was, it is believed, first built by Hughes Aircraft (El Segundo, CA) in the early 70's, and used in a Cassegrain antenna in Australia. The patterns of Figure 3.8-3 were generated from an estimated dimensional check of the finned horn while it was mounted in the antenna.



98

(a) (b)

Figure 3.8-2 Computational results of the finned horn based on a dimensional estimate of the horn in an operational antenna. (a) frequency = 8 GHz; (b) frequency = 16 GHz. By way of comparison, the corrugated horn shown in Figure 3.8-3 shows patterns given in Figure 3.8-4.

Figure 3.8-3 A conical corrugated horn with throat and aperture dimensions identical to that of the finned horn in Figure 3.8-2. Dimensions are inches. Groove depth = 0.35 inches (9mm)

Figure 3.8-4 The 8 and 16 GHz patterns associated with the conical corrugated horn These designs have not been optimized, but the results suggest that the finned horn is equivalent to the more well known corrugated horn, and may even have some redeeming features from the point of view of



99

incorporating longitudinal coupling slots in the horn throat for the purposes of polarization and/or frequency selection. 3.9 The Quad-ridge Horn See also Section 7.1.2

3.10 Small Aperture Horn 3.10.1 Introduction Satellite communications are increasingly featuring high RF power on board the spacecraft, and as a result, a decrease in earth station antenna size. This decrease in antenna size - in the order of about ≤ 50 wavelengths - is bringing with it increasing challenges in antenna design. Demands for high efficiency as well as adherence to regulatory sidelobe envelopes and cross-pol have become very difficult problems to solve. The usual approach is to utilize an offset reflector, to remove the deleterious effects of a blocked aperture. To remove the fundamental cross-pol features of a single offset, a dual offset reflector is required. Coupled with a dual offset is the need for considerable feed horn gain, which now demands a large feed horn, thereby increasing the size of the feed. An alternative design would entail the use of a ring focus reflector configuration, which permits a small feed aperture, but now the subreflector is only in the order of 5 to 7 wavelengths. The difficulties with diffraction can, in large part, be overcome with the use of a phase-matched stepped-ring subreflector design, tailored into a shaped main reflector. The remaining problem is the relatively narrow bandwidth of this configuration. A slightly different approach is to consider a dual mode cavity-backed dipole feed as a prime focus feed for parabolic reflector. The attractive features are: 1. A one-wavelength aperture at the open end of a circular waveguide cavity, excited by a crossed dipole, presents probably the smallest possible blockage. 2. The feed pattern illuminating the reflector is nearly circularly symmetric, and can be matched to about 20dB over >25% bandwidth. This is supported by delivered hardware. 3. The secondary far field pattern can be set for suppressed sidelobe envelope, characteristic of axi-symmetric prime focus antennas.



100

4. The feed can be configured to provide difference patterns, useful for monopulse tracking applications, this being useful for "satcom-on-the-move" applications, in which a very dynamic target satellite tracking performance is required. This is a new feature. 5. Linear or circular polarization configurations are possible with the use of appropriate low-loss coaxial hybrid networks. Typical insertion loss values are in the order of 0.5 to 1 db, depending on the choice of bandwidth and polarization. 6. Computational modeling has shown that two frequency bands can be accommodated by mounting a second smaller cavity-backed dipole operating at a higher frequency, in front of the aperture carrying the lower frequency band. This configuration still remains to be verified. 7. And lastly, the cost, compared to other antenna arrangements, is small. The feed is not held by a quadrupod structure, but rather by a hollow tube mounted in the vertex of the reflector, containing the coaxial dipole feeder lines. 3.10.2 Prime Focus Horn Prime focus horns are specifically tailored to illuminate the parabolic reflector without the aid of a secondary reflector system. The distinguishing mark of the prime focus horn is a small aperture. Small apertures mean small gain and large illumination angle as typically is required to satisfactorily illuminate the paraboloid from the focus. The small aperture now also precludes the use of long corrugated horns to generate symmetrical low cross-pol patterns. Rather the small flared corrugated horn with corrugated flange may be allowed for F/D > 0.4. For smaller F/D ratios, the waveguide aperture with corrugated flange will applicable. The difficulty with using just an open waveguide is that the open end cannot be adequately flared in order to match the aperture to free space. If there is a flange around the aperture (mostly for the purposes of mounting a weather protecting cover), the flange will carry large surface currents from the aperture to the flange edge, and even around the back of the flange onto the body of the waveguide. These surface currents will radiate, thereby contributing to the aperture pattern in an undesirable fashion. Unexpected sidelobes and cross-pol lobes will appear at off-axis angles, leading to unwanted spillover and loss in gain. If the aperture has no flange, then strong surface currents will be excited around the edge of the aperture that will radiate as a line current. At the same time, a surface current will travel back along the waveguide surface, to radiate as a secondary aperture. Spillover pattern lobes will be contributed to the pattern. However, there are several possible approaches to be considered.

A circular waveguide aperture with a large corrugated flange to suppress the surface currents around the aperture and reduce the cross-pol pattern components. See Figure 3.10-1(a). This is commonly called a "scalar" horn. The corrugations here will provide support for small levels of TM11 mode that will contribute to the suppression of cross-pol components in the aperture. Bandwidth will however be somewhat limited to about 1.5:1

A circular waveguide aperture with no flange, but just a series of corrugations along the outside surface of the waveguide. Figure 3.10-1(b).

(a) (b) Figure 3.10-1 Circular waveguide horn with corrugated flange



101

This type of horn possesses a phase center near the aperture which needs to be placed in the focus of the paraboloid, generally accomplished with a quadrupod. The connections to this horn configuration will need to be laid along the quad legs to the hub. 3.10.3 Cavity-backed Dipole Yet another design approach utilizes a cavity-backed dipole. This is a design that was born by the idea that the dipole effectively radiates uniformly around the dipole axis. Placing a reflective plate ¼ wavelength in front of the dipole will cause much of the pattern to be reflected backwards. Placing this device in the focus of a parabolic reflector results in an inexpensive antenna. See Figure 3.10-2.

1/4

Dipole placed 1/4 wavelength in front of small flat reflector plate

Image of dipole in reflector

Flat reflector plate

Dipole

Coaxial feed line

1/2

Figure 3.10-2 Simple dipole as prime focus feed The attractive feature of this feed was that it could be mechanically supported from the vertex/hub of the reflector, without need for a (blocking) quadrupod. It even presented the possibility of providing a set of different exchangeable feeds for the same reflector. A quick-release coaxial connector contributed to this feature. However, bandwidth and efficiency of this so-called "splash-plate" or "backfire" feed in its various configurations, were not very good. Improvement was found [4] in the idea that multimode techniques could be applied to the dipole when enclosed in a section of waveguide with diameter equal approximately 1 wavelength. See Figure 3.10-3 and Figure 3.10-4. The axi-symmetric pattern features of the cavity-backed dipole shown in Figure 3.10-3(b) can be maintained over a 35% bandwidth.

0db

10db

20db

30db

40db

0db

10db

20db

30db

40db

H-planeE-plane

Cross-pol

in 45o plane

Cross-pol

in 45o plane

Observed practical bandwidth ~ 35%

Angle off axis

-90 0 90 180-180-90 0 90 180-180

Angle off axis

Observed practical bandwidth ~ 10%

1/2 wave dipole

Full wave circular reflector

Coax line Coax line

1/2 wave dipole

Full wave circular w/g cavity 1/4

1

1

(a) (b) Figure 3.10-3 Comparison between (a) "Splash-plate" feed, and (b) Cavity-backed dipole feed



102

(a) (b)

Figure 3.10-4 (a) L-band cavity-backed dipole feed in a 7m prime focus application. (b) detail of the feed. (Photos used with permission of General Dynamics SATCOM Technologies Inc.) The circular waveguide supported the TE11 mode. Although the 1 waveguide does not support the TM11 mode, the dipole will generate this mode which will be attenuated in its cut-off condition until it reaches the aperture. Here it now has the required amplitude to combine in-phase with the TE11 mode resulting in the observed symmetric pattern and low cross-pol, The field distribution in a 1 wavelength cavity is shown in Figure 3.10-5. This mechanism is similar to that found in multimode horns discussed in Section 3.1 - where it was important to add a phasing section to ensure the proper addition of TM and TE modes in the aperture.

TE11 TM11

--

+

Figure 3.10-5 Dual modes in the Cavity-backed dipole aperture For a single linear polarization application, the dipole is excited with a single coaxial line. The dipole is connected as shown in Figure 3.10-6.

Center conductor

Outer conductorPTFE

PTFE removedDipole wings

Cylindrical cavity

Phase center

Matching ring

1.0

1.0 0.

09

~0.160.23

Slot in outer conductor

Aperture plane of the cavityShort circuit between inner and outer conductor

0.3

9

Figure 3.10-6 The cavity-backed dipole excited by a single coaxial line entering through the cavity aperture. The matching of the dipole to the coax line and the cavity is shown here.



103

For dual linear polarization, two "crossed" dipoles are employed, to support horizontal EH and vertical EV field components. This will force the excitation of each dipole wing as shown in Figure 3.10-7 requiring now four coaxial lines connected to a combiner network. Each dipole wing is connected in the same manner as the single dipole case, except that the feeding coax lines are each bundled so that the outer conductors are in contact with each other.

_

4 Dipole wings; 4-coaxial lines connected to a combiner network

1

2

4

3

1 wavelength diameter cylindrical cavity

_

+

_

+

Figure 3.10-7 Dual polarized cavity-backed dipole configuration For the case of circular polarization, the EH and EV components are combined with a 90 deg hybrid. The extension to a CP/LP switch selectable configuration is seen in Figure 3.10-8.

H

H

S S

S

S

90Hybrid

180Hybrid

180Hybrid

ΔVe

L

R

R

ΣVe

ΣHe

ΔHa

Σ

L

Δ

Linear Pol

Linear Pol

Circular Pol

Circular Pol Linear PolLinear Pol

90Hybrid

Coaxial line connections to the orthogonally oriented dipole pairs

Azimuth plane

Ele

vtio

n pl

ane

Σ

Σ

Δ

Δ

S = switch

Figure 3.10-8 A universal network combiner for the cavity-backed dipole feed for "sum-mode" functions and "difference mode" tracking operations. The difference mode can be seen to exist in the cavity by an examination of Figure 3.10-8. It is important to recognize that the central support structure holding the dipole assembly in place does not influence the difference pattern, since there is nominally no voltage there.



104

Yet a further view of the flexibility of this type of feed is seen in Figure 3.10-9 in which a second smaller aperture for a higher frequency band can be located concentrically inside the first, for a multi-frequency application. The principal constraint to this design lies in the choice of coax lines to the various dipoles. But computational modeling of this configuration suggests that there is no significant interference between the two apertures. A typical application is for combining S and X bands, or C and Ku bands.

S-bandCoax lines

S-band full wave circular w/g cavity

X-band cavity

X-band dipoles

S-band dipoles

X-bandCoax lines

S-bandCoax lines

H-polH-pol

V-polV-pol

X-b

and

term

inal

s

S-b

and

term

inal

s

Figure 3.10-9 Dual band cavity backed dipole configuration Now the interesting feature of this cavity-backed dipole concept - the dipole can be excited from either direction. See Figure 3.10-10. In this case, the feed can be a self-supporting structure which radiates back on itself - or - a forward radiating aperture that has found good use as an element of an array. See Section 6.4 on Tracking Feeds.

Coax line

1/2 wave dipole

Full wave circular w/g cavity

1/4

Impedance matching slot in outer wall of coax line

1

Figure 3.10-10 Alternative cavity-backed dipole configuration useful as an array element for monopulse applications in multiband applications; for example, as in an S-band down link and X-band uplink. The S-band array can be set to surround the X-band horn aperture. 3.11 Concentric Aperture Horn For those applications in which widely separated frequency bands are required, the idea of embedding horns inside each other can offer a compact design for multi-frequency band applications. See Figure

3.11-1. The outer horn supports the low frequency Lf signal. The central waveguide supports the high

frequency Hf signal. The waveguide is loaded with a dielectric in order to artificially reduce the guide

wavelength. Electrically, the central guide aperture will appear larger than it actually is. The result is the patterns of both horns will be similar. From this point of view, the illumination of the reflector system will be

more efficient compared to the common aperture horn working Lf and Hf .



105

Figure 3.11-1 Concentric aperture C/Ku feed system. (Photo used with permission of General Dynamics SATCOM Technologies Inc.) 3.12 Rudimentary Design Considerations for a Feed Horn A number of decisions have to be made when attempting to respond to an antenna design problem. Given

a requirement that reads “need an antenna operating over the band 1f to 2f , minimum gain to be minG ”.

The preference will be to use an existing reflector design that complies with the gain and SLE that will assure the gain and SLE requirement with the appropriate feed design. Let’s assume a Cassegrain configuration is defined. Preliminary horn design The next step is to establish a starting point for a horn design that supports the expected gain and SLE compliance. The questions to be answered are:

what type of horn is to be considered for the application how large should the horn aperture be what size is the throat end of the horn how long is the horn where should it be placed in the antenna

1. Generally the horn is selected for the lowest cross-pol performance, because this means good symmetry and high illumination efficiency. The corrugated horn is the first choice. But if the operational bandwidth is small - 5 to 15% - then the less expensive conical or multimode horn can be chosen. 2. The horn dimensions will be strictly determined by reflector geometry. Refer to Figure 3.12-1.



106

PC

a1dia

Lh

n

m

Hor

n ap

ertr

ue

Hor

n th

roat

Horn flare

Horn throat

Adia

s

Main reflector vertex

Lm

Sub

refle

ctor

a2dia ~ 10a1

dia

Phasecenter

Figure 3.12-1 Cassegrain subreflector and feed horn geometry. Estimation of the horn aperture size "A" Using the nomenclature of Figure 3.12-1, and the practical expression for the horn pattern (2.5.1) we can

write db

db

s

P

3

2

3

2

where edge taper in db. Rearranging this expression,

2

23 12 s .

Now using the expressions from (2.1.1) and (2.1.3), assuming that the horn is very nearly 100% efficient.

2

32

3

211.20341253

oh

AGgain

Substituting and solving for A

s

o

s fA

560~

32

11.203 cm (3.12.1)

with f

co .

Estimation of the horn throat size "a" At the horn throat, we want to have the smallest waveguide size a to be about 25% above the cutoff size

cd for the chosen frequency f . Depending on the mode expected in the throat of the horn, the feed

waveguide diameter can be chosen - refer to Figure 1.5-2.

GHz

inchesc f

d92.6

for TE11 mode; GHz

inchesc f

d47.11

for TE21 mode; GHz

inchesc f

d39.14

for TM11 mode

For TE11 mode, GHzGHz

inches

ffa

65.892.625.1 inches. (3.12.2)



107

Determination of the approximate feed horn phase center This idea is based on the TE11 mode in the horn, launched at the throat. By the time it reaches the aperture, the wavelength will have changed dimension, becoming shorter because the horn diameter is becoming larger. At the aperture, it will transition to free space wavelength. In the process, several other modes will also be generated, particularly if the horn possesses any discontinuities as presented by multiple flare changes or steps (Potter horn), or corrugations. At the top of the list of modes is the TM11 mode. If we

consider the TE11 mode propagating from the throat towards the aperture, the value for g will approach

free space wavelength 0 . In fact, when the horn section is about 10 times the throat diameter g will be

nearly equal to 0 . The effective phase center will be located close to this point in the horn.

Given frequency f , free space wavelength = fc0 . The cutoff wavelength for a circular waveguide

aperture is given by (1.5.1) or (1.5.3) depending on the chosen modes. The cutoff at the horn throat (a1)

shown in Figure 3.12-1 propagating TE11 is given by (1.5.1), namelymn

c

a

1 , where 11 = 1.841. The

operational dimension for 1a is about 1.3 times a1. The guide wavelength at a1 will be given by

2

1

1

amno

og

. (3.12.3)

The guide wavelength at a2 is given by 2

1101

amno

og

which will be very close to being equal to

0 . The example shown in Table 3.12-1 below shows the guide wavelength response in the horn.

From Figure 3.12-1, the total length of the horn istan21aA

L

, and the distance between the horn

aperture and the phase center will be tan2

12 aaLn

where represents the flare angle of the horn.

Typically, for Cassegrain and Gregorian systems the horn flare angle is approximately 10 to 12 degrees. For prime focus configurations, the flare will be chosen to fit the illumination angle from a slightly enlarged waveguide aperture, depending on the number of waveguide modes being used.

Additionally, tan2

Am ; (3.12.4)

This analysis will offer a preliminary horn design that can be refined with additional results obtained from more detailed computational analysis of the intended antenna system.



108

Table 3.12-1 Example of a preliminary conical horn design.

Rudimentary Feed Horn DesignDate: March 2006 Revised : December 2009Schwerdtfeger

Conical Feed Horn ParametersFeed operating frequency = 20.000 GHz horn section distance from

lambda-0 1.50 cm diameter a = lambda-g throat to PCFree space wavelength 0.59 inches a1 = 0.43 0.985 9.71Cutoff wavelength in aperture 24.43 inches 0.52 0.792 9.46Guide wavelength in the aperture 0.59 inches 0.62 0.710 9.17Cutoff wavelemgth in throat 1.88 inches 0.75 0.666 8.82Guide wavelength in throat 0.98 inches 0.90 0.640 8.39

1.08 0.624 7.88Sub edge-taper = 20 db 1.29 0.613 7.27

Subref half angle - phi-s = 20.0 degrees 1.55 0.606 6.54Feed horn gain 20.2 dbi 1.86 0.601 5.66Select mode in horn te11 mode 2.23 0.598 4.61

Horn half-flare angle - alpha = 10 degrees 2.68 0.596 3.343.21 0.594 1.82

Horn throat diameter - a1 = 0.43 iinches a2 = 3.86 0.593 0.00Horn aperture diameter - A = 5.63 inches 4.63 0.592

Horn length - L = 14.8 inches 5.55 0.592Horn aperture - PC distance = 5.04 inches 6.66 0.591

8.00 0.591Theta = 48.17 degrees 9.60 0.591

(TE11 mode) in horn throat 0.98 inches

mode TE11 TM01 TE21 TM11 TE01

6.92 9.03 11.47 14.39 14.39

Progression of guide wavelength from throat towards aperture

0.500

0.550

0.600

0.650

0.700

0.750

0.800

0.850

0.900

0.950

1.000

1.050

0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 4.5

Horn section diameter - inches

Gui

de w

avel

engt

h - i

nche

s

Guide wavelength variation in the horn

Feed operating frequency = 20.000 GHz

Sub edge-taper = 20 db

Subref half angle - phi-s = 20.0 degrees

Horn half-flare angle - alpha = 10 degrees

Horn aperture - PC distance = 5.04 inches

References: [1] A. Love, "Electromagnetic Horn Antennas", IEEE Press 1976. Contains a chronological collection of important works in electromagnetic horn designs. [2] S. Silver, “Microwave Antenna Theory and Design”, Rad Lab Series 1947; Boston Tech Lithographers 1963. [3] P. D. Potter, “A simple beamshaping device for Cassegrainian antennas”, JPL Technical Report 32-214, Jet Propulsion Laboratory, Pasadena, California, 31 Jan. 1967 [4] R. Schwerdtfeger, "A Coaxial Dual Mode Feed System", IEEE AP-Symposium, vol 17, June 1979, pp 286-289

Chapter 4 – Feed System Design


109

Chapter 4 - Feed System Design 4.1 Introduction 4.2 Linearly Polarized Rx Feed Design and Configurations 4.2.1 Example Satellite Link 4.2.2 Single Linear Polarization - with Polarization Rotation 4.2.3 Dual Linear Polarization - Receive Only 4.2.4 Linearly Polarized Tx/Rx Feed Design and Configurations 4.2.5 Linear Polarization - Two Orthogonal Rx and One Tx 4.2.6 Dual Linear Polarized Rx and Tx 4.3 Circular Polarization - Rx Only Feed Configurations 4.3.1 OMT + 90 deg Power Divider 4.3.2 Differential Phase Shifter with OMT 4.3.3 Septum OMT 4.3.4 OMT with Rectangular Horn 4.4 2-Port Circularly Polarized Rx/Tx Feed Systems 4.4.1 4-port CP Feed Network 4.5 Polarization Rotation and Switching 4.5.1 90 deg Differential Phase Shifter - CP/LP Selection 4.5.2 180 deg Differential Phase Shifter - LP Angle Adjust Only 4.5.3 CP/LP and LP Angle Adjust 4.5.4 90 deg Differential Phase Shifter - CP Adjust 4.5.5 CP/LP Selection - 2-port Rx/Tx Feed 4.6 Combined Dual Polarized Tx/Rx Feed Configuration 4.6.1 Single QJ and Magic Tee Feed System Network Layout 4.6.2 Twin QJ Feed System Layout 4.6.3 Combined CP and LP Tx/Rx Feed Configuration 4.7 Feed System Terminal Characteristics 4.7.1 VSWR - Effect of Multiple Contributions 4.7.2 Practical Matching Techniques 4.7.3 Polarization Discrimination - Axial Ratio and Cross-pol 4.7.4 Port-to-Port Isolation 4.7.5 Insertion Loss 4.7.6 Signal Delay Time 4.1 Introduction Communication satellites and their operational configurations are extremely varied - everything from single downlink, to multiband and dual linear or circular polarized, to multiband up and down links with mixed polarization. And just to keep things exciting, high power uplink requirements add a measure of complication. Each antenna operating in these specific environments will require the feed to be tailored and optimized to the mission. In this section, we will discuss those feeds which can accommodate a frequency band of nearly but less than 2:1 (one octave). This means making use of a corrugated horn geometry operating below the "first exclusion zone" of Figure 3.7-2. If the bandwidth is segmented into two narrow band regions which are separated by less than 2:1, a smooth-walled multi-mode horn may be applicable.



110

For segmented frequency bands separated by one or more octaves, modifications to the corrugated horn must be considered, and these will be discussed in Section 7. To introduce and illustrate some basic feed system designs, a number of Case Studies will be examined. These case studies will discuss some design approaches, and present typical values for the various parameters. The choice of a feed system configuration is specifically governed by the basic premise that antenna performance is to be optimized. This means that loss of signal in both up and down link signal paths must be kept low. For this reason, emphasis will be given to waveguide assemblies. Coaxial components are considered in cases where: (a) Very low frequencies are involved and coax components display inherent low loss (b) Loss may not be an important issue for the given application. (c) Packaging issues may force a compromise in using a mixture of coax and waveguide components. We will discuss a number of different waveguide feed system configurations in Section 4.2 to 4.6. Certain feed designs can only most reasonably be realized using coaxial components. Careful choice and application of low loss coax cables as interconnects goes a long way in minimizing feed system losses, even at higher frequencies. These will be discussed in Section 4.7. Of course, the earth station antenna will need to have a means of automatically tracking the target satellite. In some instances, precision tracking requirements (TTC, IOT, satellite launch support, orbit transfer control) will demand special feed system designs with additional components. These designs will be discussed in Chapter 6. TTC = Telemetry, tracking and control IOT = In orbit test Rx = Receive Tx = Transmit 4.2 Linearly Polarized Rx Feed Design and Configurations 4.2.1 Example Satellite Link Case Study No. 1 Satellite located in geosynchronous orbit ~ 42,000 km radius from the center of the earth. Frequency band: C-band with representative downlink = 4000 MHz Power output from satellite antenna = 10 Watts Satellite antenna size = 1 meter diameter aperture (assume 65% efficiency) Single linear polarization – oriented north-south along meridian 270o E Antenna axis is pointing toward equator Earth station site is 270o E longitude and 30o N latitude E.S. antenna mounted on elevation over azimuth pedestal Assume:

radius of earth = 6371.6 km = constant range from center of earth to satellite = 42187.66 km = constant receiver output at e.s. must be 0.1 mW to offer satisfactory performance. Gain of receiver = 75 db



111

Questions: What size antenna is needed? What features are needed in the feed in order to derive maximum signal?

Solution: Draw a picture of the situation presented here.

Earth station

270oE 0o+30o

SEarth

Satellite

Center of the Earth

N

Figure 4.2-1 Perspective view of the earth-satellite geometry From the given details, the satellite antenna is pointing toward the equator. But the earth station is not on the equator – it is 30o N latitude. Therefore, the signal level received by the e.s. antenna will be less than that received at the equatorial point Ps. Intermediate questions:

1. How far is it from satellite to e.s.? 2. What is the radiated power from the spacecraft? 3. What is the signal strength at the e.s.? 4. What is the signal strength requirement at the output of the e.s. antenna? 5. From these answers, what is the e.s. antenna gain, and therefore, the required aperture size? 6. What is the implication of the 65% efficiency? 7. Propose a feed design that would be compatible with this requirement.

The resolution of these questions is seen in the following analysis: First draw a picture of the problem and its configuration.



112

Ps

Pe

36807 km

4.97oSatellite

42187.6 km

6371.6 km

5517.9 km

Earth is assumed to be exactly spherical, although in fact it is not quite so, but rather slightly ellipsoidal

Pn

P3 = 3db

0db

n

3

[a]

[b]

Center of the earth

30o

Figure 4.2-2 (a) Dimensions of the geostationary orbital arc and the earth. (b) antenna pattern variation with pointing angle that will influence performance in the earth-satellite link discussed here. A1 Distance from satellite to earth station = 36807.8 km A2 Radiated power from satellite antenna in direction of main beam Psat = Transmitter Power + Antenna gain

Satellite antenna gain = Ideal gain x efficiency

2

65.0

D

87.144.32log20

D

Gaindbi = 57.30sG dbi

Therefore, radiated power = Antenna Gain + Transmit Power = dbWdbi 1057.30

And 57.40eirp dbW

A3 Since the e.s. is not in the direction of the peak of the main beam, but rather 4.97o offset, we must

find the power level on the satellite antenna pattern at 4.97o off-axis from the mainbeam peak.

Half Power Beamwidth = diamteraperture

wavelength

D 70702 3

At angle on 97.4 , the pattern relative power level will be

dbnP below db0 max

2

3

n =

db

dbn

P

P

3

dbnP =

dbnP

2

3

n = 3

2

25.5

297.4

x75.10 db



113

This means the e.s. is located at roughly 10.75 db down from the peak of the satellite antenna main beam max. A4 The power radiated from the satellite will, in effect, be attenuated as it travels the 36807 km to the

e.s. This reduction in signal is caused not by absorption, but rather by the fact that the signal is “spreading.” As we saw in sections 4.1 and 4.2, the amount of energy captured by the receiving antenna (in this case, the e.s.) is reduced as the separation is increased by capture angle squared.

The fall-off of signal level with distance is given by

24

R

pl (Also, see Section 5.5.1)

or in decibels: Rdb

pl

4log20

Therefore: “path loss” from satellite to e.s. is

secx

secmxkmPL

/1104

/100.3

18.368074log20

9

8

Hzf

secmeterx

frequency

lightofspeedwavelength

/103 8

5.74

30

104

1030

104

103

sec/1104

sec/1039

9

9

10

9

8

cmm

cm

cm

cmlossPath db

5.7

10010008.368074log20

80.195dbpl

A5 Level of the signal from the satellite in the direction of the main beam is:

Sat. antenna gain – pattern loss + Sat. Tx power – path loss + e.s. ant. Gain + receiver gain = e.s. receiver output signal level.

dbWdbdbise

dbdbWdbdbi G 407580.1951075.1057.30 ..

98.50.... gainantennaseG dbise dbi

Path loss = 195.76 db

Pattern loss = 10.75 db4.97o

Psat = 10W

Gsat = 30.57dbi

Rx

Receiver gain = 75db

Ge.s.

Signal level needed = 0.1mW = -40dbW

Direction of main beam maximum

Figure 4.2-3 Diagrammatic view of the satellite link A6 The antenna size for the earth station can now be determined.

Ideal antenna gain 2

D

Go

os GG



114

From the above calculations,

98.50sG dbi efficiency 87.165. or db 85.52 oG dbi

Aperture diameter 1.104810 10

85.52

D cm

e.s. antenna diameter = 10.48 meters

The lower the antenna efficiency, the larger the antenna aperture must be in order to achieve the same signal level for the receiver. A7 Antenna Design

A standard 11.1m Cassegrain antenna most closely meets this requirement.

The necessary feed system configuration will be as shown in Figure 4.2-4. The feed will consist of a horn and a transition from the horn (square, round, or rectangular) to rectangular waveguide.

F1

F2

LNA

Rectangular to circular transformer

Corrugated Horn

Corrugated horn chosen in order to satisfy efficiency requirements

Transformer to satisfy single vertical polarizationto

Figure 4.2-4 Example linearly polarized antenna and feed to receive satellite signal Based on this example, let us examine what happens when the earth station is located elsewhere. 4.2.2 Single Linear Polarization - with Polarization Rotation Case Study No. 2 Suppose a similar e.s. is located at longitude 330 E and on the equator (latitude = 0). Q1 What is different in the link, and how is the e.s. antenna configured relative to that in Case Study 1? A1 The only thing different is that the incoming polarization of the wave from the satellite is apparently

rotated by 90o to horizontal polarization. This is shown in Figure 4.2-5. Therefore, the e.s. antenna feed must be rotated in polarization. For any e.s. location not in the meridianal plane of the satellite, the pol. angle will be rotated CW or CCW from vertical. This means that for LP systems, a scheme for polarization adjustment must be provided, particularly if the e.s. antenna must:

a. look at a satellite located east or west of the earth station site, or

b. switch between one satellite to another.



115

View of target satellites as seen from some geographic latitude > 0 degIt is assumed the target satellite antenna axis points to the equator

HV V

H

Satellite antennapolarization orientation

Geostationary orbital arc

(a)

Equ

ator

ial p

lane

V

H

View of target satellite seen from this meridianal plane

Vie

w o

f ta

rget

sat

ellit

e se

en

from

an

equa

toria

l loc

atio

n

east

of

the

sate

llite

long

itude

Local meridian of the earth station

Satellite antennapolarizationorientation

North pole

V

H

V

H

Bor

esig

ht o

f ta

rget

sa

telli

te

Par

alle

ls o

f la

titu

de

Satellite antenna boresight direction

Earth

(b) Figure 4.2-5 (a) View of a target satellite as seen from a geographic latitude north or south of the equator. The antenna has to be turned in azimuth to see one of the targets. The resulting rotation in polarization is proportional to the required rotation in azimuth. (b) For an antenna on the equator, a nominal vertical polarization on the satellite will appear to be horizontally polarized when viewed from either east or west of the satellite position. When the satellite antenna axis is pointed to a boresight away from the equator, the pol rotation for the antenna on the equator is reduced correspondingly. The above assumes that the e.s. antenna pedestal is Elevation over Azimuth. If the pedestal were Declination over Hour Angle, no change would be necessary. See Section 8.2 for further details of the various antenna pedestal configurations. The necessary feed system configuration will be as shown in Figure 4.2-6. The feed will consist of a horn and a transition from the horn to rectangular waveguide. But now, the feed must be rotatable around the RF axis to match the LP pol orientation of the incoming signal from the target satellite.

HornOMT

vert pol terminal rotatable to hor pol

Polarization angle drive

Polarization angle adjustment

Figure 4.2-6 Linearly polarized feed system layout and its pol rotation.



116

4.2.3 Dual Linear Polarization - Receive Only Case Study No. 3 Suppose the satellite is dual polarized – meaning two downlink signals are available orthogonally polarized to each other – discrimination = 40 db. Q1 What changes are needed in the e.s. antenna?

Ensure that both signals operating at the same frequency do not interfere with each other. System polarization discrimination or isolation = -30 db.

A1 We will need a dual polarized feed network to receive both H and V polarization components, and a means to rotate the feed in polarization. The feed system will consist of a horn and an OMT (square or round) as shown in Figure 4.2-7. The feed must be rotatable around the RF axis to match both H and V components of the LP signals from the target satellite.

Horn

Rx 4 GHz WR-229

Rx 4 GHz WR-229

OMT

Polarization angle drive

Polarization angle adjustment

Figure 4.2-7 Dual polarized feed system layout and its pol rotation Additionally, with this feed configuration, and heeding the assumption that the e.s. antenna efficiency is to be 65%, we need to identify some other performance features of the feed, namely: feed losses, which are included in the antenna efficiency. These items will be discussed in Section 4.7. 4.2.4 Linearly Polarized Tx/Rx Feed Design and Configurations Let us impose the requirement for a single LP transmitted signal from the earth station to the satellite. Transmit capability must now occupy the 6 GHz band. Case Study 4 - Linear polarization - single orthogonal Rx and Tx Q1 How much power must be supplied to the e.s. antenna in Case Study 1 to offer a signal level at the

satellite of 0.1 mW at the receive chain output. (Assume: receiver gain = 45 db)

e.s. antenna size = 11.1m

Transmit frequency = 6,000 MHz = 6 GHz

Q2 What must be done to the feed network to accommodate an uplink signal orthogonal to the

downlink? A1 Write the power relationship between the satellite and e.s. antennas.

Power In e.s. antenna Path loss Satellite Receive signal required + antenna - losses - at 6 GHz + antenna - Efficiency + path gain = level gain (efficiency) gain

e.s. satellite. range to satellite.



117

Here: “Antenna Gain” =

2

D

Go

D = Antenna Diameter; = wavelength; Antenna losses = eff. = (in this case 65%)

Power required = P ; Path loss =

24

R

; R = Range to satellite

From the expression above,

dbWdbdbdbidbdbdbiP 404587.196.3532.19987.187.56

dbWP 23.25 or 333 Watts

A2 Figure 4.2-8 shows a wideband OMT, in which the side port of the OMT couples out the Rx band signal voltage EH, the straight-through port accommodates the Tx band signal EV voltage. As explained in the discussion on OMTs in Section 1.4, the Rx signal is kept out of the Tx path by means of a waveguide in cut-off condition structure. WR-159 waveguide supporting 6 GHz is in cut-off at 4 GHz.

Rx 4 GHz WR-229

Tx 6 GHz WR-159Horn

OMT

Figure 4.2-8 Single orthogonally linearly polarized Rx and Tx feed system 4.2.5 Linear Polarization - Two Orthogonal Rx and One Tx Case Study 5 If we have 2 orthogonal LP downlink signals, how do we simultaneously accommodate a single uplink signal at the e.s.? Two approaches may be examined here: Alternative 1: Two separate and different OMT structures are needed here. Figure 4.2-9 shows two side-wall coupled OMTs in series and orthogonally oriented with respect to each other. Receive band Rx1 EH signal voltage is coupled out in the first OMT. The Rx2 EV voltage component is coupled out in the second OMT. The second OMT is identical to the OMT discussed in Case Study 4 - it carries a straight-through guide to accommodate a horizontally polarized Tx EH voltage.

OMT1Tx (V)

Rx2 (H)

Rx1 (V)

Horn

Rx2 (H)

Rx1 (V)

OMT2

Figure 4.2-9 Three-port linearly polarized Rx - Tx feed system layout using two separate OMT junctions. Alternative 2:

Rx2 (H)

Rx1 (V)Rx1 (V)

Rx2 (H)

Horn

OMT

Diplexer

Tx (H)

Filter

FilterTx (H)

Filter

Figure 4.2-10 Three-port feed using one OMT and one diplexer to separate Rx from Tx functions.



118

Point of interest: Since the coupling slot for Rx EH in the first OMT presents an asymmetric discontinuity in the signal path for the Tx EH voltage, a small tilt in the outgoing LP wavefront will occur (in the plane of the coupling slot). The tilted wavefront is supported by a small voltage vector along the axis, which will represent a small loss in signal, and will cause the beam from the horn to be tilted. In practice, a short length of straight symmetrical waveguide is included in order for the tilted wavefront to straighten itself out a little, by attempting to attenuate the mode that is supporting it. The tilt is never completely suppressed. Only the more complex Symmetrical OMT originally designed by MIRAD in Switzerland will offer zero disturbance in the outgoing wavefront shown in Figure 4.2-11.

Figure 4.2-11 The symmetrical OMT. Both polarizations are coupled out symmetrically from the circular common path. One pair is readily seen on the right brought together in a "T"-junction. The same occurs for the orthogonal polarization. (Used with permission of General Dynamics SATCOM Technologies). In order to keep the Tx EH signal out of the Rx1 EH port, a filter must be installed on the first OMT to reject Tx band signals. In effect, the first OMT plus rejection filter becomes an orthogonally polarized diplexer. Here, the fundamental building block in the OMT- diplexer junction is the transmit rejection filter. Very briefly, a Tx rejection filter for this application is based on the following idea. Consider a section of waveguide that is able to support both 4 and 6 GHz frequency bands simultaneously. Now install a set of reactive elements (for example screws, pins, blades or even sidewall cavities), to create resonances that are spaced along the length of the waveguide to reflect Tx signals sequentially, so that they all sum in phase back at the input to the filter. As a result, Tx signal cannot get through, but is completely rejected. The Rx signal sees a waveguide configuration that, instead of reflecting at each pin, reinforces passage through the filter with all reinforced components in phase. The result is low loss for Rx signals. Since high frequency signals are rejected, and low frequency signals are passed, this filter is termed a LPF (low pass filter). See Figure 4.2-12 and Figure 4.2-13.



119

Figure 4.2-12 An example of a waveguide cavity filter

Figure 4.2-13 Other examples of waveguide filter designs (Used with permission of General Dynamics SATCOM Technologies). Note: Filter design is a huge subject for itself, beyond the scope of this book. The reader is referred to [1]. Since the required Tx power level for Case Study 4 was determined to be 333 Watts (55dbm), and the allowed 6 GHz power level into the 4 GHz LNA is -20dbm, (more on this in Section 5), the rejection of Tx signals is 75db. Typically, an OMT will offer about 30db of polarization discrimination. This means the filter must provide at least an additional 45db rejection.



120

4.2.6 Dual Linear Polarized Rx and Tx Case Study 6 Consider the situation for the system requiring two orthogonal downlinks, plus two orthogonal uplinks. What has to happen in the e.s. antenna? The feed system configuration is shown in Figure 4.2-14 - Horn plus OMT plus two diplexers. Notice that the OMT must carry the full bandwidth of the system. For C-band operations (3.4 – 6.725 GHz), a double ridged design will be needed. See more in Section D.1.6 in Chapter 12.

OMT

Horn

TRF

TRF

Diplexers

Rx1

Tx1

Tx2

Rx2

Viewed from the perspective of the downlink, we discriminate polarization first, and then separate frequencies in the diplexers

Figure 4.2-14 4-port dual polarized Rx and Tx feed configuration. These diplexers, to keep the high power Tx signals out of the Rx signal paths, are co-polarized. The basic structure of these diplexers is shown in Figure 4.2-15. This is a 3-port device with a common terminal. The arm carrying the Rx signal path is fitted with an LPF (low Pass Filter), similar to that described in Section 4.2.5. The other arm carrying the Tx signal path is fitted with a HPF (high pass filter) to reject Rx frequencies.

WR-159 rectangular waveguide

WR-229 rectangular waveguide

2.125" diameter circular

waveguide

Bandpass filter

OMT

Required to match the field condition at the junction with the OMT and the WR-229 waveguide at the bend

Commonfeed hornterminal

To Rx terminal

From Tx terminal

Matching Section

Figure 4.2-15 4/6 GHz Diplexer assembly The HPF design is essentially easier than the LPF, since in the case being considered here (separating 6 GHz from 4 GHz), WR-159 waveguide for the Tx signal path will inherently not support 4 GHz signals.



121

But for the case in which Tx signals are close in frequency to Rx signals, and in many instances at frequencies lower than the designated Rx band, filter design will need to be carefully tailored to suit the mission.

Figure 4.2-16 2.0/2.2 GHz diplexer drawing An alternative feed configuration is to use a wideband symmetrical OMT and a diplexer on both input terminals. The symmetrical OMT offers two attractive features to the feed system performance. (a) Structural symmetry offers good cross-pol behaviour (b) The device has a well matched continuous bandwidth of about 1.8:1 in both polarizations. Referring to Figure 4.2-11, the common port is symmetrical. And EH and EV voltage components are coupled off to the side in opposing pairs. The horizontally oriented pair, each carrying ½ EH, and the vertically oriented pair each carrying ½ EV. After some interconnecting ½ - height waveguide, the respective pairs are summed in separate y-junctions into standard size waveguide, to finally reach horizontal pol port 1, and vertical pol port 2. Since there are no complex and frequency sensitive waveguide components in this interconnect, there is no real frequency band limitation (except of course for that expected from standard waveguide - a nearly 2:1 bandwidth). The only critical aspect of this symmetrical OMT lies in the transition from the square (or round) common port to the symmetrical junction of 4 rectangular waveguides. This is accomplished with a mode transformation from TE11 to the symmetrical TM01, and then taking advantage of a complete coupling to the rectangular TE10 mode in the junction. The EV and EH voltage components are split symmetrically, so that when the respective components are recombined in the y-junctions, the voltages add - and do not subtract. Both port 1 and port 2 can be fitted with co-polarized diplexers to accommodate dual pol Rx and Tx functions. The QJ or Quadrature Junction, mentioned in Figure 1.5-7 and to be discussed in Section 7.1, represents a symmetrical 6-port device which is simultaneously a symmetrical OMT and a diplexer. The diplexing function is built into the QJ with TRFs, or transmit rejection filters, in each of the 4 arms of the OMT. Figure 4.2-17 shows the use of this junction. [ ]

QJ = Quadrature Junction TRF = Transmit Reject Filter

OMTQJ QJHornTx1

Tx2

OMT

TRF

TRF

TRF

TRF

Rx1

Rx2

Viewed from the downlink, we first separate frequencies, and then discriminate between polarizations

Figure 4.2-17 A dual frequency band feed network employing two QJs



122

4.3 Circular Polarization - Rx Only Feed Configurations So far, we have discussed a satellite communication system which is linearly polarized. However, other operational systems exist which use circular polarization. A definition of circular polarization was given in Chapter 2. Here is a quick review: Requirements for the existence of a CP wave are shown in Figure 4.3-1.

RCP

EH

EV

90o


Figure 4.3-1 Circular polarization condition requires two orthogonally polarized fields that are shifted by 90 degrees in phase with respect to each other. So long as EH and EV are equal in magnitude, and remain separated in space by 90o phase, then E1 and E2 will represent two circularly polarized signals which are independent and isolated from each other. For this case:

0,1 VHVH EEandEE

If either or both of these two conditions are not met, then the resultant traveling wave will not be circularly polarized, but rather elliptically polarized. Therefore, a measure of the “polarization purity” or “polarization discrimination” PD can be determined with the following relationship:

2

2

1

E

E= Pol Discrim =

2

2

1

1

H

V

H

V

HV

HV

E

EE

E

EE

EE (4.3.1)

(sometimes also referred to as “cross-pol”)

where 1E and 2E are derived from signals available at the common port of the OMT.

The ratio H

V

E

E = r > 1 is called var (voltage axial ratio), and for the purposes here, considered 1 .

1

1

r

rPDationminDiscrionPolarizati (4.3.2)

For example, PD is measured as 30db

In terms of voltage, this is 623.3110 2030

voltage ratio

1

1623.31

r

rPD

1

1

PD

PDrVAR =

623.30

623.32 = 1.065:1

Axial ratio expressed in db is now:

550.0065.1log20log20.. rra db



123

Given two equal magnitude orthogonal LP field (voltage) components, phase shifted by ¼ , or 90o phase: Sense of polarization is defined as RCP when the resultant field rotates cw looking into the direction of propagation, LCP when rotating ccw. The essential components needed are:

A symmetrical waveguide section able to support two orthogonal field vectors. A device which can change the travel time through the device of one of the field vectors, with

respect to that of the other. The differential time should be ¼ period (or 90 deg time phase). The "symmetrical waveguide section" is clear enough. What does the "device which can change the travel time" look like? Several possibilities present themselves, and are discussed next. 4.3.1 OMT + 90 deg Power Divider For an RCP signal arriving at the common port of the OMT, the EV and leading EH components will appear at the respective ports 1 and 2. In terms of time-phase, they are still shifted by 90 degrees with respect to each other. Connecting these component signals to a 90-deg hybrid junction, the time phase shift can be removed. This configuration is shown diagrammatically in Figure 4.3-2.

OMT

E1

E2

Horn

EV

EH

EV

EH

EH

EV


RCP 90o hybrid 3db power divider

equal electrical path length interconnects

One OMT, one 90o hybrid power divider with equi-length interconnecting waveguide.E1 will represent EH + EV of an incoming RCP wave. E2 will represent EH - EV .

So long as EH = EV in magnitude, and remain separated in space by 90 phase, then E1 and E2 will represent two circularly polararized signals which are independent and isolated from each other.For this caseEH + EV = 1 , and EH - EV = 0

1

2 4

3

H

Figure 4.3-2 Circularly polarized feed network employing a 90o hybrid The EH and EV voltage components at the two inputs to the hybrid will combine and emerge at the output terminal (4). The combining process goes like this: See Figure 4.3-3 below.



124

4

2

1

3

E H in with 90o relative phase

(relative to that at port "2")

E V with 0o relative phase

The added path length to "4" here

causes the 90o time/phase delay in the signal relative to that travelling straight through to port "3".

1/2 E V (0) + 1/2 E H (90 - 90)

corresponding to the total incoming RCP signal from the OMT ports

1/2 E V (0 - 90) + 1/2 E H (90)

= 0

RCP incoming signalto the OMT

Figure 4.3-3 90 deg hybrid combiner and its operation For an incoming RCP signal, EH will lead EV by 90 deg time phase. EH enters the hybrid at port 1. At the coupling slot in the hybrid, EH splits - half going to port 3 and half going to port 4. ½ EH at port 4 will suffer a -90 deg time phase shift relative to the ½ EH at port 3 due to the extra path length travelled in the coupling slot. While this is happening, EV, entering the hybrid at port 2, splits in the coupling slot of the hybrid, arriving at port 4 as ½ EV with 0 deg relative phase (because it lagged the EH component by 90 deg in the RCP condition from the very beginning). At the same time, ½ EV suffers -90 deg phase shift in the coupling slot, and arrives at port 3 with -90 deg total relative time-phase shift. The two components at port 3 will sum to zero - that is no signal will be seen at port 3. All the constituent signal of the incoming RCP signal will appear at port 4. The same arithmetic will show the sum of the voltage components for an incoming LCP signal to the feed system as appearing completely at port (3). Point of interest: Since in a side-port coupled OMT, the electrical path lengths from the common port are not equal and will vary slightly with frequency, the connecting path from the OMT ports to the hybrid must be equalized. This is done with waveguide segments which have slightly different internal dimensions, resulting in small differential velocities of propagation that compensate for the physical length differences. General performance features A well designed OMT-Hybrid assembly may offer a bandwidth = 20%, Return Loss = 23db (VSWR = 1.08:1), and axial ratio = 0.5db (Port-to-port Isolation = 35db). Physically, the length of the assembly will be approximately 4 to 6 guide wavelengths, depending on the nature of the interconnecting waveguide segment. Applications: Narrow band inexpensive receive only antennas 4.3.2 Differential Phase Shifter with OMT An alternative CP polarizer assembly is shown in Figure 4.3-4, in which power split and phase shift occurs in a 2-port instead of a 4-port device – a differential phase shifter. The differential phase shifter can be realized in circular or square section waveguide. The construction is shown here:



125

EH

EV


RCP

90o

EH

EV


LCP 90o

E1

EV

EH

EH

EV

z

45o

45o

90o

or g/4

y

x

(a) Reactive elements, e.g., a periodic structure of conducting posts OR (b) a dielectric vane

Sense of rotation "Right Hand"

Sense of rotation "Left Hand"

90o differential phase shifter

OMTHorn


Figure 4.3-4 Circular polarization derived from the periodic reactive elements in a circular waveguide As the E-field of the signal from the E1 terminal of the OMT enters the differential phase shifter, it sees the set of inductive posts in the 45o plane or “path of least resistance,” and “rotates” into that plane. This “rotation” can also be interpreted as an effective vector summation of two components EV and EH. One of these two components (in this case EH) will be oriented into the plane of obstacles, and EV will be 90o separated in space in the plane carrying no obstacles. As the wave travels down the O-guide, the inductive effects of the obstacles cause the EV field to travel more quickly than the EH field. If the obstacle geometry - a double linear array of pins penetrating into the waveguide - has been dimensioned properly, then by the time both EH and EV reach the other end of the phase shifter, they will be separated by 90o along the axis of propagation. At this time, the resultant wave emerging from the phase shifter will be LCP. If the plane of the obstacles is rotated 90o (into the other 45o plane) with respect to the E1 field from the OMT, then the resultant wave at the output will be RCP. As a rule of thumb, the sense of polarization is determined by judging the direction of the shortest angular path from the orientation of E1 to the plane of the pins, CW or CCW, and that will represent the sense of circular polarization. If the required rotation is cw, the polarization sense for the vertical E1 will be RCP, and LCP for the ccw rotation. Nomenclature: For dual-polarization requirements:

The combination of OMT and differential phase shifter is called a CP – Polarizer The OMT by itself is an LP – Polarizer

General design and performance features: 1. A well designed OMT- differential phase shifter may offer a bandwidth = 20%, Return Loss = 25db (VSWR < 1.1:1), and a.r. < 0.5db (Port-to-port Isolation > 35db). Physically, the length of the assembly will be approximately 6 guide wavelengths.



126

2. The rotational position of the phase shifter with respect to the OMT determines the differential phase shift . Deviation from 45 degrees leads to elliptical polarization with axial ratio

tanr (4.3.3)

where = rotational angle of the plane of the phase shifter pins from reference vertical. For = 45 deg,

and differential phase shift = 90 deg, we have circular polarization. = 0 or 90 deg corresponds to linear polarization for var = 0 (VLP) or infinite (HLP). 3. Typical response of the phase shifter is shown in Figure 4.3-5 and Figure 4.3-6.

+ve

ph

ase

shift

-ve

ph

ase

shift

0o

Frequency band of interest

plane with no pins - phase = 0o

plane of pins - phase = - 90o-90o

- 2 deg

+ 2 deg

4.2 GHz3.4 GHz

Total differential phase = +/- 2 deg

(b)

(a)

(c)

Circular waveguide diameter = 2.5 inches23 pins; diameter = 0.200 inch; spacing = 0.563 inch

Figure 4.3-5 The phase response for the phase shifter. (a) phase for the signal polarization in the no-pin plane; (b) in the plane of the pins showing the phase as -90o relative to the reference measurement (a); (c) is the transposition of (b) onto (a) to show the phase variation between the "no-pin" path and the "pin" path.

+ve

ph

ase

sh

ift-v

e p

ha

se s

hift

0db


- 0.3db

+ 0.3db

4.2 GHz3.4 GHz

Maximum a.r. = Axial ratio = 0.30db

(a)

Differential Phase Shifter DesignCircular waveguide diameter = 2.5 inches23 pins; diameter = 0.200 inch; spacing = 0.563 inch

(b)

Points where differential phase shift = 90 degand axial ratio = 0db by definition

Bandwidth = 21%

xial ratio

Figure 4.3-6 The axial ratio (amplitude) response for the same phase shifter. (a) represents the normalized response for reference 0o (vertical) polarization. (b) shows the collection of traces corresponding to a number of additional discrete polarization orientations between 0o and 90o. The envelope of all these traces represents the axial ratio of the phase shifter and OMT combination. The question arises - why the curved shape of the phase response ?? The phase response to the passage of signal in the plane of no-pins increases with frequency. The phase response to the passage of signal along the line of pins decreases with frequency, and is shifted by -90 degrees with respect to the no-pin case. This is shown in Figure 4.3-7. The overlay of these two effects shows two points at which differential phase will be 90 degrees. The design trick lies in the choice of waveguide size, the geometry of the pins and their spacing, to optimize for smallest difference in shape between these two responses. The smaller the difference in shape, the larger the possible bandwidth for acceptably small axial ratio.



127

< - 90o

= - 90o

> - 90o

= - 90o

< - 90o

(a) phase responsein plane with no elements

(b) phase response in plane of phase shifting elements

+ve

ph

ase

sh

ift-v

e p

ha

se s

hift

0o

low frequency

high frequency


(c) phase response (b) superimposed onto (a)

low

high

Figure 4.3-7 The phase response as a function of frequency of (a) the circular waveguide in the plane with no obstacles, and (b) in the plane of the inductive obstacles. Various "pin" geometries have been examined over the years. Figure 4.3-8 shows some examples, but the smooth rounded pin seems to offer the smallest axial ratio over the widest bandwidth.

blade blade and nipple pin or screw

corner blade and nipple diagonal blade Figure 4.3-8 Differential phase shifter pin geometries that have been examined. Circular waveguide configuration is adopted for applications for polarization switching and polarization ellipse rotation. Square waveguide configuration may be used for fixed CP applications, particularly if the OMT has a square section. As a result, for a given circular waveguide size, it has been possible to relate expected axial ratio

performance to guide wavelength g .

dbrameang

avg

182.6..

(4.3.4)

where 2

highglowgavg

and highglowgmeang

Performance enhancement can be achieved by modifying the low frequency phase characteristics of the signal path in the plane of no-pins. As shown in the Figure 4.3-9 (a) and (b) a coupled resonant cavity has



128

phase response features that can be added to the pin-loaded phase shifter to extend the bandwidth. By choosing the coupling slot size and adjusting the resonant frequency of the cavity, very low axial ratios can be achieved. Note that to maintain symmetry in the differential phase shifter, two coupled cavities will be needed as shown in Figure 4.3-9(a). Greater than 35db pol discrimination (a.r. = 1.03) over 20 percent bandwidth has been achieved with this method [2]. Applications: High polarization discrimination CP feed system requirements over 20% bandwidth.

Cavity coupling slot

Cavity coupling slot

Cavity tuning screw

Cavity tuning screw

Filter phase responsePin-loaded phase shifter response

Cavity-loaded phase shifter

response


4.2 GHz3.4 GHz

Filter resonant frequency

(a) (b) Figure 4.3-9 (a) Coupled resonant cavity differential phase shifter design, and (b) its expected very low axial ratio response. 4.3.3 Septum OMT The septum OMT in Figure 4.3-10 shows diagrammatically the transition from an incoming CP signal to the

LP signals at ports 1 and 2. Consider an LCP signal, with the VE component leading (in time) the HE

component at the symmetrical port of the septum OMT. The HE component will travel straight through the

square body, and appear as

HE21 at "b", orthogonal to the septum blade, and

HE2

1 at "b", each pointing

to the right. Its propagation velocity will stay almost constant since the L

HE vector is parallel to the "B"

dimension of the output rectangular waveguide. The VE component, on the other hand, slowly starts to

run into cutoff conditions as it attempts to go down either side of the rising septum, and starts to slow down.

At the same time, the field vector VE will start to rotate (the voltage vector wanting to take up the shortest

distance to be orthogonal to a conducting surface (waveguide wall). This is shown in the vector diagram at

"b" and "c". By the time the VE voltage has turned completely into the horizontal position, it has slowed

down to coincide in time position with the HE component, well inside the rectangular portion of the OMT.

VE has also split --

VE21 is pointing to the right in the rectangular waveguide going to port 1, and

VE2

1

is pointing to the left in the rectangular waveguide going to port 2. By the time the slowing

VE21

component has reached port 1, the

HE21 component has caught up with

VE2

1 .

HE21 plus

VE2

1 will

appear at port 1, and

HE21 plus

VE2

1 will appear at port 2. This says, if the design is correct,

HE21 will

cancel to zero with

VE21 , and no component of the original RCP signal will appear at port 2.



129

EHL

EVL

EVR

EHR

90o

EHL

EVL

EVL

EHL

45o

a

c

d

Diagonal longitudinal blade

RCP

LCP

CP signal input

Equivalent LP signal output

Port 1

EVL

EHL

b

Y

X

Z

A

B

90o

RCP

Symmetrical port supporting both horizontal and vertical polarization

Port 1 and Port 2 rectangular waveguide terminals

Septum blade

Port 2

Figure 4.3-10 The transition from an LCP wave at the common port of a Septum OMT to an equivalent LP wave at output port 1. The "red" horizontal wave vector travels all the way through. The "blue" vertical wave vector must slow down as it rotates into the horizontal plane. The right hand half of EV adds to the right hand half of the EH component. The left hand half of EV is cancelled by the left hand half of the EH vector which is of opposite phase. A similar argument applies to the division of voltages when an LCP signal enters the common port of the septum OMT. And from this one can see, upon examining a septum OMT and looking into the common port - the right hand port 1 will offer the RCP signal component, and the left hand port will offer the LCP component of a dual polarized incoming CP signal. By reciprocity, signal injected into port 1 will become RCP at the common output port, and similarly, signal injected at port 2 will become LCP. Point of interest: Since the diagonal septum presents an asymmetry in the common (usually square) guide, a small tilt in the outgoing CP wavefront will occur (in the plane of the septum). The tilted wavefront is supported by a small voltage vector along the axis, which will represent a small loss in signal. A similar asymmetry, caused by the coupled port for the orthogonal polarization, is evident in the normal sidewall OMT. In practice, a short length of straight symmetrical waveguide is included in order for the tilted wavefront to straighten itself out a little, by attempting to attenuate the mode that is supporting it. The tilt is never completely suppressed. Only the more complex Symmetrical OMT will offer zero-disturbance in the outgoing wavefront. For additional reading, see [2]. General performance features: A well designed septum OMT may offer a bandwidth ~ 25%, Return Loss < -25db (VSWR < 1.1:1), and Axial Ratio < 0.3db (Port-to-port Isolation = 35db). Physically, the septum length will be approximately 2 to 3 rectangular guide wavelengths, depending on the choice of straight waveguide that can be connected to the common port before reaching the horn. In practice, to achieve these performance features, the septum blade will be stepped for matching purposes. Applications: High quality single CP feed system requirements.



130

4.3.4 OMT with Rectangular Horn Here, we make use of the different rates of propagation in a horn with two different flare angles, see Figure 4.3-9. EV reaches the aperture more quickly because of the larger flare angle – it gets to free-space condition more quickly than EH. If the horn length is dimensioned such that the differential g between EH and EV at the aperture = 90o, then a CP wave will result. The discussions above indicate that for dual polarization requirements, an OMT and a differential phase shifter type CP-polarizer is needed in the feed network.

90o


Rectangular w/g to square transition or an OMT

A

B

z

x

y

a

b

Figure 4.3-11 Circular polarization derived from differential phase in a rectangular horn Question: As the LCP and RCP waves occur in the feed horn, why do they not interfere? After all, while the field of the LCP wave is rotating ccw, and the field of the RCP wave is rotating cw, there must be points in which the two fields will be co-incident, and interfere with each other. Is this the case?

E2L

E1L


E2R

E1R

ccw

RCP

cw

LCP

Fi 6 3 Vi f T O h l CP W

Figure 4.3-12 View of an RCP and an LCP wave propagating with no interference In this picture, we see that the points of co-incidence occur in the nulls of the respective field components, and therefore, so long as perfect CP condition is maintained, no interference will take place. General performance features: A well designed OMT-Rectangular Horn may offer a bandwidth ~ 15%, Return Loss < -25db (VSWR < 1.1:1), and Axial Ratio ~ 0.1 to 0.5db, (Port-to-port Isolation ~ 30db). Physically, the length of the assembly will depend entirely on the horn design and its length. Applications: Typically, this design approach is reserved for possible use in 4-horn CP arrays for multi-band tracking feed systems. See more in Section 6.3



131

4.4 2-Port Circularly Polarized Rx/Tx Feed Systems A special case of particular interest is the 2-port CP feed used in those cases where the Rx and the Tx frequency bands lie within the bandwidth capabilities of the differential phase shifter. Figure 4.1-1 shows the configuration, and the differential phase shifter configuration for the designated sense of circular polarization for Rx and Tx signal paths.

Tx1 (LCP)

Rx2(RCP)OMT90o

ph. sh.Horn

45o

Pins

Progation into page

leading

lagging

Input vertical polarization

Figure 4.4-1 Block diagram of the 2-port Tx/Rx CP feed system Consider the network shown in Figure 4.4-2. Imagine a signal being injected into the Tx terminal. The nominally linearly polarized (LP) waves (entering the phase shifter via the OMT) encounter the phase shifter pins, divide into two orthogonal components, and by the time the wave has reached the horn, these two components have been time phase-shifted by 90o relative to each other. This is the condition for perfect LCP. If the horn is perfectly transparent, then a perfect LCP wave will be launched into free space. If the OMT is perfectly polarized, then no signal will be coupled from Tx to Rx terminals. (This must, however, remain a dream.) Conversely, if an RCP wave enters the horn, the phase shifter will cause the 90o time phase shift between the incoming orthogonal components to go to zero, and allow these components to add in phase to appear at the (LP) Rx terminal. If the phase shifter and OMT are perfect, then all of the power related to the incoming RCP signal will be transferred to the Rx terminal, and nothing to Tx, meaning an infinite polarization discrimination. In practice, however, several mechanisms contribute to reduce the equality of polarization purity.

a. If the OMT is not perfectly orthogonally polarized, then some port-to-port coupling will occur between Tx and Rx.

b. If the phase shifter (due to bandwidth limitations in particular) cannot support perfect

orthogonality between the two components of the CP wave, and/or provide exactly 90o time phase shift between the two orthogonal components, then the wave will not be CP or circularly polarized.

c. An incident LCP wave from Tx encountering a discontinuity in the horn will be partially reflected.

The reflection will travel back into the phase shifter RCP. Obviously, this RCP wave will appear at the Rx terminal, together with whatever is coupled directly from Tx. The magnitude of the RCP wave at Rx is going to be directly proportional to the magnitude of the reflection in the horn. Therefore, the ratio of power received at the Rx terminal due to unit power injected at the Tx terminal will represent the return loss of the horn.

At this point, if the Tx power arriving at the Rx port is completely absorbed, then the axial ratio of the Tx LCP signal will remain unaffected. If however, the RCP Tx signal at the Rx port is caused to re-enter the polarizer (by reflection from the TRF - transmit reject filter), it will re-enter the phase shifter as an LCP component. In the worst case, it will add in-phase with the signal from Tx. Now the axial ratio of the Tx wave will be changed by an amount proportional to the magnitude of the reflection from Rx port.



132

As an example:

Tx1 (LCP)

Rx2 (RCP)

OMT90o differentialphase shifter

Horn

Return loss = -25dbRCP

Total signal here = -24.8db

Isolation = 35db

VAR = 1.023a.r. = 0.2dbSignal out

LCP

Horn

Filter to rejectRx frequencies

Filter to rejectTx frequencies

TRF

RRF

Figure 4.4-2 View of the components contributing to a finite axial ratio in a 2-port Rx/Tx CP feed system

a. With a termination at the Rx port, all Tx signal is absorbed. b. With a 20 db mismatch (as represented by absence of a TRF), -42 db is returned to the

polarizer.

From Section 4.3, polarization discrimination (PD) is related to axial ratio (AR). For a PD = 42 db

dbPD

PDAR

compreflected 129.0015.1

1

1

)(

023.12.0)( dbAR incident

Total (degraded) voltage axial ratio = 0.329 db which corresponds to a polarization discrimination PD = 34.4 db.

c. With a 0 db mismatch (short circuit) as seen in the presence of a transmit rejection filter, the

-22 db is thrown right back into the phase shifter. For PD 22 db and reflAR 1.173 db or

1.38 db. Therefore, the total voltage axial ratio is 1.38 + .2 = 1.58 db or PD 20.8 db.

If the short circuit can be moved in phase with respect to the RCP signal from Rx, then the magnitude of the axial ratio can be altered in its frequency response, and in some circumstances even reduce the axial ratio by a small amount. But this will depend on the bandwidth requirements. The wider the bandwidth, the more difficult things become. In the case of Tx at 6 GHz and Rx at 4 GHz, the bandwidth is too large for a 90o diff. ph. shifter to be even realized, to offer an axial ratio of less than about 2 to 2.5 db in both bands. Fundamentally this is because the guide size will support various higher order modes at 6 GHz. It is possible to realize about 0.5 db axial ratio in the 6 GHz band, but at the same time achieving only 1.5 to 2.0 db at 4 GHz – this with the aid of dielectrics in the phase shifter. However, the use of dielectrics generally lowers the power handling capabilities of the polarizer. A thin quartz blade is a possible candidate for such an application. It has quite good power handling capacities - in the order of 1 kW. This configuration is mechanically quite fragile. A dielectric such as Teflon has undesirable thermal properties that causes mechanical distortion, leading to degraded axial ratio. Inevitably, 2-port Receive/Transmit polarizer networks are equipped with transmit rejection filters, (least expensive route), or diplexing junctions connected to the Rx terminal of the OMT – causing an inherent improvement in axial ratio/PD. To escape such difficulties, and achieve best polarization performance, the best solution is a 4-port dual polarized feed system with Rx and Tx ports which are not required for the mission, terminated.



133

General performance features: A well designed 2-port CP Tx/Rx feed system may offer a bandwidth ~ 15%, Return Loss < -25db (VSWR < 1.1:1), and Axial Ratio = 0.5 to 1.5db, equivalent cross-pol = 21.3db, Port-to-port isolation dependent on Tx to Rx rejection requirements. Physically, the length of the assembly will be approximately 6 wavelengths Applications: Single orthogonal pol CP receive and transmit feeds, which operate in a satellite link that is single uplink pol, and single orthogonal pol downlink. Typically used in Military single pol X-band operations. 4.4.1 4-Port CP Feed Network

QJ = Quadrature Junction TRF = Transmit Reject Filter

OMTQJ1 QJ2HornTx1 LCP

Tx2 RCPOMT

TRF

TRF

TRF

TRF

Rx1 LCP

Rx2 RCP

90o

ph. sh.90o

ph. sh.

QJHorn

TRF

TRF

TRF

TRF

90o Hybrid

Magic Tee

Magic Tee

Rx1

LCPRx2

RCP

MT

MT

Tx1 LCP

Tx2 RCPOMT

90o

ph. sh.

Note:The two magic tees perform the same function as the QJ2 in (a) .

The 90o hybrid performs the same

function as the 90o ph.sh.

[a]

[b]

Figure 4.4-3 Four-port CP feed networks 4.5 Polarization Rotation and Switching Operational situations arise when it is necessary to be able to quickly reconfigure the antenna system from CP to LP. For example, in the event the target satellite starts to tumble in its orbital position. When this occurs, the polarization of the signal arriving from the spacecraft will change from RCP to LCP. (The satellite antenna pattern main lobe is RCP, the wider angle side and back lobes will be LCP). To maintain the link, the earth station antenna will need to be able to follow by changing to an LP condition. In the LP mode, the e.s. antenna will be sensitive to both LCP and RCP signal components simultaneously, thereby maintaining contact for telemetry and corrective commands. For monitoring operations, having to move quickly from one satellite to another, changes in polarization condition will be necessary - some satellites being CP and others LP. In some instances, phenomena in the physical environment around the earth - atmosphere (rain), troposphere, ionosphere, various radiation belts - contribute to differential amplitude and phase shift between orthogonal polarization components, and even between uplink and downlink signals. The result of these errors is an elliptical polarization condition in which the ellipse can take on an arbitrary orientation. Corrections for these signal path errors can be accomplished by rotating the antenna polarization ellipse to the same orientation as that of the incoming signal, and independently adjusting for the same degree of ellipticity or axial ratio. Combinations of the components discussed in Sections 4.3 and 4.4 can be assembled for more complex feed systems that offer polarization control. All assemblies rely on mechanical means to adjust (rotate)



134

polarization angle, and select (switch) between polarization conditions. [This is mainly because feed system designs are predicated upon the use of low loss waveguide components which can be rather bulky. And electronically activated (ferrite) switches, which don't employ any moving parts, are relatively lossy elements]. These techniques are applied to both Rx and Tx signal paths. In a few limited cases, feeds operating single polarization Rx/Tx (CP or LP) are provided with quick release flanges with which to manually rotate the differential phase shifter. At the time of writing, only small aperture antennas with low uplink eirp and working C or separately X band Rx and Tx frequency bands are being handled in this manner. More in Section 4.5.1. 4.5.1 90 deg Differential Phase Shifter - CP/LP Selection Section 4.3.2 discussed the 90 differential phase shifter and OMT configuration. The differential phase shift is generated by the fact that the linear array of inductive pins has to be placed in a plane rotated 45 degrees from the horizontal or vertical polarization as referenced by the OMT. If the plane of the phase shifter pins is rotated into either the horizontal or vertical, then the E1 signal voltage from the OMT will not split into EV and EH components. E1 will remain linear vertically polarized. So the basic requirement to be able to switch from LP vertical to CP conditions can be fulfilled by simply rotating the 90 differential phase shifter around the feed axis between 0 (vertical pin orientation) to + or - 45 deg to get to CP - either RCP or LCP. An example is shown in Figure 4.5-1.

Figure 4.5-1 Photograph of the CP/LP selection polarizer assembly. On the left, a rotary joint that will connect to the horn. On the right the OMT. In between, a second rotary joint. The fixed plate carries a lever mechanism that allows the phase shifter to rotate between fixed limits. (Used with permission of General Dynamics SATCOM Technologies). Therefore, mount the 90 phase shifter between rotary joints, and connect mechanical means for rotation. The mechanical positioning of the phase shifter in the 45 deg latched position, needs to be accurately held from the point of view of achieving best axial ratio. For manual CP/LP switching in small antennas (with accessible feeds), quick-release flange connections at each end of the phase shifter may be adequate for the mission. Important Note: Differential phase shifters can be designed in circular and square waveguide. For fixed polarization applications, square phase shifters can be accurately designed. Circular phase shifters are somewhat more complicated in the design process. For the rotation of polarization, it is necessary to maintain axial symmetry. Since the circular phase shifter maintains axial symmetry for all angles of rotation, it is applicable for the purpose. However, square waveguide has only two distinct axes of symmetry, and therefore cannot be utilized for pol rotation. Additionally, since rotary joints are built on the basis of rotational symmetry in circular waveguide,



135

it would mean square waveguide components to be matched to circular waveguide for all polarization positions. Because of the differences between square and circular waveguide modes, attempting to rotate square/circular w/g components with respect to each other will result in mode mismatches, most commonly seen as mode spikes. Mode spikes represent discontinuities in the signal path. This will be discussed in Section 5.3 under the subject of system interference. Therefore, square phase shifters are never used in feed systems featuring adjustable polarization. 4.5.2 180 deg Differential Phase Shifter - LP Angle Adjust Only Suppose now two 90 deg differential phase shifters are connected in series, each in the same sense CP orientation. Intuitively, one can see the result will be 180 deg differential phase shift at the output, which represents LP, rotated by 180 deg from the 0 deg input (at the OMT interface). But what is not immediately evident is the fact that as the 180 phase shifter is rotated 45 deg, the output LP voltage vector rotates by 90 deg. This is shown in Figure 4.5-2.

E1 EV

EH

45o

y

x

(a) Reactive elements, e.g., a periodic structure of conducting posts OR (b) a dielectric vane in a plane orthogonal to the plane of the pins

EV

EH

y

EH

EV

90o

or g/4

EH

Ev

EH

LCP

180o

EV

E1

Figure 4.5-2 Layout of a 180 differential phase shifter. Input polarization is linear vertical. Output polarization is linear horizontal. Rotating the entire assembly will result in a corresponding polarization rotation. This represents a convenient method of adjusting LP pol angle, without having to rotate the entire LP feed assembly, or the rotation of the OMT with respect to the horn. The feed assembly can be bolted into place in the antenna, with only a small internal component needing mechanical rotation. Further, for 180 deg pol angle adjustment, the 180 phase shifter needs only to be rotated by 90 deg. Branch-line 180 degree Phase Shifter Noting that the bandwidth achievable with the pin-loaded phase shifter is only approximately 25%, greater bandwidth can be achieved with a waveguide branch-line assembly as shown in Figure 4.5-3.



136

1

3

42

42

3

1

Q1

Q2

"a"

"b"

Resultant 180 deg differential pol rotation

Figure 4.5-3 Wideband branch-line 180 degree differential phase shifter. For linear vertical input polarization, output is linear horizontal. Rotating the entire assembly results in a corresponding polarization rotation. (Used with permission of General Dynamics SATCOM Technologies). Two simple dual polarized junctions Q1 and Q2 transfer the vertically polarized input voltage "a" in circular waveguide, into two rectangular waveguide terminals 1 and 3. In a similar fashion, the horizontally polarized input voltage "b" is transferred from terminals 2 and 4 on Q1 to terminals 4 and 2 on Q2, thereby introducing 180 phase shift for “b”. Four equi-length waveguide interconnects link Q1 and Q2 as seen in Figure 4.5-3. Since the components in this scheme are wideband in nature, the 180 differential phase shift characteristic can be expected to be wideband also. Typically, one can expect 1.8:1 bandwidth, or about 55%. Bandwidth is defined here as the frequency band over which a polarization discrimination of >35db can be achieved. As an extension of the discussion on the branch-line 180 deg phase shifter, one can consider a 90 deg branch-line phase shifter, to achieve a significant increase in bandwidth. See Figure 4.5-4. Bandwidth is defined here as the frequency band over which an axial ratio of 0.5db can be achieved.

3

42

42

3

1

+45 deg ph sh

+45 deg ph sh

-45 deg ph sh

-45 deg ph sh

90o

Direcion of propagation

1 E1EV

EH

EH

EV

LCP

Figure 4.5-4 Branch-line 90 deg differential phase shifter The 45o phase shifters required here are waveguide components possessing wave propagation characteristics different from that of standard waveguide. The design involves a means of slowing or increasing the wave propagation velocity. Figure 4.5-5 shows a simple means to do this.



137

0o phase-45o

+45o

Figure 4.5-5 + and – 45 deg phase shifters as used in a 90 deg branchline differential phase shifter 4.5.3 CP/LP and LP Angle Adjust A feed system with complete polarization control can be assembled in one of two ways. (a) Use two 90 phase shifters with three rotary joints as shown in Figure 4.5-6(a) (b) Use one 90 and one 180 phase shifter mounted between three rotary joints as in Figure 4.5-6(b)

Horn

Rotary Joint

OMT180 differential phase shifter

90 differential phase shifter

Rotary Joint Rotary Joint

CP/LP selectPol angle adjust

Horn

Rotary Joint

OMT90 differential phase shifter

Rotary Joint

CP/LP select

90 differential phase shifter

Pol angle adjust

Support frame

1 2

Rotary Joint

Figure 4.5-6 (a) Two coupled 90 deg phase shifters; (b) two coupled 180 deg phase shifters; to achieve full polarization control. In (a), when both 90 phase shifters are locked (the array of phase shifting pins need to be in the same line), and rotated with respect to the fixed OMT, the result is a rotating LP. When the first 90 phase shifter is fixed with respect to the OMT (with the plane of the pins set to one of the principal planes of polarization), and the second is latched to a 45 deg rotated position, the result is CP for the feed. Question: What happens if both 90 phase shifters are locked while 90 degree rotated with respect to each other ?? Both are 90 diff ph sh. Does one still get 180 phase shift at the output ?? This requires the pol control system to possess: (a) an LP pol drive with angle encoder to monitor pol angle (b) a CP/LP select drive with limited +/- 45 deg rotation, and a lock between both phase shifters. In (b), independent of each other, the 90 phase shifter can be latched for CP/LP selection, and the 180 phase shifter rotated for LP pol angle adjustment, with pol angle encoder.



138

Point of interest: The 180 diff ph sh rotates the polarization ellipse, and changes the sense of polarization. In LP applications, horizontal pol changes to vertical; in CP applications, RCP becomes LCP. 4.5.4 90 deg Differential Phase Shifter - CP Adjust Suppose that the incoming signal from a target satellite is elliptically polarized, meaning, it has a non-unity voltage axial ratio. The orientation of the ellipse axis can be anywhere between horizontal and vertical. In the extreme, when voltage axial ratio >> 1, the incoming signal will look very similar to a linearly polarized condition. In rotating the 90 phase shifter from nominal 0 deg position to a 45 deg position with respect to the OMT, the polarization condition of the feed is changing from LP to CP. Therefore, for in-between positions, the polarization will be elliptical. To receive the incoming signal completely, we will need to rotate the 180 phase shifter to line up the polarization ellipse of the feed to match the orientation of the incoming elliptical polarization. This will require the pol control system to possess: (a) a pol drive mechanism for the 180 phase shifter with angle encoder to monitor pol angle over +/- 90 degrees. Note: In dual polarized satellite links, the nominal EV and EH signals will represent the vertical and horizontal polarized signal channels, and designated as such - often called "Pol A" and "Pol B". If the feed polarization must be rotated through 90 degrees or more (while moving from one satellite to another for example), the polarizations of "A" and "B" will be exchanged. However, from the communications control system aspect, the polarizations of "A" and "B" do not change. The impact of this is that the feed system must be able to change pol angle from 0 to 180 deg, and not just 0 to 90 degrees. (b) a pol drive mechanism for the 90 phase shifter with angle encoder to monitor pol angle over +/- 45 degrees. 4.5.5 CP/LP Selection - 2-Port Rx/Tx Feed The function of the 2-port Tx/Rx CP polarizer was discussed in detail in Sections 4.3 and 4.4. The differential phase shift is generated by the fact that the linear array of inductive pins has to be in a plane rotated 45 degrees from the horizontal or vertical polarization dictated by the OMT.

Horn OMT90 differential phase shifter

Rotary Joint

CP/LP select

Pol angle adjust

Support frame

Rotary Joint

Tx Rej Filter

Rx terminal

Tx terminal

Figure 4.5-7 2-port Rx and Tx CP/LP switchable feed network If the plane of the phase shifter pins is rotated into either the horizontal or vertical, then the E1 signal voltage from the OMT will not split into EV and EH components. E1 will remain vertically polarized. Tx pol will be vertical, and Rx pol will be horizontal linear. Rotate the plane of the pins cw into the +45 deg plane, Tx becomes RCP and Rx becomes LCP. Tip the plane of the pins ccw to -45 deg plane, Tx becomes LCP and Rx becomes RCP.



139

So the basic requirement to be able to switch from LP to CP conditions can be fulfilled by simply rotating the 90 deg differential phase shifter around the feed axis between 0 (vertical pin orientation) to + or - 45 deg to get to CP in either RCP or LCP. Therefore, mount the phase shifter between rotary joints, and connect a mechanical drive. The mechanical positioning of the phase shifter in the 45 deg latched position, needs to be accurately held from the point of view of achieving best axial ratio. Linear pol angle adjustment is obtained by rotating either (a) the entire feed package - horn plus polarizer assembly, or (b) just the OMT + Phase shifter at the back of the horn. 4.6 Combined Dual Polarized Tx/Rx Feed Configuration A frequently encountered satellite frequency plan includes Rx and Tx bands which are spaced in such a way that a common horn design is applicable. Table 4.6.1 Sample set of operational frequency plans (as of 2009) (a) Commercial C-band - Rx = 3.4 - 4.2 GHz and Tx = 5.85 - 6.65 GHz (b) Commercial "dbs" band - Rx = 10.7 - 12.75 GHz and Tx = 17.3 - 18.4 GHz (c) Variant of "dbs" - Rx = 10.7 - 12.75 GHz, Tx1 = 12.75 - 14.5 GHz, and Tx2 = 17.3 - 18.4 GHz. (d) Commercial Ka band - Rx = 17.7 - 20.2 GHz and Tx = 27.5 - 30.0 GHz (e) Military Ka-Q band - Rx = 20.2 - 21.2 GHz and Tx = 43.5 - 45.5 GHz This type of frequency plan can easily be handled with the use of a new frequency selective coupler called a QJ (Quadrature Junction). This is a 6-port device in which high and low frequency bands can be separated from a common path - in this case the horn. At the same time, the QJ represents a symmetrical transformer from symmetrical guide (square or circular) to rectangular waveguide. The QJ also represents a means for diverting one signal path away from that occupied by another - in this case, the Rx path from out of the way of the Tx path. Its application is shown in Figure 4.6-1 as the throat section of a tapered horn.

(a) (b) Figure 4.6-1 (a) Basic QJ; (b) feed network employing the QJ with an MT combining network. The straight-through path from the QJ ends in a pin-loaded differential phase shifter and OMT. (Used with permission of General Dynamics SATCOM Technologies).



140

4.6.1 Single QJ and Magic Tee Feed System Network Layout The basic design principle of the QJ/MT feed is as follows: (a) The smallest dimension of the QJ is set to pass the highest frequency band - in each of the examples here, the Tx band. (b) The Tx signal can be injected through an OMT for both linear polarization components EH

Tx and EVTx.

(c) The lower Rx frequency band signal will be in cut-off in this horn throat. (d) In a larger dimension of the QJ, four coupling slots are cut in the horizontal and vertical planes. This is done to preserve symmetry, and maintain low cross-pol features of the feed horn. (e) The Rx horizontal pol signal is coupled and summed in the magic tee MTH, the Rx vertical pol signal is summed in MTV. (f) The QJ is fitted with filters to reject Tx power from the Rx signal path. The output of the MTs now represent the EH and EV signal components of the Rx signal. At this point, if the feed is to be linearly polarized, the system is fully described. If the feed is to be circularly polarized, the addition of differential phase shifters will complete the system. In this case, the addition of a 90 deg hybrid will do the trick. See Figure 4.6-2.

QJHorn

90o Hybrid

Rx1

LCPRx2

RCP

MTH

MTV

Tx1 LCP

Tx2 RCPOMT90o

ph. sh.

V

H

V

H

H

EH EV

Figure 4.6-2 Single QJ and magic tee feed network. The QJ here is understood to be equipt with transmit reject filters in the coupled H and V side arms. The Rx paths should be fitted with band-pass filters or additional transmit reject filters. For the requirement to select CP/LP, a 90 phase shifter mounted between two rotary joints and connected to the OMT will be the choice for the Tx band. For the Rx band, the 90 deg hybrid will need to be switched in/out of the signal path. This is accomplished with two waveguide switches. The most difficult segment of this feed system is the design of the waveguide interconnects between the QJ and the MTs. The interconnects need to be mechanically identical, in order to preserve signal symmetry in terms of low cross-pol. Symmetry errors indicate phase errors between the EH and EV components, mean unwanted cross-pol components, and leading to lost signal (increased overall feed loss). To be noted, for example (c) in Table 4.6.1, Rx and Tx1 can together be coupled out from the horn to the side in the QJ, while Tx2 is left to go straight through. Further, the apparent over-lapping of Rx and Tx1 frequencies at 12.75 GHz represents an either/or situation which can only be solved with switches - a switch between (a) Rx = 10.7 - 12.5 GHz with Tx1 = 12.75 - 14.5 GHz, and (b) Rx = 10.7 - 12.75 GHz with Tx1 = 13.0 - 14.5 GHz. 4.6.2 Twin QJ Feed System Layout Here, instead of combining the EH and EV components coupled from the QJ1 into magic tees, we recombine them into a second QJ2. See Figure 4.6-3. The transformation from symmetrical circular guide can now be reversed, to move back into circular guide. This scheme is particularly useful when wanting to have independent pol control between Rx and Tx bands. Attached to the QJs we have differential phase shifters as required by the mission - one for Tx and one for Rx signals. These can be operated independently.



141

QJ1

QJ2

Rot

ary

Join

t

Rot

ary

Join

t

Rot

ary

Join

t

180 deg diff phase shifter




OMT

OMT

Corrugated Horn Rx: 5.850 - 7.025 GHz

Rx: 3.625 - 4.800 GHz

Feed Enclosure

Pol Angle Adjust Drive

Pol Angle Adjust Drive CP/LP

Select Drive

CP/LPSelect Drive

Hor/RCP

Vert/LCP

Hor/RCP

Vert/LCP

Feed Hub Interface

Note: QJ1 and QJ2 = Quadrature (Polarization) Junctions

Control

Control

TE21 Tracking Coupler

Optional

Combiner Network

(Optional) Error3.625 - 4.800 GHz

Super-extended C-band CP/LP Feed System Block Diagram Figure 4.6-3 Twin QJ feed system for full polarization control In fact, as need has occurred, the Tx path can be operated LP while the Rx path may be set up for CP operations. 4.6.3 Combined CP and LP Tx/Rx Feed Configuration Problem: Propose a feed configuration for the following application. A somewhat unusual satellite frequency and polarization plan has been built with two Rx bands working CP and LP, and two transmit bands working CP and LP, has been deployed. Specifically: Rx1 = 1.67 - 1.70 GHz horizontal polarization (HLP) Tx1 = 2.10 - 2.11GHz HLP Tx2 = 2.06 - 2.072 GHz RCP Rx2 = 2.23 - 2.25 GHz RCP Notice that the LP frequencies are very close to the CP frequencies, and it is not possible to adequately separate them with a QJ approach, to apply a CP network to one, and an LP network to the other. Figure 4.6-4 shows the idea. Step 1: Separate EH and EV components in the OMT. Then apply a 90 hybrid to generate the CP condition. Attach a Rx2/Tx2 diplexer. This satisfies the RCP requirement for Rx2/Tx2. Step 2: Build two diplexers to separate Rx1 and Tx1, and at the same time pass Rx2/Tx2. Connect to the EH terminal of the OMT This satisfies the HLP requirement for Rx1/Tx1



142

Tx2 = 2.06 GHz

Rx2 = 2.2 GHz

Tx 1

2.1

0 G

Hz

Rx 1

1.6

7 G

Hz

D3 diplexer

D1 d

iple

xer

D2 d

iple

xer

T T

T

H2H1

H3

F1 F2

F3

F4

H H

OMTFeed Horn

HLP

VLP

HLP

RCP

Nomenclature:HLP = horizontal polarizationVLP = vertical polarization

H = 90 degree hybridD = diplexer

F1 rejects 2.06 to 2.25 GHzF2 rejects 1.67 to 2.06 GHzF3 rejects > 2.1 and < 1.67 GHzF4 bandpass 2.23 - 2.25 GHz

OMT = orthomode transducerT = termination

path length equal to "a-b "with two compensators

a b

Figure 4.6-4 Multi polarization function feed system The most significant problem is to keep Rx1 and Tx1 separated. So the trick here is to use a variant in diplexer design based on the 90 deg hybrid. The diplexer configuration is based on the method of short-circuiting two of the hybrid ports to provide continuity of signal passage through the hybrid with no reflected components being lost. See Figure 4.6-5 to see this mechanism. Tx is applied to port "a" of the hybrid H. When both ports "b" and "c" are short-circuited, Tx is channeled to port "d".

a

b

c

d

1 watt in here

1 Watt out here = 2 times 1/2 Watt arriving in phase

The added path length to "c" here causes the time/phase delay in the signal relative to that travelling straight through to port "b".

Reflecting short circuit

Figure 4.6-5 Short circuited hybrid Now consider the short circuit to be generated by two filters "F" which reject F2 frequencies at H1, but pass F1 frequencies. See Figure 4.6-6. F2 signals in at port 2 will emerge at port 4. Connecting a second hybrid H2 to the reject filters, provides the means to inject F1 signals into these filters. H1 and H2 in tandem provide the path for F1 signals to reach port 4 of H1. Since no signal appears at port 3 of this diplexer assembly, it can be fitted with termination T. The only losses of this network are those related to the filters and any power split errors in H1 and H2.



143

Filter "F" to pass F1

and to reject F2

0db-3db

-3db0db

90o Hybrid H 1 90o Hybrid H 2

Termination

T

Input F1

CommonOutput for F1 and F2

Input F2

Diagramatic function of Hybrid-Diplexer

F

F

12

4

Eff

ectiv

esh

ort

circ

uit

for

F2

sign

al

Figure 4.6-6 Hybrid diplexer explained Applying this idea to the required feed system, we have one diplexer D1 for Tx1, and a second diplexer D2 for Rx1, coupled directly to the HLP port of the OMT. A third diplexer connected to the first and second diplexers to accommodate Rx2 and Tx2. Since Rx2 and Tx2 must work RCP, a single hybrid H provides EH

and EV field components with 90o differential phase shift, to be applied to the OMT which provides the 90 deg polarization rotation. An additional condition for the diplexers D1 and D2 is that Rx2 and Tx2 be able to pass directly to the horizontal OMT port. To complete the circuit for Rx2/Tx2 to operate in CP mode, EH and EV must have equalized electrical length for H to the OMT ports. 4.7 Feed System Terminal Characteristics What are some of these losses:

Terminal VSWR Port-to-port isolation Polarization discrimination Insertion loss

Let’s just review these items:

VSWR (related to return loss and reflection coefficient) - is a measure of the signal unavailable to the receive path since it is being reflected back out of the system.

o Acceptable system VSWR = 1.30:1 or = 17.7 db return loss. Port-to-port Isolation – a measure of the decoupling between the two output terminals.

o Acceptable isolation = 35 to > 40 db for LP configurations o Acceptable isolation = 17 to > 23 db for CP configurations

Why the difference between LP and CP port-to-port values ?? The answer lies in the discussion of Section 4.4. In CP networks, the RCP signal that is reflected from all components in front of the CP-polarizer is returned to the OMT as LCP, and vice-versa. Now, "port-to-port isolation" really means return loss of everything forward of the polarizer; and the "return loss" measurement effectively means return loss of everything behind the OMT.

Polarization discrimination – for an incoming (vertical pol.) signal, a large portion is guided by the

OMT to V-pol. terminal, and a small portion is guided to the H-pol terminal. The larger the ratio between V-pol and H-pol signals, the less the interference between the two. This measurement is performed with an LP test signal

o Acceptable polarization discrimination is 35 to > 40 db.

For circularly polarization - for an incoming (RCP) signal, a large portion is guided by the OMT to the RCP terminal, and a small portion is guided to the LCP terminal. The larger the ratio between RCP and LCP signals, the smaller the interference between the two. This measurement is performed with a CP test signal.

o Acceptable polarization discrimination is 30 to > 35 db.



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Insertion loss – signal that is absorbed in its passage through the network from horn to OMT terminals. The longer the length of this path, the smaller the waveguide, or the larger the VSWR, the greater the insertion loss.

o Acceptable insertion loss for standard feed networks ~ 0.25 to 0.5 db. o More complex feeds involving longer and/or fractional-height waveguide sections ~ >0.5db

4.7.1 VSWR - Effect of Multiple Contributions But we see that the feed is made up of several components, each contributing to the system VSWR, or return loss. Let us try to calculate the effect of each contributor. Remember that VSWR refers to voltage effects when a reflected wave interacts in phase with the incident wave at a reflective discontinuity in the path of travel. When two reflections meet in phase, they will add (constructively) to increase in magnitude. If they meet out-of-phase, the two will partially cancel each other. Since we generally have no phase information (normal bench measurements of return loss do not include phase) the worst case situation should always be considered, particularly if wide bandwidths are being considered. Suppose we have the following measured data on the horn and OMT. Return Loss

(db)

Reflection Coefficient

VSWR S

Horn

-30 →

0.0316 →

1.0653

OMT

-37 →

0.0447 →

1.0935

log20

= 10/20

S =

1

1

Immediately to be seen here, is that rapid deterioration in system return loss takes place when several components are added.

Worst Case Addition

-22.35 db ←

0.0763 →

1.165:1

Now let’s take into account the influence of the horn window, which may typically have a 1.02:1 VSWR. Return loss Reflection

Coefficient VSWR

Horn Window

-40.08 db ←

0.0099 ←

1.02:1

Worst Case System Addition Seen at OMT terminal

-21.3 db ←

0.0763 0.0862 →

1.189

And as far as the antenna as a system is concerned, we have not yet taken into account any reflective component from the subreflector, or the receiver assembly which is hooked onto the OMT terminals. Assuming for the moment that the contribution from the reflector is included in the reflector analysis (it is not negligible), the above calculated return loss represents the return loss of the feed as it would be measured in the lab. Or is it? It, of course, assumes that the contribution from the test setup (anechoic chamber) is negligible. But, in order to measure about 20 db return loss on the feed, we notice that contributions to the



145

measurement must be at least 20 db lower in magnitude – or less than 40 db. This is a rule of thumb. How do we evaluate an anechoic chamber? One easy way is to compare a RL measurement in a chamber with a measurement taken outside with the feed pointing to zenith. Reflected power in a feed is not available to the receiver, and can be considered lost. This is a loss component over and above that called insertion loss, which is caused by electrical resistance to the currents supporting the fields of the traveling wave in the waveguide. Return loss (db)

Power Ratio (PR) (loss power/total power)

Remaining Power = Efficiency 1 – PR

Reflection Loss (db)

RL

10RL/10

1 – 10 RL/10

10 log (eff.)

-21.29

0.007429

0.9926

0.032

4.7.2 Practical Matching Techniques All waveguide components will demonstrate a mismatched condition at any of several possible input and output terminals. Mismatch occurs internally at points in which discontinuities exist, as exemplified by bends, obstacles in filters, the presence of coupling slots, power dividing branches, or a combination of all of the above. Rectangular waveguide components:

mismatches may be tuned by adding extra mismatches (tuning elements) which are out of phase with the natural VSWR of the component

extra mismatches may be induced by squeezing/deforming the waveguide single tuning elements usually represent a narrow band feature a distributed set of tuning elements will increase bandwidth of the matched device when coupling more than one component, each must first be optimally tuned subsequent to connecting components, minor adjustments may be necessary

Component obstaclein rectangular waveguide

Tuning screws

MatchedVSWR

ScrewVSWR-1

ObstacleVSWR-2

Obstacle

tuningscrews

Signal in Signal out

Reflected signal out

Vmax

Vmin

Waveguide

Figure 4.7-1 A diagrammatic view of the mechanism for VSWR matching with tuning elements As discussed in Section 1.2, terminal VSWR or return loss will be given by

min

max

V

VS and Return loss =

1

1log20

S

S (1.2.1)



146

Rectangular waveguide components which are part of a “bridge” network – for example: Monopulse combiner network; QJ network with four equal and coupled arms; Array network requiring specifically phased sections In these cases, the technique of squeezing the guide to reach optimum matched conditions is NOT recommended. Squeezing deforms the guide in an uncontrolled manner, and it is unlikely that this action can be repeated equally in each network arm or section. This technique will lead to differential phase loss which can be significant for small matching phase errors. The approach instead is to determine by squeezing, where tuning elements are needed, then to install (tuning) screws. Screws can be set with precision and repeatability. Square/circular waveguide components

It is imperative to not disturb the symmetry of square/circular section waveguide components tuning elements must be distributed symmetrically with respect to the cardinal axes of the

component, or equally around the perimeter of the guide. generally, if the inherent VSWR of a component is high (poor match condition), then attempting to

find an acceptable match at the terminals will be unsuccessful. generally, a computer modeling of a component can be quickly optimized on the bench. Details of

necessary tuning elements are subsequently easily added to the model. 4.7.3 Polarization Discrimination - Axial Ratio and Cross-pol Definitions: Voltage axial ratio = r

Axial ratio = rra db log20.

Polarization discrimination1

1log20

r

rPD (4.3.2)

4.7.4 Port-to-Port Isolation Signal in at one port, the level of signal emerging from another port in the system. In a 2-port Tx/Rx system, the isolation should be high – in the order of 80 to 150db, depending on

Rx signal level Receiver signal level sensibilities Tx power level

For a 4-port Tx/Rx system, Tx1 – Tx2 and Rx1 – Rx2 isolations will be about >35db for LP systems, and about 20db for CP systems. 4.7.5 Insertion Loss Ohmic losses (w/g absorption and connection losses) For simple 2-port waveguide components or subassemblies, loss can be measured by injecting a test signal at one end, measuring how much appears at the other end, and compare input and output levels. If the device has coupled ports, this method is not always valid, since the coupled ports may be terminated or not be accessible. If the test device is a complete feed system with a horn, the only way of measuring insertion loss is to

measure the signal power emerging from the feed ports whilst knowing the power available at the horn aperture. However, to do this one has to understand the gain of the horn, something that is not easily measured.



147

measure the noise power emerging from the feed ports whilst knowing the noise power available at the horn aperture. Chapter 12 Section A.1 describes in detail how this is done. The measurement relies on knowledge of the noise power available from the clear sky, takes into account VSWR, port-to-port isolation of all the feed terminals, and therefore the result reflects the true insertion loss.

Important notes: The nominal insertion loss of a feed system is that associated with the waveguide size and metal composition of each component. Additional factors are:

flanges, and how well they are closed. Excessive lapping and gaskets problematic method of manufacture –

o electroforming - expensive o casting - expensive, but relatively inexpensive in quantity o full block machining - less expensive, but limited in scope o split-block design - inexpensive, but subject to mal-fitting parts leading to loss

Split block designs usually are made up of two segments separated along the length of the guide. When machining aluminum plate, it will inevitably warp once taken out of the machine. The mating surfaces will not close completely, regardless of how many fastening screws are utilized. This leads to micro-gaps in the current lines supporting the internal fields. These micro-gaps will radiate, thereby increasing the loss of signal. Further, it means external signals can gain access to cause interference. 4.7.6 Signal Delay Time For some special antenna applications, time and phase features of the satellite link signal are important for signal processing purposes. Since waveguide components will introduce phase and group delay for a band of frequencies, time for travel through the feed must be measured. Details about phase and group velocities are given in Section D.1.1 of Chapter 12. References [1] G. Mathei, L. Young, and E. M. T. Jones, "Microwave Filters, Impedance-Matchiing Networks, and Coupling Structures" - Artech House, 1980. [2] R. Gruner, “Earth Station antenna technology Seminar”, Comsat Laboratories, Clarksburg, MD 20734, April 1980. [3] J. Bornemann, V. A. Labay, "Ridge Waveguide Polarizer with Finite and Stepped-Thickness Septum", IEEE Trans Microwave Theory and Techniques, vol 43, No.8, Aug 1995 pp 1782-1787.

Chapter 5 – Antenna System Design Issues


148

Chapter 5 - Antenna System Design Issues 5.1 Polarization 5.1.1 Linear and Circular Polarization 5.1.2 Aspects of Cross-polarization in Antennas 5.1.3 Polarization in Offset Antennas 5.1.4 Cross-pol Matched Feed System for Single Offset Reflector Applications 5.2 Noise in Antennas 5.2.1 Noise Mechanisms 5.2.2 Signal-to-Noise Ratio 5.2.3 Noise Power 5.2.4 Equivalent Noise Temperature 5.2.5 Noise Figure 5.2.6 Antenna Noise Temperature 5.2.7 Noise in a Satellite – Earth Station Link 5.2.8 Antenna System G/T 5.2.9 Antenna Noise Temperature Components 5.2.10 Sky Noise Temperature Variation with Ambient Temperature and Humidity 5.3 Interference in Antennas 5.3.1 Introduction 5.3.2 Interference by the Transmitter 5.3.3 Interference by Tx Signal Power 5.3.4 Interference due to Tx Noise Power 5.4 Passive Intermodulation in Antennas 5.4.1 Brief History 5.4.2 Theory 5.4.3 Some Interesting Observations 5.5 Link Analysis 5.5.1 Uplink Analysis 5.5.2 Downlink Analysis 5.5.3 EIRP and Power Density



149

5.1 Polarization 5.1.1 Linear and Circular Polarization Linear polarization An important aspect of an electromagnetic wave is its polarization, a feature which describes the behaviour of the electric field. As we saw in Section 1, the electric field that is associated with a dipole is linearly polarized and lies in the plane of the dipole. If the dipole with terminal E1 is oriented vertically, the wave

VE is vertically polarized, and the dipole is considered vertically polarized.

E V

Dipole

E V

Wave approaching the dipole

Figure 5.1-1 Vertically polarized wave approaching dipole A second dipole with terminal E2 oriented horizontally on the same line of propagation will be considered horizontally polarized. An LP wave approaches the dipole pair. If the incoming field E is vertically oriented, it will be accepted

completely and seen at E1. If E is tilted by an angle , then a vertical field component cosEEV will

be detected at terminal E1, and the horizontal field component sinEEH , the cross-polarization

component, will be seen at terminal E2.

E V

E H


E V = Ecos

E H = Esin

E

E V

E H

= r = cosa

sina= cota

E1

E2

Figure 5.1-2 Tilted wave approaching dual dipole

The discrimination between VE and HE is measured in terms of a power ratio between terminals E1 and E2

22

2

1

H

V

E

E

E

E

Polarization discrimination is given by

2

2

1log10

E

EPD (5.1.1)

Power not received at the EV port is then

10101log10PD

lostpower (5.1.2)



150

If the dipole assembly is rotated by 90 degrees, HE will be reduced to zero, and all of the VE signal will be

received at terminal E1. This then suggests that a second independent LP wave could be received at the dipole assembly without interfering with the first, so long as it is oriented at right angles (orthogonally) to the first, as shown in Figure 5.1-3

E V

E H

Crossed Dipolesindependent

signal sources

E V

E H

Wave approaching the dipole

Figure 5.1-3 Two independent orthogonal waves approaching dual dipole The degree of independence is defined as the ratio of voltage seen at the vertical port E1, to the voltage

seen at the horizontal port E2 for an incoming vertical polarized field VE . Namely E1/E2 HV EE / .

If the incoming signal is tilted to exactly 45 degrees from vertical, then both E1 and E2 will receive the same

power level EEE 21

21 . Conversely, exciting E1 and E2 with the same signal source will result in a 45

deg polarized wave leaving the dipole pair, as shown in Figure 5.1-4.

E V

E H


E R

Crossed Dipolescommon signal source

E V

E HE R

Signal in

Figure 5.1-4 Horizontal and vertical excitation at E1 and E2 causes 45 deg tilted wave to leave dual dipole assembly An alternative to the cross-dipole, an OMT is a device which "merges" horizontal and vertical oriented

waveguide into a common symmetrical port - square or round - to support both VE and HE . The accuracy

of merging will define the magnitude of the cross-talk or "cross-pol", typically about -45 to -50db. Circular polarization In Section 4, the generation of circular polarized waves was considered by devising a scheme to divide an LP wave into two orthogonal components, and introducing 90 deg of time phase shift between them, as shown in Figure 5.1-5.



151

EREV

y

x

EH

Resultant ER rotating CCW field is left hand circular polarization - LCP

EV


z

EH

EV

On the other end, EV leading EH

by 90o phase produces right hand circular poalrizartion - RCP

90o

Figure 5.1-5 View of a circularly polarized or rotating wave

In this case, looking along the line of propagation, VE appears to rotate from the vertical to the horizontal

HE with the same frequency as that of the wave. While VE has decreased to 0 after 90 deg time phase,

HE has increased to its maximum value. For HV EE , the wave is circularly polarized - VE rotating ccw

as shown in the direction of propagation.

The measure of circularity is given by the ratio HV EE / , and termed voltage axial ratio.

HV EErva /r expressed as a voltage ratio (5.1.3)

and axial ratio or a.r.

dbE

Era

H

V

log20)var(log20.. (5.1.4)

expressed as a power ratio.

This condition can be achieved by introducing an LP wave at 1E into a differential phase shifter as

discussed in Section 4, and shown in Figure 5.1-6. 1E is split into components VE and HE at the pins.

The array of pins presents an inductive impedance to the wave, and the propagation velocity of VE will be

increased slightly relative to HE . If the array of pins is set appropriately, VE will reach the end of the row of

pins in ¼ of the time cycle ahead of HE , or leading by 90o time phase. The result is an LCP (Left hand

Circular Polarization) wave, with axial ratio )/(log20.. HV EEra .

Launching E2 orthogonally to E1 results in a reversal of polarization sense, with an RCP (Right hand

Circular Polarization) wave at the end of the phase shifter, with axial ratio )/(log20.. HV EEra .



152

E 1

E V

E H

E H

E V

z

45o

45o

90o or g/4

y

x

Reactive elements, e.g., a periodic structure of conducting posts


LCP

(a)

E 2

E V

E H

E H

E V

z

45o

45o

90o or g/4

y

x

Reactive elements, e.g., a periodic structure of conducting posts


RCP

(b) Figure 5.1-6 Circular polarization set up by a differential phase shifter. The direction of rotation of the incoming field vector towards the closest set of pins defines the sense of circular polarization. In (a), the closest set of pins to E1 is to the left; the resulting outgoing wave is LCP. In (b), the closest set of pins to E2 is to the right, resulting in an RCP wave. Given a feed with an OMT and a differential phase shifter, the two ports of the OMT will carry

simultaneously 1E and 2E to support LCP and RCP respectively.

Consider two orthogonal LP waves 1E and 2E at the input to the differential phase shifter. 1E is split

into 1VE leading 1HE corresponding to an LCP wave. 2E , because of its orientation by 90 degrees to that

of 1E , is split into 2VE lagging 2HE , corresponding to an RCP wave.

The ratio between 1E and 2E seen at the OMT terminals can be expressed as

21

12

2

1

HV

HV

EE

EE

E

E,

which says a component of 1HE is added to the vertical signal path 2VE (the numerator), and at the same

time, a component of 2HE is added to the 1VE signal path. But, since the 2HE component will be out of

phase with 1VE , the denominator will be 21 HV EE . For most OMT structures, 21 HV EE and

21 VH EE .



153

Therefore, HV

HV

EE

EE

E

E

2

1 (5.1.5)

Dividing top and bottom by HE , we get

1

11/1

2

1

r

r

E

E

E

E

E

E

H

V

H

V . (5.1.6)

2

2

1

E

E represents the power ratio at the OMT terminals, and equals the polarization discrimination, or

polarization isolation, between the RCP and LCP waves as generated in the phase shifter. Therefore,

Isolation or discrimination dbr

rPD

2

1

1log10

(5.1.7)

Or, in another practical way, axial ratio is given by

dbrra PD

PD

110

110log20..

20

20

(5.1.8)

The larger PD can be made, the greater the discrimination between RCP and LCP conditions, and the smaller the interference between the two signals. Notice these expressions do not give any indication as to sense of polarization. Elliptical polarization A definition of circular polarization can be stated as the path traced by the projection of the rotating field vector as shown on the right side of Figure 5.1-6. The tracing is a circle. If the tracing is not circular, but elliptical in shape, then the wave is considered elliptically polarized. There are two mechanisms that can prompt elliptical polarization. 1. The effect of differential amplitude

If HV EE , and assuming differential phase shift is 90o, then RE will appear to trace an elliptical path.

For the case 0HE , we end up with VE remaining vertically polarized. The general state of a wave may

be seen as elliptically polarized, ranging from circular to very nearly vertical or very nearly horizontal, depending on the differential amplitude between the H and V components. This is shown diagrammatically in Figure 5.1-7.

E VE H

RCP

E1

E V

E H


= - 90o

E H

E R

RCP

View of the polarization ellipse in the direction of propagation

E V lagging E H by 90o

E V

cw rotation of the pol ellipsewith E V > E H

Figure 5.1-7. Elliptical polarization prompted by differential amplitude

Further, if HV EE , and VE leads in time phase by +90 deg, then resultant RE will appear to rotate ccw

and defined as LCP. On the other hand, if VE is lagging HE by -90 deg, RE will appear to rotate cw, and

defined as RCP. This is shown in Figure 5.1-8



154

E VE H

RCP

E1

E V

E H


d = - 90o

E HE V

RCP


E V = E H

(a)

= 90o

E V

E HE V

E H


E HE V

LCP

E1

E V = E H

(b) Figure 5.1-8 Elliptical polarization prompted by differential phase 2. The effect of differential phase shift

If the differential phase shift is not equal to 90o, then for HV EE the resulting polarization will be

elliptical, and the orientation of the ellipse will be in the 45 deg plane between EV and EH. As approaches 0 deg (or 180 deg), the polarization of the wave tends toward the linear in the 45 deg plane. This is shown in Figure 5.1-9.

= 90o

E V

E HE V

E H


< 90o

E V

E H

E1

E V

E H


E HE V

= 90o

E H

E V

LCP

= 90o

E VE HE V

E H

Direction of propagationE H

E V

> 90o

cw rotation of the pol ellipsewith increasing

ccw rotation of the pol ellipsewith decreasing



E1

E1

LCP

LCP

E V = E H

E V = E H

E V = E H

Figure 5.1-9 The effect of change in differential phase shift on the ellipticity and sense of rotation of the polarization ellipse.



155

If HV EE , and is +ve, the resulting polarization ellipse will take on an orientation approaching the

vertical. The sense of rotation around the ellipse will be cw (RCP) by virtue HE leading VE ( = +ve) and

ccw (LCP) for = -ve.

If HV EE , and +ve, the resulting polarization ellipse will take on an orientation approaching the

horizontal. An interesting view of the changes in the polarization condition as changes from -180 to 0 to

+180 degrees, and as the relationship between VE and HE changes from 0/ 21 EE , is shown in

Figure 5.1-10.

Infinite

2

1

½

0

-180 -135 -90 -45 0 45 90 135 180

differential phase shift -

RCP LCP

counter clockwiseclockwiseE 1

E 2

Figure 5.1-10 Polarization ellipses as a function of the ratio E1/E2 and differential phase error with the wave going into the page. The phase error is positive for EV leading EH

Analytically, these ideas can be expressed as follows: Consider a plane wave with electric field E with V and H components

)sin(1 tEEV and )sincoscos(sin)sin( 22 ttEtEEH

tEEV sin/ 1 and tt 2sin1cos 21)/(1 EEV

Therefore sin1cos2

222

E

E

E

E

E

E HHH

2

12

2

1

2 cos1sin

E

E

E

E

E

E VHV

and 2

21

2

2

2

1

sincos2

EE

EE

E

E

E

E HVHV (5.1.9)

This expression has the form

122 VHVH EcEEbEa



156

which is the equation for an ellipse.

Here

22

22

2122

1 sin

1;

sin

cos2;

sin

1

Ec

EEb

Ea

The angular orientation of the major axis of the ellipse is given by

ca

barctan2

1

from which

22

21

2121 cos2E

arctanEE

E (5.1.10)

These expressions are diagrammed in Figure 5.1-11

Figure 5.1-11 The polarization ellipse

Providing 21 EE , the ellipse will always lie in a 45 degree orientation with respect to VE and HE .

Interaction between two elliptically polarized waves Consider two antennas as part of a communications link. Antenna 1 is transmitting an RCP signal with

voltage axial ratio 1r to antenna 2.

Question: What signal can be expected at the RCP (E1) and LCP (E2) terminals of antenna 2 with a voltage axial ratio

2r ??

The CP transmit features of antenna 1 are characterized by

2

1

1

2

1

2

2

1

1

1

r

r

EE

EE

E

E

HV

HV

The transmitter is connected to terminal E1. The phase shifter in the antenna will generate RCP waves. If

1r not equal to 1, a small amount of power has been converted to an opposite sense LCP component,

which is also transmitted.



157

The CP receive features of antenna 2 are described by

2

2

2

2

2

2

1

1

1

r

r

E

E

The larger the ratio E1/E2, the smaller the amount of power lost in E2 Antenna 1 is RCP. If antenna 2 is RCP, the wave from antenna 1 will be accepted by antenna 2. If antenna 2 is LCP, the incoming wave from antenna 1 will be largely rejected. The resultant power ratio seen at antenna 2 will be the vector addition of the power ratio due to antenna 2 and the power ratio of the incoming wave from antenna 1.

cos1

1

1

12

1

1

1

1

2

2

1

1

2

2

2

2

1

1

2,1

2

2

1

r

r

r

r

r

r

r

r

E

E (5.1.11)

From this expression it can be seen that the acceptance of the RCP wave from antenna 1 will depend on the phase angle between the wave from antenna 1 and the CP wave associated with antenna 2. For = 0 (in-phase condition), the power ratios will add, leading to a high cross-pol condition. For = 180 (out-of-phase condition), the power ratios will partially cancel, leading to a low cross-pol condition. This is shown graphically in Figure 5.1-12.

E1

E2

E1

E2

E1

E2

1,2

1

2

x

y

Resultant

E1

E2 2

E1

E21

E1

E2 1

E1

E22

[c] Cross-pol maximum

E1

E2 1,2

Resultant

R

[a]

[b] Cross-pol minimum

Figure 5.1-12 Cross-pol vector addition The variation in polarization discrimination as the wave axial ratios are changed can be seen in Figure 5.1-

13 for various tilt angles between ellipses. Here, for two polarization ellipses with axial ratios 1r and 2r , the

polarization discrimination PD is calculated for = 0 (in phase), = 45 deg, and = 180 (out of phase).

When 21 rr , the PD increases to infinite db.



158

Polarization Discrimination between 2 antennas with differing axial ratio and polarization ellipse orientation

0

10

20

30

40

50

60

0 0.5 1 1.5 2 2.5 3

Antenna 2 Axial Ratio - r2 - db

Re

su

lta

nt

Po

lari

zati

on

Dis

cri

min

ati

on

- d

b

0.00

0.05

0.10

0.15

0.20

0.25

0.30

Po

lari

zati

on

Lo

ss

- d

b

Antenna 1 a.r. r1 = 0.5 db

opposite sense dPsi = 0.0001 degrees

same sense dPsi = 179 degrees

dPsi = 45 degrees

Pol Loss db ___ dPsi = 0.0001 deg

Pol Loss db ___ dPsi = 45 deg

Pol Loss db ___ dPsi = 179 deg

Figure 5.1-13 Plot of resulting system

2,1PD vs axial ratio a.r.2 for a fixed value of axial ratio a.r.1.

Note: Psi = Pol angle . Another form for (5.1.11) is

2cos)1)(1(

)1)(1(4)1)(1(2

22

1

22

2121

22

21

21

2,1

2

2

1

rr

rrrrrr

E

E (5.1.12)

and

2,1

2

2

12,1

log10

E

EPD

From this discussion, we can see that attempting to measure the var (voltage axial ratio) of antenna 2 while receiving signal from antenna 1 is only possible if the var of antenna 1 is known. The only way of identifying the axial ratio of antenna 1 is by measuring the var of the signal received from antenna 1 with a rotatable perfectly LP reference in antenna 2 with var = infinite. This can have an enormous impact on the verification of antenna performance when attempting polarization measurements with a satellite test signal, since in most instances, the var of the satellite test signal is not known. For antenna 1 and antenna 2, the system axial ratio is

dbraPD

PD

110

110log20..

202,1

202,1

(5.1.13)

given that PD is measured in db .



159

At the same time, one can see that the "polarization loss", or power loss due to the presence of cross-pol,

goes to zero for 21 rr , but rapidly ramps up for large axial ratio differences. This lost power will be given

by

dbLossPD

10

2,1

101log10 (5.1.14)

An example of (5.1.7) is included in Figure 5.1-13 with the scale on the right side of the graph.

For the special case rrr 21

)cos1(1

12

2

2,1

2

2

1

r

r

E

E

For 180 , 0

2,1

2

2

1

E

E, meaning that dbPD

meaning that the system has no cross-polar component

For 90 ,

2

2,1

2

2

1

1

12

r

r

E

E

For 0 ,

2

2,1

2

2

1

1

14

r

r

E

E

The worst case situation is represented by 0 - when the polarization vectors add in phase, there is a

nominal 2 times increase in cross-pol level compared to that when 90 .

How is polarization discrimination affected by polarization angle rotation ??

Consider two nearly LP waves with axial ratio 1r and 2r , whose polarization ellipse positions are as shown

in Figure 5.1-14, with tilt angle .

Antenna 1

E 1V

E 1H

Antenna 2

E 2V

E 2H

Figure 5.1-14 Polarization ellipses of antenna 1 and antenna 2 tilted with respect to each other by angle . The vertical and horizontal components will add as follows.

sincos 221HVV EEE

cossin 221HVH EEE

The resultant ratio R is then

cossin

sincos

221

221HVH

HVV

H

V

EEE

EEE

E

ER



160

Dividing top and bottom by HE1 ,

cossin

sincos

1

2

1

2

1

1

1

2

1

2

1

1

H

H

H

V

H

H

H

H

H

V

H

V

E

E

E

E

E

E

E

E

E

E

E

E

R

(5.1.15)

Assume that 21 rr . This implies that VV EE 12 and HH EE 12 .

Therefore

cossin1

sincos

r

rrR

For 0 , rR and for 90 ,1

1

r

rR

This expression is plotted in Figure 5.1-15 for the case of 21 rr . For 0 , both ellipses are aligned,

and the minimum cross-pol is equal to r . As the polarization ellipses are rotated with increasing , the

resultant axial ratio or polarization discrimination decreases. For example, assume both waves have an axial ratio of 40db. This implies that the waves are nearly linearly polarized. If they overlay each other, then the resultant axial ratio (or polarization discrimination) will be 40db. If one is rotated or misaligned with respect to the other by just 1 degree, the resultant PD = 34.5db; a 5.5db loss in discrimination.

Sum of Two Tilted, Equal Magnitude, Same-sense Elliptically Polarized Waves

a.r. antenna 1 = a.r. antenna 2

0

10

20

30

40

50

60

0 1 2 3 4 5 6 7 8 9 10

Tilt Angle - degrees

Res

ult

ant

Po

l. D

iscr

imin

atio

n -

db

a.r. 50 db

a.r. 40 db

a.r. 35 db

a.r. 30 db

a.r. 25 db

a.r. 20 db

Figure 5.1-15 The change in system axial ratio (or PD) as two waves of equal axial ratio are tilted with respect to each other.

Referring to the earlier question - What signal can be expected at the RCP ( 1E ) and LCP ( 2E ) terminals of

antenna 2 with a voltage axial ratio 2r ??



161

Answer: The system polarization discrimination will be given by

2,1

2

2

1

E

E. The orientation of the

effective polarization ellipse will be found by rotating antenna 1 or antenna 2 around its axis to an angle

at which

2,1

2

2

1

E

Eis maximized. The small angle rotation between two nearly linear polarized waves

will have a significant impact on the system polarization condition. Example: (a) Antenna 1 emits a CP wave with axial ratio = 0.5db. Antenna 2, possessing an axial ratio characteristic a.r. = 0.3 db, receives this wave. The system PD when both waves are RCP will be 38.8db. When antenna 1 is RCP and antenna 2 is LCP, the system PD will be 26.7db (b) antenna 1 emits a nearly LP wave with axial ratio = 30db. Antenna 2, rotated in polarization orientation with respect to antenna 1 by an angle = 2 deg, and possessing an axial ratio characteristic a.r. = 30db,

receives this wave. The resultant system PD will be 26.2db. To correct for this degraded PD, we will need to rotate antenna 2 with respect to antenna 1 by 2 degrees This then suggests that in a 2 antenna system, each with an axial ratio of r , if the major axis of the polarization ellipse of antenna 1 can be rotated to be parallel to that of antenna 2, the cross-polar component of the system can be minimized. 5.1.2 Aspects of Cross-polarization in Antennas The near-field As described in Chapter 1, a signal as associated with a dipole is defined as “linearly polarized” and oriented in the direction of the electric field vector. If the field is viewed end-on from along the z-axis, the field vector can be represented by a straight line – that is, it is not curved. Viewed from the side, an elemental view of the field is curved near the dipole, and straight far away from the dipole, as shown in Figure 5.1-16.

y

x

E

Null along y-axis

z

Vy

Vy

-Hz

+Hz

VyDirection of propagation

[a] [b]

Figure 5.1-16 Near field cross-polar components of a dipole As stated earlier, rectangular waveguide is also considered linearly polarized. In contrast, circular waveguide carries curved field components across the plane of the circular aperture, Vx which can be considered as combinations of orthogonal field vectors, Vx, Vy and Vz seen in Figure 5.1-17. Where the field is curved, the field vector can be viewed as consisting of two orthogonal components – one vertical (Vy), another horizontal (Vz), but in the direction of propagation.



162

H-plane

E-plane

E

[b]

+Vx

Vy

-Vx

+Vz

Vy

-Vz

Vy

[a] [c]

+Vx

-Vx

Figure 5.1-17 Near field curved phase fronts for a waveguide aperture The far-field The region of the radiated field close to the dipole is called the “near field,” or Fresnel zone; far from the dipole, where the field is no longer seriously curved and approaching being planar, with a phase error of less than 16/ , it is called the “far-field” or the Fraunhofer zone. Polarization sensitivity How can we identify these aspects of rectangular and circular waveguide? Imagine letting these apertures radiate into free space, and measuring the radiation patterns. Figure 5.1-18(a) shows a linearly polarized horn being illuminated by a linearly polarized signal source. The setup is vertically polarized. Maximum signal is transferred from the source to the horn. (b) shows the signal source as having been rotated by 90 degrees. No signal is transferred along the axis from the source to the horn. (c) indicates a similar cross-polar condition when the horn is rotated 90 degrees instead of the source. (d) shows the horn and source co-polarized, and maximum signal is transferred from the source to the horn.



163

H-plane (azimuth) pattern

E-plane (elevation)

Azimuth

Elevation

Phase center

Rectangular horn vertically polarized

Fixed probe signal source - vertically polarized

There are no horizontal components here; therefore, when the source signal arrives at the aperture, it sees in effect a short circuit. Therefore, no signal is received.

Azimuth

Elevation

Phase center

Rectangular horn vertically polarized

ENo cross-polarized condition

Fixed probe signal source - vertically polarized

No cross-polarized condition

E

Elevation

Azimuth

Rectangular hornhorizontally polarized

Phase center45o plane pattern

-45o polarized

45o polarizedrectangular horn

45o

Azimuth

Elevation

[a]

[b]

[c]

[d]

Figure 5.1-18 Measurement of the linear polarization characteristics of a rectangular horn in the lab. (a) Horn and signal source are co-polarized. Az and El patterns as expected. (b) Signal source polarization rotated into the cross-pol condition. Ideally, no cross-pol. (c) Horn polarization rotated into the cross-pol condition. Ideally, no cross-pol. (d) Horn and source turned to the 45 deg plane and co-polarized. Az and El patterns as expected. As the source is rotated as shown in Figure 5.1-18(a) and (b), the signal received by the horn is zero. The signal level variation at the horn as the source is rotated is shown in Table 5.1-1.



164

From (5.1.12), it can be seen that polarization discrimination is dependent on 2cos which is also equal to

1cos2 2 and we can write PD as being proportional to )log(cos10 2 .

For a linearly polarized system, the pol angle will follow the very sensitive pattern as shown in Table 5.1-1 Table 5.1-1 Variation of PD with polarization angle

= 0o PD = 0 db co-polarized = 45o PD = 3 db = 88o PD = 29 db = 89o PD = 35 db = 90o PD = db cross-polarized This gives an idea as to the precision required to pol-match two antennas in a communication link. If the rectangular horn is exchanged for a circular aperture conical horn, the curved field components in the aperture lead to off-axis cross-pol lobes, as shown in Figure 5.1-19

Elevation

Azimuth

0o polarized

Cross-pol pattern

for the 45o plane

Elevation

Azimuth

+45o polarized signal source

45o plane

Co-pol reference

45o polarizedconical horn

Conical horn

Azimuth plane

Ele

vatio

n pl

ane

[a]

[b]

Figure 5.1-19 Co-pol and cross-pol features of the conical horn in the test chamber Notice that the cross-pol lobes in the 45o plane are equi-phase, but that between -45o and 45o planes, the cross-pol lobes are 90o out of phase. On axis, cross-pol signal is zero. Any asymmetries in the field distribution across the aperture will cause cross-pol shift with attendant on-axis null filling. In the presence of other modes, cross-pol peak levels can move across the axis. This is shown in Figure 5.1-20.



165

Ideal cross-pol

pattern in 45o planeAsymmetry in aperture

Other modes in cross-pol aperture fields

Pol. rotated component of the copol signal in the presence of a polarizer-OMT assembly.

[a] [b] [c] [d]

f C O C

Figure 5.1-20 Possible variations in the cross-pol patterns, depending on the presence of other modes and pattern symmetry Various forms of the cross-polarized pattern can occur as shown in the series of patterns above. From the above, it can be seen that for the LP signal from the source to be completely accepted by the receiving antenna, the pol orientation of both must be equal, within less than a degree, if a pol discrimination of greater than 35 db is to be achieved. Normally, as will be described (Section 6.0), the earth station antenna will be tracking the target satellite (either no-track, step-track or monopulse tracking). In the process, the target satellite will be moving slightly with respect to the RF axis of the e.s. antenna. In so doing, the cross-polar pattern will intercept off-axis signal in the orthogonal polarization, particularly if the target drift is not in a principal plane. See Figure 5.1-21

Cross-polpattern

Co-pol pattern1db

35db

0db

To satellite

Angle off-axis0 deg

Figure 5.1-21 Definition of specified cross-pol "under the 1db points" A specification frequently adopted is that not less than 35 db pol discrimination exist under the co-polar 1 db off-axis point – as shown in Figure 5.1-22. Why? Typically, a satellite link will be permitted a variation of 1db over a 24-hour period. This includes tracking errors and signal instabilities in both up- and down-links. Allowing amplifier instabilities equal to 0.5 db, the target may wander within the angular range associated with the signal variation of 0.5 db from maximum gain. During this movement, one would like to constrain cross-polar interference to more than 35 db below the co-pol maximum. Example: D = 4.5m F = 14 GHz

deg609.010 db ; deg333.03 db ; deg192.01 db ; deg136.02

1 db



166

1/2db = 0.068 deg

db = deg Corresponds to 1db contour

0db

0.5db

1.0db

0o

0.068o

0.096o


35db

3db

Cross-pol pattern

Co-pol pattern

Figure 5.1-22 Three dimensional view of co- and cross-pol pattern relationship The square around the circle of the ½ db beamwidth possesses an angular range across the diagonal in the 45o plane of 1 db. The cross-polar component is largest in the 45o plane. Therefore, the importance of the cross-pol level under the 1 db beamwidth. 5.1.3 Polarization in Offset Antennas Axi-symmetric reflector systems suffer from the effects of blockage by subreflector and feed. The offset reflector geometry becomes attractive because of a much reduced or even zero blockage condition. However, the asymmetry of the offset introduces cross-pol components. For the case of a pure LP illumination by a feed in the prime focus, significant off-axis cross-pol power can be expected. For the case of a pure CP illumination, the antenna pattern main beam of the reflector will be displaced. These effects are particularly important for the dual pol earth station antenna operating into a closely spaced satellite environment; even for the satellite mounted antennas looking into a wide area of earth stations. Let's examine the example of an offset design shown in Figure 5.1-23. The F/D = 0.61. The edge illumination (taper) of the reflector by the feed is 15db below the central peak value. In LP mode, the off-axis cross-pol will be about 22db. For the case of CP, the main beam of the antenna pattern will be displaced or squinted by an angle of about 18% of the half power beamwidth. If the antenna is transmitting in both RCP and LCP modes, the LCP beam will be displaced to the right, the RCP beam to the left, with a total difference between the two of 36% of the 3db beamwidth. This will also mean a decrease in the on-axis gain by approximately 1 db.



167

Focus

X

Z

Pa

rab

olic

re

flect

or

0.0

29.0

36.0

45.2o

43.2

22.3o

44.4o

44.4o

70.0

0db

10db

20db

30db

40db

0.5 0.3

Peak Xpol = 22db

1db BW Xpol = 27db

1db BW

LP Cross-pol pattern LP Co-pol pattern

1db

Spec = 35db


0db

10db

20db

30db

40db

0.5 0.3

1db


Circular polarization mode patternsRCP and LCP

Assumption: Feed system has no cross-pol Assumption: Feed system has no cross-polLinear polarization mode patterns

Co-pol and Cross-pol

Loss in on-axis gain

RCP beam displacement

LCP beam displacement

+/- 0.09 deg

00

Figure 5.1-23 A 1.8m antenna operating 20 GHz; F/D = 0.61 (a) is the cross-pol response (22db) in linear polarization mode; (b) is the beam displacement or squint (0.09 deg off-axis) when working in the dual CP mode. Note that the RCP beam is squinted to the left, and the LCP beam is squinted to the right, looking from behind the reflector. In accordance with acceptable levels of interference[1], the cross-pol discrimination should be more than 35db, at least under the 1db beamwidth. It is clear that this particular design will not fulfill this requirement. Compliance can only be achieved by one of three means (a) Increase the focal length to aperture diameter (b) Utilize a two reflector offset system (c) Use of a feed designed to compensate for the reflector generated cross-pol (see Section 5.1.4) Single offset reflector with prime focus feed With reference to Figure 5.1-24, a feed illuminating the reflector has a beam two times c. If there is to be no blockage by the feed, then o needs to be greater c. Some useful expressions for the offset reflector

design to determine the feed clearance and consequent maximum size mD of the reflector are given here:

FhF

ho 4/

arctan2

(5.1.16)

FDF

D

m

mco 4/

arctan2

(5.1.17)

co

FR

cos1

2 (5.1.18)

coRc sin (5.1.19)

Useful aperture cDD m (5.1.20)



168

o

Focus

X

Z

Pa

rab

olic

re

flect

or

0,0

D

h

c

c

c

RCP LCP

3db

s LCP

On-axis Gain

s RCP

Mechanical center

RF centerAzimuth

Ele

vatio

n

Azimuth antenna pattern

LP Cross-pol pattern

Focus

3db

1db

1db

3db

35dbLinear PolCross-pol

Requirement

No

Cro

ss-po

l

Elevation plane pattern

Condition: Feed pattern assumed with no Cross-polCP beam-squint

Dm

Figure 5.1-24 The single offset prime focus reflector geometry, and its polarization characteristics. These features assume that the feed is not contributing to the cross-pol condition. The cross-pol analysis for the offset prime focus geometry shown in Figure 5.1-24 has been very nicely described by Turrin in [2]. For the case of o = c, the cross-pol features of the offset antenna are summarized in Figure 5.1-25. Here it can be seen that for an F/D = 0.61, the cross-pol can be expected to be about 22db; and the CP beam displacement approximately 0.1deg. From Figure 5.1-25, the displacement /DN between RCP and LCP beams = 0.09 radians. For the D = 70 inch reflector,

operating 20 GHz, the displacement will be

044.0/180)54.270/(5.109.022 cmcmD

N degrees

Cross-pol vs F/DOffset Reflector geomtery - =

0

5

10

15

20

25

30

35

40

0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8

F/D

Cro

ss

-po

l -

db

0

0.02

0.04

0.06

0.08

0.1

0.12

0.14

0.16

0.18

- r

adia

ns

o c

D/λ

Figure 5.1-25 Theoretical LP cross-pol and CP beam displacement for a single offset reflector in which o = c for the condition that the feed does not contribute any cross-pol components.



169

Cross-pol vs Aperture Angle for offset parabolic reflectors

0

5

10

15

20

25

30

35

40

45

15 20 25 30 35 40 45 50 55 60 65 70 75 80 85 90

Aperture Angle - degrees

Cro

ss

Po

lari

zati

on

- d

b

o

c = 15o

o

c = Illumination Angle

c = 45o

c = 30o

c = 20o

Figure 5.1-26 shows the inter-relationship between o, c and achievable cross-pol. The smaller the aperture angle o and illumination angle c, the greater the cross-pol discrimination.

To help with the connection between o and F/D, see Figure 5.1-27.

Aperture Angle vs Offset F/DFor = = 0

10

15

20

25

30

35

40

45

50

0.5 0.6 0.7 0.8 0.9 1 1.1 1.2 1.3

F/D

Ap

ertu

re A

ng

le -

deg

o

o

o c

Figure 5.1-27 The relationship between aperture angle o and F/D for an offset parabolic reflector, for the

condition co .

As the F/D is increased, the cross-pol discrimination in the LP mode increases. In the example above, increasing the F/D to 1.2db will increase the cross-pol discrimination to 26db. Under these circumstances, the cross-pol under the 1db beamwidth will reach 35db for the LP case. And for the CP case, the beam displacement will decrease to 0.012 deg. On axis gain loss will decrease to about 0.1db. A good approximation for the beam displacement or squint angle is given by

/4

sinarcsin

Fo (5.1.21)



170

To achieve a 35db cross-pol system, an F/D = 1.2 would need to be considered, particularly if the feed chosen for the design contributes a cross-pol component. The choice of c will be made based on the required sidelobe envelope. For a low sidelobe envelope, choose c consistent with high edge taper (>20db). The structure will possess a very long feed support arm which will need to be accurately supported in a manner that the feed does not shift out of the focus. Pointing accuracy requirements (discussed in Section 8) will demand that the feed position be held to within less than 1/20 of a wavelength. If the operational polarization requirements are RCP or LCP alone, then the resulting beam squint associated with a short focal length reflector can be tolerated. The feed can be oriented in the focus to compensate for the squint. Example: Inmarsat operates L-band at Rx=1.55 GHz and Tx=1.65 GHz RCP only. Various S-band Tx=2.025 and Rx=2.2 GHz systems are operated RCP only. Because of the relative mechanical difficulty to build an accurate large offset antenna and maintain the necessary tolerances, offset antennas are generally kept below 5m in reflector diameter. If the antenna functions require a large feed causing blockage in the reflector, either as a result of a low frequency, or a multi-purpose application (such as dual polarization or cp/lp selection), the prime focus offset may not be an appropriate choice. An important point to note for the mounting of the feed. In contrast to the axi-symmetric reflector, there is no immediately obvious manner of physically locating the focus. The feed axis is tilted with an angle o. The focal line is parallel to the antenna beam axis. The easiest approach to locating the feed is to use a tool or template. To focus the system, the feed needs to move along the focal line - not along the feed axis, as it would if it were mounted into an axi-symmetric reflector. Dual offset reflector antenna The dual offset Gregorian geometry is shown in Figure 5.1-28. The subreflector presents a means to increase cross-pol discrimination. The field distribution in the subreflector and the main reflector are shown. The subreflector fields, when super-imposed on the main reflector, in large part cancel those on the main reflector, thereby increasing the antenna cross-pol discrimination. This occurs because the image of the subreflector is inverted, changing the direction of the cross-pol components.

o

X

Z

Pa

rab

olic

re

flect

or

0,0

D

h

c

c

c

RF center

Ele

vatio

n

Focus

Dm

F1

F2

Curved field components generated in the subreflector

Subreflector fields transformed into the main relfector aperture

The field lines associated with the offset parabolic main relfector

Parial cancellation of the cross-polar components for improvement in cros-pol performance compared to the single offset parabolic reflector

Elliptical subreflector

a

Figure 5.1-28 A view into the cross-pol condition in the dual offset reflector system and the mechanism for partial cross-pol cancellation with the use of a second curved reflector. Notice that the subreflector fields are inverted into the parabolic reflector aperture.



171

It is the radius of curvature in the respective reflectors which will leads to cross-pol. When these can be selected to cancel cross-polar components, then reasonable cross-pol discrimination can be achieved. For the dual offset Gregorian, an F/D = 0.6 can be chosen for the main reflector, and achieve 35db cross-pol discrimination. If one were to select a shifted segment of the subreflector so that the feed axis were co-linear with the reflector axis Z, the radius of curvature in the subreflector will decrease, thereby causing cross-pol to increase. For this reason, the feed will always be tilted along the "F2 - a" axis. Interestingly, the dual offset Cassegrain does not offer this benefit. Figure 5.1-29 shows that the cross-pol components of the subreflector actually add to those of the main reflector. The dual offset Cassegrain only becomes useful if the focal lengths of both sub and main reflectors are very long. An F/D > 1.2 will need to be selected to realize 35db cross-pol discrimination.

o

X

Z

Pa

rab

olic

re

flect

or

0,0

D

h

c

c

c

Ele

vatio

n

Focus

Dm

F1

F2Curved field components generated in the subreflector

Subreflector fields transformed into the main relfector aperture

The field lines associated with the offset parabolic main relfector

Parial reinforcement of the cross-polar components for a degradation in cros-pol performance compared to the single offset parabolic reflector


a

Figure 5.1-29 The dual offset Cassegrain shows the subreflector, curved in the same direction as the main reflector, without field vector inversion, reinforces the cross-polar component. The only approach to reduced cross-pol in this configuration is by choice of a significantly longer focal length F1. Possible design parameters for a compact dual offset Gregorian are: F/D = 0.6; o = 40 deg; c = 35 deg; Cross-pol = 35db under the 1db beamwidth; Sidelobe envelope as specified by ITU/FCC/Mil Std. The fundamental condition for this configuration is that the subreflector present at least a 10 wavelength aperture to the feed. If significantly smaller, the antenna sidelobe performance will not meet the international requirements. If the mission requires multiband functions, space for the feed conglomerate can be found between the two reflectors.

If the frequency demands a horn size that cannot offer a c to adequately illuminate the subreflector

without blocking either the subreflector or the main reflector, then the only choice is to redesign the subreflector. Some examples of large dual offset antennas which have been built are shown in Figure 5.1-30 1. 2.4m Ku band 2. 9m dual offset 2.8 GHz weather radar antenna built for CSU. This antenna demonstrated 38db peak off- axis cross-pol over the band 2.7-2.9 GHz for H and V polarizations.



172

(a) (b)

Figure 5.1-30. (a) 2.4m - for transportable applications, offset antennas are attractive since they can be "folded" into a small volume. (b) for a high-gain, very-low cross-pol (-40db) weather radar application. (Used with permission of General Dynamics SATCOM Technologies

Figure 5.1-31 Azimuth and Elevation antenna patterns the 9m dual offset Gregorian S-band weather radar antenna, showing measured 38db cross-pol discrimination.



173

5.1.4 Cross-pol Matched Feed System for Single Offset Reflector Applications As was mentioned in Sections 2.7 and 5.1.3, single offset reflector antennas possess an inherent cross-polar feature due to the asymmetry of the reflector aperture as seen from the feed in the focus of the reflector. This cross-polar component can be canceled by the introduction of an equal, but oppositely phased cross-polar component in the feed system [3]. See Figure 5.1-32.

Feed horn

F

Parabola

Focal Length "F"

Diameter "D"

Diameter "D"

Azim

Elev

Co-pol horizontal

Co-pol vertical

Azimuth pattern

Elevation pattern

No cross-pol

Cross-pol pattern

90o 270o

Field distribution required to compensate reflector generated cross-pol fields.

Azim

Elev

Field distribution in the aperture of a single offset reflector antenna

Co-pol vertical

Azimuth pattern

Cross-pol pattern90o 270o

Co-pol horizontal

Elevation pattern

No cross-pol

Figure 5.1-32 Offset reflector cross-pol compensation technique Let’s examine the details of a number of modes that can be generated in a circular waveguide feed horn to create cross-polar components equal and opposite to the cross-polar distribution in the aperture of the offset reflector.

45o planeco-pol pattern

H-plane (vertical) co-pol

H-plane (horizontal) cross-pol

45o plane cross-pol

-45o +45

-45o+45o

TE 11 - Pattern Features

E-plane (horizontal) co-pol pattern

-45o +45o

-45o phase+45o

+45o-45o

+45o -45o

H-plane (vertical) co-pol pattern


H-plane (horizontal) cross-pol pattern

45o planecross-pol

+45o

+45o

TM 11 -Pattern Features

Figure 5.1-33 Circular waveguide modes TE11 and TM11 and corresponding patterns



174


H-plane (vertical) co-pol

H-plane (horizontal) cross-pol

45o plane cross-pol

-45o +45

-45o+45o

TE 21 - Principal plane pattern features

E-plane (horizontal) co-pol pattern

-45o plane

+45o-45o

+45o phase

+45o

H-plane (vertical) co-pol pattern


45o planecross-pol

+45o

+45o

TE 21 - 45 o plane pattern features

90o

270o

180o 0o

180o

90o

0o

270o

Cross-pol (Horizontal)

Cross-pol (vertical)

Co-pol (Horizontal)

Azimuth - Vertical

Elevation - Horizontal

Figure 5.1-34 (a) Circular waveguide mode TE21 and corresponding patterns

Azim

Elev

90o 270o

0o 0o

90o

For horizontal components

TE21H + TE11

H modes

For vertical components

TE21V + TE21

V modes

Azim

Elev

Figure 5.1-34(b) Combining TE11 and TE21 modes for cross-pol compensation purposes If the feed is arranged to be as shown in the Figures 5.1-35, and turned upside down, such that the TE21 generating cavities are on the underside, then the resulting cross-polar components will offer partial cancellation of the offset reflector components.



175

Azimuth plane OMT

Rotary Joint

TE11

waveguide

TE21 supporting w/g diameter

TE21 generating cavitiesElevation

plane

Horn dimensioned so that phase of TE21 and TE11 are equalized in the horn aperture.

Figure 5.1-35 Cross-pol compensation feed for single offset reflector assembly If the horn is a corrugated structure, HE21 and HE11 modes must be generated and phased. Typically, this is a relatively narrow band device. To be noted: the horn must be maintained in this orientation with respect to the reflector principal planes. Therefore, the presence of the rotary joint. Small rotations of 20 to 30o can be tolerated without generating cross-polar levels. The resulting field distribution in the offset reflector fed with such a feed will then be as shown in Figure 5.1-36.

Co-pol (horizontal)Elevation patternLow level cross-pol

Co-pol (vertical)Azimuth patternLow level cross-pol

30db

0db

Feed

Projected view of the cross-pol compensated reflector aperture

0db

30db

Figure 5.1-36 Configuration of feed to “match” the cross polarization of the offset reflector.



176

5.2 Noise in Antennas 5.2.1 Noise Mechanisms Any mechanism which distorts, degrades, or masks the information carried by a signal in a communication link is termed interference. Two types of interference can be recognized: 1. “same signal” or coherent interference, which includes fading, reflection, depolarization effects and

intermodulation products. 2. Incoherent interference, which covers:

a. Thermal noise, phase noise, digital noise as system “internal” effects, meaning that these are system generated.

b. Lightning, ignition noise, and static, since antenna systems are exposed to these “external”

phenomena. At this time, we will consider only thermal noise. Let us examine, to get a feel for the mechanism of thermal noise, the following analogy: Look at a volume of water in a glass container. At cool temperatures, the water appears to be still. Upon heating, the particulate structure of the water visibly appears to move in a random motion – this even before the appearance of “bubbles” – showing that molecular motion is dependent on heat energy. This molecular activity reduces to zero when the water is cooled to “freezing.” Any material, and in particular a conductor, consists of “free electrons” (analogous to the molecules of water). With increasing temperature, the free electrons become more agitated and will collide with each other in a random fashion. The higher the temperature, the greater the propensity for collision. Hindrance to free passage for the electrons is termed resistance, or attenuation. The random electron motion generates a “secondary” voltage consisting of short duration pulses between collisions. This voltage can be measured across the ends of the conductor. From the above, we can infer that if the conductor is cooled sufficiently, electron collisions or “thermal noise” and therefore, resistance to current flow can be reduced to zero. In fact, this phenomenon can be observed if the temperature is reduced to -273oC. This temperature is called absolute zero, or 0o Kelvin. 5.2.2 Signal-to-Noise Ratio

Consider a signal current si flowing in a conductor at room temperature. Noise current ni will also be

present. If ns ii , then the signal will be masked by the noise and it will be difficult to extract the wanted

signal. Therefore, the system parameters must be dimensioned so that the wanted signal power at the detector be larger than the inherent noise power, and by a predetermined value that allows the signal to be processed with a “minimum acceptable quality” – i.e., minimal distortion. The “quality factor” here is NS / (Signal to Noise Ratio). 5.2.3 Noise Power What is the magnitude of the noise generated? This is best answered by looking at an equivalent circuit for the random current. The random current is operating in a conductor with resistance R and, therefore, generates an open circuit voltage. The magnitude of this open circuit voltage has been determined to be:



177

eo

R

dfe

kT

hf

kTRekThf

f

f

1

4/

20

2

1

(5.2.1)

The bandwidth of devices limits the frequency spectrum of the generated noise voltage. For typical applications kThf / << 1 and the bracketed function in the integral reduces to approximately 1.

T = physical temperature for the conductor (Kelvin) R = resistance (ohms) f = frequency (Hz)

k = Boltzmann constant = 1.380658 x 10-23 (Joules/Kelvin)

h = Planck constant = 6.626068 x 10-34 (Joule-sec)

Therefore, the expression for kTRe 420 • (Bandwidth)

Since the noise voltage is a randomly fluctuating value, it is convenient to consider the “average available

noise power.” The average voltage is 20e

. The average equivalent power in this conductor with resistance

R is

kTBR

e

P

o

n

2

2 (5.2.2)

From this expression, noise power from a resistor is independent of the resistance value. Further, it is seen that Pn is directly proportional to the physical temperature of the resistor, and thus we can consider this to be an “equivalent noise temperature.” For example, the resistor at 100 Kelvin physical temperature will have an equivalent noise temperature of 100K. 5.2.4 Equivalent Noise Temperature This leads to the concept that the equivalent noise temperature of a source is the absolute temperature of a resistor that would produce the same noise power as the actual source. Therefore, we can compare noise emissions of sources such as stars, the sun, the sky, electronic devices (receivers and amplifiers), transmission lines and attenuators, by knowing their equivalent noise temperature. Consider a 2-port device. Output noise power in bandwidth B is

nNGkTBN (5.2.3)

Where Nn is the noise power produced by internal noise sources in the system. G is amplification or signal gain of the device. Ti is the equivalent noise temperature of an externally connected noise source. Rearranging this expression slightly,

GkB

NTGkBN n

i

then )( ei TTGkBN (5.2.4)



178

where we are declaring the internal noise sources as having an equivalent noise temperature eT .

The total system noise temperature is then

eis TTT (5.2.5)

5.2.5 Noise Figure Another measure of the internal noise generated by a 2-port system is the noise figure F , defined as the

output noise power divided by the output noise power of the noiseless system (i.e., nN = 0), assuming input

noise is at refT reference temperature.

That is BGkT

NBGkTF

N

N

ref

nref

o

i

ref

e

T

T 1

and, refe TFT 1 (5.2.6)

Now consider two cascaded 2-port systems M1 and M2 with noise source Ti.

M1 M2

G1, Te1 G2, Te2

Noise source

Ti

Noise power 1N at output of M1 is

)( 111 ei TTkBGN

This is amplified by M2 and appears at its output as

)( 1212,1 ei TTkBGGN

The noise power produced by internal noise sources in M2 is given by

BkTGN e222

Total noise power is the sum of 2,1N and 2N

BkTGTTkBGGNNN eei 2212122,1 )(

1

2121 G

TTTkBGG e

ei

Total system gain 21GGGs

Total equivalent noise temperature 1

21 G

TT e

e

Now consider n – stages of 2-port devices in series.

21

3

1

21 GG

T

G

TTT

eeee (5.2.7)

21

3

1

21

11

GG

F

G

FFF (5.2.8)



179

If we consider a 2-port which has not gain, but attenuation – or inverse gain – and the input noise source is

refi TT .

From earlier eref TTkBN 1

Note: G corresponds to 1

; 1

But the noise power associated with refi TT is

BkTN ref

erefref TTkBBkT 1

and erefref TTT 1

or refe TT 1 (5.2.9)

from which we can see that the noise figure of a purely lossy 2-port is F .

5.2.6 Antenna Noise Temperature Now consider an antenna and feed configuration with an LNA, and an IFL (interfacility link) waveguide or

coax cable interconnect to a receiver. patternT is the effective temperature seen by an antenna and its

pattern from its surroundings.

G2, Te2a1, Te1 a3, Te3 G4, Te4

Feed Network

LNA ReceiverInterconnecting

w/g or cable(a)

Tpattern

The objective is to find the noise power due to all of these link components at the reference point (a). a. The noise power due to the antenna and feed is:

refpatternepattern TTkBTTGkBN 11

11

1

from which the “Antenna Noise Temperature” aT as seen at (a) is:

refpatterna TTT

1

1

1

11

(5.2.10)

Note: the IEEE Standard refT = 290K or 17C

Practically, refT = Ambient Temp

b. The noise power due to the LNA is always cited as that noise power seen at its input. And

therefore, the noise

2eLNA TT (5.2.11)



180

c. Since the IFL will have attenuation, its equivalent noise temperature will be seen through the LNA,

buffered by LNA gain. The noise temperature of the IFL with attenuation 3 is written in the same

manner as the effective temperature of the feed with attenuation 1 .

That is

refe TT 133 (5.2.12)

Therefore, the noise due to the IFL as seen at (a) is

refe

IFL TGG

TT

2

3

2

13

(5.2.13)

d. Receivers typically have a noise figure which represents a relatively high noise temperature. For example, a Noise Figure F = 12 db represents:

refe TFT 14

Kelvin4306290110 10/12

As seen from (a), this noise temperature will be attenuated by the IFL, and further reduced by the gain of the LNA. Therefore, the noise due to the receiver, as seen at (a) is given by:

23

23

4

1

1

/1 G

TF

G

TT refe

receiver

(5.2.14)

As an example, typical values encountered in an earth station system:

patternT = 50 K (freq – 4000 MHz, elevation angle = 10o)

1 = 0.30 db (feed losses) = 1.072 power ratio

refT = Tambient = 23oC = 273 + 23 = 296 Kelvin

2eT = TLNA = 65 Kelvin

2G = LNA gain = 50 db

3 = IFL cable attenuation = 20 db → 100

F = Noise Figure of the receiver = 15 db From the above considerations,

aT = 52.66296072.1

1072.1

072.1

150

Kelvin

LNAT = 65 Kelvin

IFLT =

29.029610

110010/50

Kelvin

receiverT

06.910010

29611010/50

10/15

K



181

Therefore, the total noise temperature at the reference point (a) is:

rceiverIFLLNAasystem TTTTT

= 66.52 + 65 + 0.29 + 9.06

sT 140.87 Kelvin

5.2.7 Noise in a Satellite – Earth Station Link What is the magnitude of this noise power in a typical communications link? And, why should we be concerned with it? Let us revisit the case study of Section 4.2.1. We had determined that the signal level budget for the satellite link was: Satellite transmitter power = 10 dbW Antenna gain = 30.57 dbi Satellite EIRP = 40.57 dbW Pattern loss = 10.75 db Path loss to e.s. = 195.8 db signal level at e.s = -165.98 dbW or -135.98 dbm e.s. antenna gain = 50.98 dbi Signal level at e.s. antenna terminal – ref. pt. (a) = - 85.00 dbm The effective antenna system noise temperature, as determined in Section 5.2.6 above is:

sT 140.87 Kelvin

The equivalent noise power is given by

BkTN ssystem

where B represents the bandwidth of the signal. For a broadband transmission, which occupies 1 transponder (40 MHz), we need to calculate:

systemN = 1.380658 x 10-23 x 140.87 x 40 x 106

= 7.78 x 10-14 Watts = -101.09 dbm This means the effective signal-to-noise ratio for this transmission will be NS / = -85.00 - (-101.09) = 16.09 db.



182

5.2.8 Antenna System G/T Since the signal to noise ratio is dependent on bandwidth, the nature of the transmission, and the power level of the signal carrying the information, some other measure of the quality of the antenna system needs to be determined. Since e.s. antenna gain is included in the determination of signal level and is an antenna characteristic, we

will represent “signal” with “gain.” Noise from just the antenna is best described by sT , neglecting the

bandwidth requirement since it will be a variable. Now a new “quality factor” can be written as:

eTemperaturNoiseSystem

gainAntenna

T

G

s

(5.2.15)

dbKs

dbi TGain )(log10

For our case study, sT

G = 50.98 dbi – 21.49 dbK = 29.49 dbK

Therefore, one major objective of any antenna design is to maximize sTG / , and for a given antenna size,

this will mean minimizing sT .

5.2.9 Antenna Noise Temperature Components Sky noise Earlier we stated that any noise source could be characterized by its effective temperature. This says that the earth is a noise source. The sky with all the stars, suns, galaxies and the atmosphere, because of its attenuation characteristics, in total represents a noise source. Some of these naturally occurring noise sources have been calibrated and demonstrate a variable frequency dependence. When an antenna is pointed into the sky, then it will see the integrated effect of the sky (stars, suns, galaxies, etc.), atmosphere, and whatever portion of the earth is captured by the sidelobe envelope. The sum total of all these noise contributors as seen at the aperture of the antenna is termed “Antenna Pattern Noise Temperature.” Since the atmosphere thickness (and therefore attenuation) varies approximately as

1/sin, the value patternT will be elevation angle dependent. Therefore, aT (antenna temperature) will be

related to the sidelobe envelope of the antenna pattern.

Earth surface

90o

Effective atmospheric height= approximately 10 km

5o

Local horizon

Antenna

Main beam

Sidelobes

Troposphere

Ionosphere

Atmosphere

GalaxySun

Local horizon

Earth

(a) (b) Figure 5.2-1 (a) The finite thickness of the atmosphere around the earth’s surface causes the atmospheric attenuation, and therefore noise temperature, to vary with elevation angle as represented by the magnitude of the arrow. (b) The noise at the output terminals of the antenna is the combination of external noise picked up by the pattern from its environment, and internal noise generated by ohmic losses in the antenna.



183

Figure 5.2-2 represents an antenna looking into the sky at an elevation angle of 30o. The boundaries for the ground are marked at elev = 0o and 180o. The temperature profile for the atmosphere is shown as a 1/sin

(approx) relationship, with the ground temperature equal to refamb TT = 290 Kelvin.

Knowing the antenna pattern, either by computation or measurement, and the profile of the atmosphere for the required frequency, then the antenna temperature for any particular elevation angle can be determined with the following expression:

180

180

180

180

90

0

sin

sincos

i

ij

ii

iijielev

pattern

G

GT

T

Where elev = Elevation angle for which Tpattern is to be determined

i = ith angle point in antenna pattern

j = jth angle point in polarization plane pattern

This expression is valid for circular symmetry patterns, but can be used to handle patterns without circular symmetry by averaging the results.

0o 90 180

Antenna Pattern Angle Off-Axis - degrees

Relative Power - db

0

10

20

30

40

30 120 1800-90 270

-90-180

ground

Tg = 290 K

Tatmosphere = a/sinelev

Local horizon

ground

sky temp due to stars, galaxies, sunTsky = 3.5 K

Elevation Angle - degrees

50

Figure 5.2-2 The superposition of the full antenna pattern in the elevation plane onto the temperature profile of the sky and the ground. This routine has been programmed, taking into account various ground conditions, local horizon configuration, and the noise temperature of the atmosphere for any frequency between 100 MHz and 60 GHz.



184

A short cut expression for antenna noise temperature is given in (5.2.8) which makes use of sky noise values shown in Figure 5.2-3. See also [4], [5].

11

1 fgeground

geskya TT

T

TTT (5.2.16)

where: skyT = value of sky noise temp given in Figure 7.9.3

geT = noise caused by sidelobes captured by the ground

groundT = effective temperature of the ground

= antenna (feed) loss (>1.0)

fT = effective thermal temperature of the feed components contributing to loss ( )

Sky Noise Temperature vs Frequency and Elevation Angle

1

10

100

1000

10000

0.1 1 10 100

Frequency - GHz

No

ise

Te

mp

era

ture

- K

elv

in

0 deg

1 deg

2 deg

3 deg

4 deg

5 deg

7.5 deg

10 deg

12.5 deg

15 deg

17.5 deg

20 deg

25 deg

30 deg

45 deg

60 deg

90 deg

0

90

2 5 10

30 60

20

Figure 5.2-3(a) Sky Noise Temperature vs Frequency and Elevation Angle for frequencies up to 50 GHz, and elevation angles 0 to 90 degrees



185

Sky Noise Temperature vs Frequency and Elevation Angle

1

10

100

1000

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22

Frequency - GHz

No

ise

Tem

per

atu

re -

Kel

vin

0 deg

1 deg

2 deg

3 deg

4 deg

5 deg

7.5 deg

10 deg

12.5 deg

15 deg

17.5 deg

20 deg

25 deg

30 deg

45 deg

60 deg

90 deg

0

90

2 5 10

30 60

20

Figure 5.2-3(b) Sky noise temperature vs frequency for frequencies ranging from 1 to 22 GHz, and elevation angles 0 to 90 degrees Antenna noise temperature A possible configuration of the antenna is listed here: Radome – antenna protection Beam waveguide Frequency selective surface – frequency diplexing Multi-port feed system – with selectable polarization conditions and tracking functions Redundant LNA assembly Connection to the receiver Each element will add noise to the system by way of ohmic loss, or a noise component that is coupled in from another source, or remove noise by way of mismatch reflections. Figure 5.2-4 shows a generalized noise temperature flow diagram.



186

Noise Temperature Flow from the Sky through the Antenna Ssystem to the LNA Input

Tsky (a function of frequency and elevation angle) Reference: "Antennas" by V. Blake Also: H. Schrank, "AP Newsletter", Dec 1984

Tpattern = (Tsky + Tradome). Tg

Tamb + Tg . 1

(abwg + aFSS)

+ Tamb . (abwg + aFSS) - 1

abwg + aFSS

Tg = 26 Kelvin - a fudge factor slightly dependent on elevation angle = noise temperature captured by a 29-25log(t) with -10dbi wideangle

envelope. = 30 Kelvin for a -5dbi wideangle envelope = 36 Kelvin for a -3dbi wideangle envelope Tx Gain

Tx Port 1 and Port 2

Rx Port 2

LNAAss'y T*lna

Rf Rf

RfRx Port 1

afeed

Ifeed

w/gFilter

Receiver

InterconnectLossai/c

ReceiverNoise

LNA

GLNA

NF

T*lna

as

Sw

Rs

Rx Gain

(abwg + aFSS) - 1

abwg + aFSS

+ Tamb

Tpattern

(afeed + aw)(1 - Rs) + T*lna . Ifeed . (1 - Rs)

2Tant =

Definitions: a = Insertion Loss (attenuation) I = Port-to-Port Isolation R = Return Loss T*lna = (273 + Tamb) noise from front end circulator on LNA NF = Noise Figure

abwg

Feed horn aperture

Tsky + Tradome (transmission and reflection components)

1 -

Note: "Tpattern" is an expression that approximates the integratednoise from the sky and the ground by the antenna pattern for elevationangles > 5 degrees for "large" antennas. It is assumed the main beam is always clearing the ground.

FSS

Radome

Reflectorsystem

Tant = total antenna noise temperature as seen at the switch Sw

RLNA

Rs = Rf + RLNA

Rf.RLNA

= worst case reflection loss

Figure 5.2-4 Diagram of signal and noise temperature flow through a reflector and feed system The following points offer a summary of the noise generators and their summation resulting in the expression for the overall antenna noise temperature.

1. skyT = Sky noise temperature as captured by the antenna pattern - function of frequency and elevation

angle. [4] 2. The radome has reflective, attenuative, and diffractive properties which add to the pattern of the

antenna, resulting in radomeT . radomeT = (transmission and reflection components as published by radome

vendor).



187

Alternatively,

10

10

10

10273

10

110273

rad

rad

radR

ambambrad TTT

(5.2.17)

will be a practical approximation for a nominal radome of current design.

3. patternT is an expression that approximates the integrated noise from the sky and the ground by the

pattern. The main beam will generally clear the horizon. gT ~ 26 Kelvin, a fudge factor slightly dependent

on elevation angle in approximation.

10

10

10 10

110273

10

26273

261273

FSSbwb

FSSbwb

FSSbwbamb

ambambattenradome

pattern TT

TT

T

(5.2.18)

4. Beam waveguide, when included, is an extension of the feed horn, and illuminates the reflector system. The small spillover and diffractive losses in the beam waveguide system will be partially absorbed by the

bw/g support tube called bwg .

bwg will have a value of about 1 to 3 Kelvin for a well designed bw/g system

5. The FSS, when included, is part of the feed aperture, and will contribute a noise temperature

component due to attenuation FSS .

6. The feed system signal path from horn aperture to nominal feed terminal, to which an LNA assembly is

connected, will attenuate received noise from the sky by feed .

6. Junctions in the feed network which can couple noise from terminations, other LNAs, or other functions

(transmit, tracking), will be isolated by nmI , .

7. The feed system terminals will show a Return Loss fR (VSWR).

2

101010

10

10

10

10110273101

10

110273

10

ff

filterfeed

filterfeed

filterfeed

RIsol

amb

Ramb

patternant T

TT

T

... (5.2.19) 8. The path between the feed terminal and the LNAs is usually equipt with a test coupler, possibly an extra

filter and a short length of connecting waveguide, all adding up to s with reflection sR . Redundant LNAs in

the assembly are equipt with a select switch and connecting waveguide to the LNAs with reflection lnaR .

LNA network insertion loss = db

s



188

9. The LNA input terminal also has a return loss lnaR which combines with that of the feed. Some of the

noise arriving at the feed terminal will be reflected back toward the feed horn aperture, and essentially lost.

LNA input return loss = db

lnaR

10. LNA – Feed interface return loss is given by

2020

2020

10101

1010log20

LNAf

LNAf

RR

RR

dbinterfaceR (5.2.20)

11. Equivalent network noise temperature is given by

10

RR

ambequiv

lnaf

s

s

TT 101

10

110273

10

10

(5.2.21)

12. The output of the LNA is generally routed through a coaxial switch network and some length of cable to a second stage receiver (downconverter). The receiver will possess a noise figure, the cabling attenuation, a residual of which will be seen at the input of the LNA as noise.

LNA Gain =dbi

LNAG

Post LNA attenuation = db

attenLNApost

Receiver Noise Figure dbNF Post LNA noise temperature contribution at LNA input is given by

10

10

10

110273

lossslnaPostlnaG

NF

amb

oncontributiLNAPost

T

T

(5.2.22)

13. Published/measured LNA noise temperature = LNAT . LNA reference temperature = temperature at

which LNA was calibrated/measured = refLNAT

14. The LNA, when equipt with an input circulator (to optimize VSWR), presents a noise temperature

component *lnaT which is radiated back towards the feed aperture. The junction VSWR at the select switch

will reflect some of this (not insignificant) noise back into the LNA.

15. LNA operating temperature = *lnaT

16. The LNA noise temperature LNAT is defined as the noise seen at the input terminal, calibrated at some

reference temperature. LNA operating temperature compensation

LNArefLNALNA

lnaLNAlnatempoperLNA T

TT

TTTT

5.1

*

273

273 (5.2.23)



189

17. Effective LNA temperature = network equivtempLNA postLNAcompoperLNALNAeffective TTTTT (5.2.24)

18. Antenna system noise temperature = LNAeffectiveant TT (5.2.25)

Table 5.2.1 Sky Noise Temperature vs Frequency and Elevation angle (digitization of Figure 5.2-3(a))

0 1 2 3 4 5 7.5 10 12.5 15 17.5 20 25 30 45 60 900.1 3000 3000 3000 3000 3000 3000 3000 3000 3000 3000 3000 3000 3000 3000 3000 3000 3000

0.15 1150 1150 1150 1150 1150 1150 1150 1150 1150 1150 1150 1150 1150 1150 1150 1150 11500.2 575 569 563 547 542 538 534 530 528 526 524 522 520 520 520 520 520

0.25 370 370 370 369 368 367 365 360 358 355 353 350 347 343 340 335 3300.3 242 242 242 242 242 242 242 241 240 239 238 237 236 235 234 232 230

0.35 178 177 174 173 172 171 170 170 170 170 170 170 170 170 170 170 1700.4 150 150 150 150 150 150 150 150 150 150 150 150 150 150 150 150 150

0.45 135 130 129 128 127 126 125 125 125 125 124 124 124 124 124 123 1230.5 120 112 108 104 103 103 103 102 102 102 102 102 102 102 102 102 102

0.55 109 99 94 90.5 89 88 86.7 86 85.6 85.2 84.8 84.5 83.7 83 82.6 82.3 820.6 102 89 83 78 75 73 71 70 69.5 69 68.5 68 67.5 67 66.7 66.5 66

0.65 97 81 74 69 66 63 61 60 58.7 58 57.5 57 56.3 56 55.8 55.5 550.7 94 76 68 62 58.3 56 53 51.5 50 49.5 48.8 48.1 47.3 47 46.7 46.4 46

0.75 92 72 63 57 54 51.5 47.8 46 44.5 43.5 43 42.5 42 41.6 41.2 40.5 400.8 91 70 60 54 50.2 47.8 44 41.5 40 38.3 39 38 37 37 36.2 35.5 350.9 90 67 55 48.7 44.7 42 37.3 34 33 32.8 32 31.5 30.8 30 29.3 28.3 27

1 91 66 52 46.5 41.8 38 32.7 30 28.5 28 27.7 27.5 27.2 26 25 24 231.5 93 65 46 40 34 29 24 21 19 17.7 17 16.5 15.5 15 14 13.8 12.52.0 94.7 64 45 37 31 26 21.5 18 16 14.5 13.5 12.7 12 11 10.5 10 9.4

3 97 65 44 36 29 24.5 19.7 15.5 13.2 12.2 11.2 10 9.5 9 8.4 7.5 74 100.5 66 45 36.2 29 24 19.4 15 12.7 11.5 10.5 9.7 8.8 8.3 7.5 6.9 6.25 105 68 47 37 29.5 24.5 19.5 15.1 12.7 11.4 10.5 9.6 8.8 8.1 7.4 6.8 66 110 70 49 38.4 30.7 25.2 20 15.5 13 11.6 10.5 9.7 8.9 8.1 7.5 6.7 5.97 115 73 51 40 32 26.3 20.4 16 13.3 12 11 9.9 9 8.2 7.5 6.8 5.98 120 76 54 42.5 34 27.5 21.5 16.7 13.8 12.5 11.5 10.2 9.3 8.5 7.7 6.9 5.99 127 80 57.5 45 36 29.5 22.7 17.5 14.5 13 12 10.7 9.6 8.7 8 7 6

10 135 84 61 47.5 38.5 31.5 24 18.7 15.5 14 12.7 11.3 10.2 9.1 8.2 7.2 6.111 144 90 65 51 41 34 26 20 16.5 15 13.5 12 10.8 9.6 8.7 7.5 6.312 153 97 70 55 45 37 28 21.5 18 16 14.3 12.7 11.4 10.1 9 7.8 6.613 165 105 77 61 49 41 31 23.5 19.5 17.5 15.5 13.6 12.2 10.8 9.7 8.2 6.914 180 115 84 67 54 45 34.5 26.3 22 19.5 17.5 15 13.3 11.5 10.2 8.7 7.315 195 130 95 75 62 51.5 39.5 30 24.7 22 19.5 16.8 14.7 12.3 11 9.4 7.816 215 150 110 88 72 60 47 36 29.2 25.7 23 19.5 17 14.2 12.1 10.3 8.617 236 175 133 102 85 71 57 43 35.5 31.5 28 24 20.2 16.5 14 11.5 9.518 258 205 160 128 107 88 69.5 54 45.5 40 35 31 25.5 21 17 14 11.319 275 235 195 160 135 113 89 70 60 53 47 41 34 28 22 18 14.120 287 260 228 192 166 145 114 92 80 72 64 55 47 39 30 24 19.521 291 280 260 230 208 183 149 123 106 97 88 80 66 55 42 35 29.522 292.5 290 280 265 245 220 192 155 135 126 117 110 90 70 53 44 4023 293 290 274 250 232 212 178 140 125 115 104 94 80 65 49 40 3724 293 286 260 230 211 190 155 120 108 98 87 77 66 54 42 34 3125 292 277 247 212 191 170 138 105 92 82 73 63 54 43 35 29 2626 291 267 232 194 178 154 124 93 81 72 63 54 46 38 31 25 2327 290 255 219 180 162 140 112 82 72 64 57 48 40 33 27 23 20.528 288 245 205 170 151 130 103 75 64 58 51 44 37 31 25 21 1929 286 240 195 164 144 123 96 71 60 54 49 42 36 30 24 20 1830 283 236 191 162 140 118 90 68 58 53 47 41 35 29 23 19 1731 280 235 190 161 139 116 87 67 57 51 46 40 34 28 22 18.5 16.732 277 235 190 160.5 138 114 86 66 57 50 45 40 34 28 22 18.5 16.533 276 235 190 160.5 138 114 85 66 57 52 46 40 34 28 22.5 18.5 16.534 277 235 190 161 139 116 86 67 58 52 47 41 34.5 28.5 23 18.8 16.535 280 236 193 164 140 118 88 70 60 53 49 42 35 29 23.5 19 1740 290 260 220 198 170 148 113 95 82 72 64 56 45 38 30 24 2145 290 280 260 239 218 190 164 130 110 95 85 78 68 60 44 39 3250 290 289 280 266 252 240 217 200 184 170 159 149 134 125 107 97 8555 290 290 289 286 278 270 263 260 258 256 255 253.5 251.5 250 247.5 245 24060 290 290 290 290 290 290 290 290 290 290 290 290 290 290 290 290 290

Fre

qu

ency

- G

Hz

Elevation Angle - degrees above horizon

5.2.10 Sky Noise Temperature Variation with Ambient Temperature and Humidity The earth’s atmosphere consists of oxygen (O2) 20.9% by volume, nitrogen (N2) 78% by volume argon (A) 0.93% by volume, plus some trace gases including carbon dioxide (CO2). They are mixed to a height of about 80km above the surface. The principle mixture is water vapour (H2O). The so-called “atmospheric reduced-equivalent thickness”, used to gauge air mass in the atmosphere at its zenith is defined, as the equivalent thickness of an isothermal atmosphere at 15oC at a standard pressure of 1 standard atmosphere. This thickness is about 8.5 km. The air mass decreases with increasing height, so that for all practical purposes, beyond 8 to 10 km above the ground, there is effectively no atmosphere. In the frequency range 1 to 60 GHz, the atmosphere is characterized by an absorption of microwave signals at 22.235 GHz due to the presence of water vapour, and at 60 GHz due to oxygen. It is the attenuation of microwave signal by water vapour at frequencies below and above 22 GHz, as well as in particular at



190

22.235 GHz, that leads to the emission of noise. Attenuation will increase as water content or density increases. Considerable work on understanding this phenomenon has been presented [5],[6]. References appear to show some discrepancy at low elevation angles for the noise temperature values, but for the purposes here, reasonably small in magnitude. The most important issue here is that sky noise temperature is quite dependent upon the ambient water vapour content usually measured as relative humidity at ambient temperature. The following extract from [6] – Figure 5.2-5 - gives some insight into the need, when making star measurements or satellite link analyses, to know the ambient temperature and the relative humidity. If necessary, in order to demonstrate compliance with specification, corrections can be applied.

0

100

200

300

1 2 5 10 15 20 30 40 50 60

Sk

y N

ois

e T

em

pe

ratu

re -

Ke

lvin

Frequency - GHz

90o

Elevation 5o

0o

Ambient Temperature

15oC 20oC 25oCRelative Humidity Water Vapour

100% 100% 75% 17 g/m3

80% 60% 45% 10 g/m3

25% 20% 15% 3 g/m3

Extracted from ITU-720

Sky Noise Temperature Variation with Relative Humidity

10o

20

40

60

80

120

140

160

180

220

240

260

280

3 4 6 7 8 9

Example 2

Example 1

Figure 5.2-5 Sky noise temperature dependence on ambient temperature and relative humidity that will influence antenna noise temperature values. The red dots indicate noise temperature conditions described in the following examples [6],[7]. Examples:

1. At Ku-band, f = 12 GHz, at 20oC and RH = 60%, skyT = 22 Kelvin

at 25oC and RH = 15%, skyT = 18 Kelvin

A variation in sky noise temperature = 4 Kelvin

2. At Ka-band, f = 20 GHz, at 20oC and RH = 60%, skyT = 103 Kelvin

at 25oC and RH = 75%, skyT = 148 Kelvin

A variation in sky noise temperature = 45 Kelvin



191

5.3 Interference in Antennas 5.3.1 Introduction Interference in the operations of an antenna, whether for the purposes of satellite communications, listening to small signals involved with remote sensing, deep space communications, or for radio astronomy observations, is always a severe problem for the antenna designer. We have discussed in Section 5.2 how noise, generated by the antenna itself, can interfere and limit small signal communications. However, the antenna and its surroundings are not the only sources for performance limiting interference. To be useful, communications antennas are fitted with one or more transmitters and high power amplifiers generating large signal power ... and noise. To receive small signals, antennas are fitted with low noise amplifiers and receiver systems, which also generate noise. It is an important part of feed design to limit the impact of these interferences on system performance. Amplifiers all have a number of important qualifying features, prompting the designer to pose the following questions: (a) Over what bandwidth does the amplifier provide the prescribed gain (signal amplification) (b) how much power can be fed to the input before the output starts to become non-linear (c) what is the degree of non-linear behaviour at this point (d) over what bandwidth does this non-linear behaviour occur (e) how much self-generated noise does the amplifier inflict on the wanted signal being amplified So we can see here that antenna design is guided not only by gain requirements, and (regulatory) sidelobe envelope and cross-pol requirements, but also by the performance parameters of the electronic equipment connected to the feed to ensure that a desired signal quality is maintained. Interference can be classified as self-inflicted or generated by external means. Self-inflicted interference refers to the possible interaction between the antenna and feed, and the various operational amplifiers that are connected to it. Specific filter and feed network design will handle these problems. Sources of interference (a) Self-inflicted by the transmitter

signal overpowering the desired receive signal by leakage of power from some part of the line connecting the transmitter to the feed, or even from the transmitter/HPA itself.

intermodulation signal products with resulting frequencies appearing in the designated receive band, which occur as a result of mixing two or more signals under non-linear conditions in the transmitter/amplifier and/or the antenna/feed.

wideband noise power - particularly that occupying the designated receive band - that leaks through the feed system network to overpower the desired receive signal.

(b) Self-inflicted by the chosen communications link

the target satellite radiating an eirp level which overpowers the low noise amplifier, leading to saturation and non-linear behaviour

by cross-polarized components from misaligned satellite traffic (c) Inflicted by others

by signal coupled from the sidelobe envelope of neighbouring antennas by signal captured from a neighbouring satellite because of a high satellite eirp

(d) Obstacles

by reflections from the radome (if present), other antennas, towers, buildings, or other natural boundaries such as trees or mountains (local horizon) in or near the signal path

(e) Environment

by the effects of rain attenuation and depolarization depolarizaton due to Faraday rotation in the ionosphere



192

Corrective filter application Some of the above interference mechanisms can be controlled with the use of appropriate filters. (a) Preventing RF leakage requires quality design and fabrication to ensure that there are no gaps in the RF signal path. Intermodulation effects can be minimized if not removed by the use of rejection filters in the output of the transmitter and the Tx and Rx signal paths of the feed. Special design features in the feed and antenna structure are required to reduce intermodulation to acceptable levels. The amplifier noise and power characteristics can be controlled with careful filter design, which in turn can have a strong bearing on the design of the feed system. These topics are of particular importance, and are discussed in Section 5.4. (b) Excessive signal level received from a satellite can only be checked with low gain devices or even attenuators. Interference from neighbouring satellites cannot be controlled except by regulatory agency, or by operating with a different satellite. (c) When neighbouring antennas transmit in frequency bands only slightly shifted from the receive band in the antenna of interest, transmitter power in over-lapping bands is often intercepted, causing unacceptable interference. Special rejection filter designs will reduce the interference. (d) Nothing can be done about local horizon effects (e) Polarization issues cannot be handled with filters. 5.3.2 Interference by the Transmitter The objective here is to determine the amount of filtering needed that will suppress the disturbing effects of the transmitter. The design of the necessary filters will not be addressed. The following case study illustrates the process for establishing the required filters needed for a Ku-band feed system. Case Study 1 Let's consider a Ku-band satellite link Rx downlink = 10.7 - 12.75 GHz, and Tx uplink = 13.75 - 14.5 GHz; linear polarization. A signal may be radiated to earth with an eirp = 20dbW.

This signal may be a modulated carrier in a 40kHz bandwidth channel at 12 GHz. The path loss for an average range of 36,000 km is 205db at 12 GHz. The signal level arriving at the antenna will be = -185dbW or -155dbm. System downlink For a 2.4m antenna looking toward the target satellite at 10 deg elevation angle;

with a feed loss of 0.5db, the antenna noise temperature is about antT = 76 Kelvin

For the LNA (Low Noise Amplifier), LNAT = 65 Kelvin, gain = 60db

Typical Ku LNA has a gain response depicted in Figure 5.3-1 1db compression = -20dbm Tx "desens. threshold" = -20dbm, damage threshold = 0dbm

Antenna system noise temperature sT = 141 K or 21.5dbK

Therefore noise power density in 1Hz bandwidth is

1.2075.216.228 kTNo dbW/Hz

= -177.1dbm/Hz. Antenna gain (assuming 70% efficiency) = 48.0dbi Antenna system G/T = 48.0 - 21.5 = 26.5 dbK at 12 GHz and elevation look angle to the satellite = 10 degrees.



193

8.35 9.38 10.41 11.44 12.47 13.50 14.53 15.55 16.58 17.61 18.64

Frequency (GHz)

Figure 5.3-1 Ku-band LNA gain vs frequency response. The response at 13.5 GHz has been suppressed with a built-in filter, in order to add isolation from the Tx, and keep the TRF filter losses adequately low. System uplink Frequency band = 13.75 to 14.5 GHz Antenna gain = 49.2 dbi eirp = 70dbW, therefore power = 120 Watts.

HPA (High Power Amplifier) gain = 70db A typical transmitter/amplifier may have a noise figure of about 20db, which means a noise temperature = 29300 Kelvin as seen at the input of the HPA. Unconstrained Ku amplifiers may have a gain response similar to that depicted in Figure 5.3-2.

Rx Tx

Gai

n -

db

Frequency - GHz

Over-lapping response of LNAand Tx amplifier (HPA) output

Rx

Tx

10.7 12.75 13.75 14.5

60db

70db

Figure 5.3-2 Example of the gain response of Ku amplifiers without special frequency constraining filters. Note: The overlap of gain response for LNAs and HPAs can be particularly harmful in the Ku band because of the proximity of the Tx and Rx bands operating in the same size waveguide. By way of contrast, at C



194

band, the separation between 4 GHz and 6 GHz bands is much larger, and there is practically no overlap. Besides, 6 GHz waveguide (WR-137 or WR-159) will not support 4 GHz frequencies. The gain response of Figure 5.3-2 suggests that about 300 MHz of Tx power will be seen by the LNA through the coupling between Tx and Rx signal paths. Furthermore, any noise generated by the Tx, particularly in the overlap band, will be picked up by the LNA. This overlap band is approximately 1600 MHz. In the case of a 4-port feed network, Tx and Rx functions can be co-polarized, meaning that 1. unless the Tx signal is suppressed or completely decoupled from the Rx signal path, the LNA is going to be overwhelmed with Tx power. 2. unless the Rx frequency signals from the Tx are suppressed or decoupled from the Tx signal path, the LNA is going to be overwhelmed with transmitter noise 5.3.3 Interference by Tx Signal Power Before being able to proceed, we need to understand how the system will be operated (a) multiple modulated carriers spread over the Tx band (b) single unmodulated Tx carrier (a) would represent "normal" operations for which all (or most) of the Tx power would be used. That is, 120 Watts (20.8 dbW) would be spread out over the Tx overlap-band of 300 MHz.

HzdbmHzdbmdbmMHzdbWdensitypoweroutspreadThe // 0.348.848.50300log108.20

This power density will be seen at the LNA, unless some suppression mechanism is installed into the Rx path. Question: How much suppression is required ?? Idea 1. We could say the total Tx power density "should not exceed Rx noise power density" = -177.1dbm/Hz, since the modulated Tx signals will, in effect, look like noise for the Rx path. This solution would represent a suppression of Tx power by a transmit rejection filter

dbTRF HzdbmHzdbm 1.143)1.177(0.34 //

If the LNA has a built-in 40db rejection of Tx band signal, as shown in Figure 5.3-1, then the power density at the LNA will be -74.0 dbm/Hz, and the rejection will only need to be 103.1db. Idea 2. Or we could suggest that this Tx power density of -74.0 dbm/Hz represented just an extra load on the power handling capacities of the LNA in the Tx band. Considering the Rx band channel (40kHz) resides in the "over-lap" band: The total Rx power for this channel at the LNA input will be

inputLNAatlevelsignalTGapertureantennaatlevelsignalRx

dbmdbKdbm 6.1285.261.155

dbmHzdbmHzdbm kHzinputLNAatlevelsignalTx 28)40log(100.74 //

So the TRF must now suppress Tx power from -28dbm to -128.6dbm

dbTRF dbmdbm 6.100)6.128(0.28

The C/N of the receive path = C/kTB, and for the 40kHz band

dbkHzNC 5.32))40log(101.207(6.128

Therefore the total TRF = 100.6 + 32.5 = 133.1db

dbTRF dbdb 1.1335.326.100



195

Either one of these TRFs could be placed in the Rx signal path to reject Tx band signal for the stated conditions and assumptions. However, to be remembered - filter insertion loss quickly ramps upward with increasing rejection performance. An approximate feel for the relationship is shown Table 5.3-1. Table 5.3-1 Approximate insertion loss characteristics of high rejection filters Ratio of closest Tx/Rx frequencies

Signal path insertion loss for each 100db rejection

>10% 0.1db

5% 0.2db

2% 0.4db

1% 0.8db

Rx path insertion loss as contributed by large filters can have a severe effect on Rx band noise temperature. Therefore, the inclusion of some of the filter requirements in the LNA, rather than all in the feed, is an important feature which LNA designers have successfully addressed, without dramatically impacting the LNA noise temperature. Note: If we are dealing with a 2-port feed in which the Tx polarization is orthogonal to Rx, and the OMT port-to-port isolation of (for example) 35db used to accomplish this, then the TRF would only need to be 133db minus the 35db in the LNA, giving 98db for the TRF. The above analysis requires detailed information about the system and its mission, not always available. To simplify the process for determining minimum Tx band rejection filtering, the following idea is generally accepted as appropriate. Idea 3. We could say LNA compression begins when total input power exceeds -20dbm, leading to the conclusion that we need only dbTRF 8.70)20(8.50

So now we have three different approaches for the TRF. In principle a big difference, caused primarily in the assessment of LNA power handling/rejection capabilities. But for accuracy, each application should require specific analysis, using available systems information. Question: How much Tx power can the LNA handle without affecting the Rx band performance ?? Often the necessary LNA gain response for the LNA is not available. Instead, what is sometimes published is a feature called "desens. threshold" for the LNA, and nothing at all about the suppression of Tx power in the Rx band. Desensitization threshold is defined as the signal level in the Tx band at the LNA input that causes the Rx band signal to compress by 1db. A typical value for "desensitization threshold" is -20dbm. Note that the desens level of an LNA cannot be determined just studying its transfer/gain response. Additional information with respect to the location of the filtering in the LNA and the dynamic range of the amplifying stages is required. Under these circumstances, in order to assess the necessary TRF filter in the feed, the following has to be done: Tx power density at the LNA input = 50.8 dbm LNA desens threshold = -20 dbm Damage level = 0 dbm Safety margin = 5 db The Tx power must be reduced to at least 0dbm. The "desens" level of -20dbm says that the Tx power must be suppressed by another 20db in order not to cause a 1db compression in the LNA.



196

Therefore dbTRF 8.755)20(08.50

Generalized:

dbdb

dbmdbmdbm

marginsafetycouplingRxtoTx

leveliondensitizatleveldamagepowerTxTRF

(5.3.1)

5.3.4 Interference due to Tx Noise Power While transmitting useful power, the Tx is also generating noise, as expressed by its Noise Figure NF .

This corresponds to an equivalent noise temperature

110 10

NF

ambHPA TT and for dbNF 20 ,

HPAT 29304 Kelvin. This noise is seen at the HPA input. A klystron amplifier can be expected to offer

this noise response. This noise will be amplified by the PA to reach GkTHPA , and the resulting noise power

will be

71029304231038.1log10 xxx = -113.9 dbW/Hz = - 83.9dbm/Hz

This level needs to be suppressed to at least the Rx band noise floor established in Section 5.3.2 equal to be -177.1dbm/Hz. To accommodate an addendum to the G/T specification (often times not specified, never-the-less usually intended) " Decrease in G/T < 0.1db when the Tx is turned on". 0.1db corresponds to 2% differential power. This means -16.3db. It is also equivalent to about 7 Kelvin noise temperature. Therefore the RRF (Receive band Rejection Filter) should provide suppression of Rx frequencies of

dbRRF dbdbmdbm 5.109)3.161.177(9.83 .

The RRF would be placed in the Tx signal path. Just as LNAs are designed with Tx band rejection filters, Tx amplifiers, particularly SSPAs (Solid State Power Amplifiers) are also equipt with internal filtering with typically a value of 50 to 60db.

dbRRF dbdbHzdbmdbm 5.5950)3.161.177(9.83 /

Figure 5.3-3 shows a typical response for an SSPA (Solid State Power Amplifier)



197

10.0 10.5 11.0 11.5 12.0 12.5 13.0 13.5 14.0 14.5 15.0 Frequency (GHz)

Figure 5.3-3 Gain response for a typical SSPA at Ku frequencies, showing a suppression of Rx frequencies in the range 10 to 13 GHz. Frequently, the exact Tx noise response is not available, and one must rely on an amplifier noise power statement in the instrument specification. Case Study 2 shows the error in RRF value that can be incurred for a TWTA (Travelling Wave Tube Amplifier). Case Study 2 A typical noise power density value for a TWTA (Travelling Wave Tube Amplifier) in the Rx band = - 65dbW/4kHz = - 29dbW/Hz = -71dbm/Hz. The rejection of Rx noise in the transmitter is 50db. Now

dbRRF dbdbHzdbmHzdbm 4.7250)3.161.177(71 //

All this to say that there must be an accurate understanding between antenna designers and the folks who build amplifiers that are to be clipped on the feed terminals. Generalized expressions for TRF and RRF are now: 1(a). Given a frequency response for the internal suppression of Tx band power:

dbdb

dbHzdbm

dbHzdbm

marginsafetypathssignalRxandTxbetweencoupling

nsuppressiosignalbandLNAfloornoisesystemRx

bandwidthTxterminalTxfeedatpowerTxTRF

/

)log(10

(5.3.2)



198

1(b) Given an amplifier desensitization threshold value:

dbdb

dbmdbmdbm

marginsafetycouplingRxtoTx

levelationdesensitizleveldamagepowerTxTRF

(5.3.3)

2. Given the Rx band noise characteristics of the HPA:

dbdb

dbdbHzdbm

Hzdbm

marginsafetypathssignalRxandTxbetweencoupling

rejectionsignalbandRxHPAlevelnoisesystemRx

terminalTxfeedatdensitypowerbandRxRRF

3.16/

/

(5.3.4)

Figure 5.3.4 shows the general rejection model for a feed system working Rx and Tx in close frequency proximity. To ensure rejection of signal noise power within the guard band, the filter cross-over rejection levels must add up to at least the rejection in the Rx band.

Rej

ectio

n -

db

Frequency - GHz

10.7 12.75 13.75 14.5

60db

85db

Guard band

Rx band Tx band

30db = minimum rejection in the guard band

Figure 5.3-4 Frequency response requirements for the feed system Point of interest: Figure 5.3-5 shows another operational Ku band frequency configuration which demands a much tighter Tx/Rx rejection in slightly shifted frequency ranges. The amplifiers for this application cannot be utilized for that shown in Figure 5.3-4. This sometimes becomes a dilemma for operators interested in converting their antenna systems for new Ku band operations, and wanting to use the same Ku LNAs.

Rej

ectio

n -

db

Frequency - GHz

10.7 12.25

12.75

14.5

60db85db

Guard band

13.25

13.75Rx band Tx1 Tx2

30db = minimum rejection in the guard band

Tx band

Figure 5.3.5 Variation in feed system filter requirements, dependent upon satellite system configuration. Rejection values will depend on the operational Tx power and the features of the transmitter and LNA.



199

If the LNA and/or the HPA responses do not overlap, then the filtering requirements can be reduced by the difference in response from "uniform" conditions just discussed. Points of Interest:

If the operational boundaries demand observing very low level satellite signals, then the size of the TRF with need to increase correspondingly.

If the Tx power must increase (e.g., due to weather), then the TRF will need to increase correspondingly.

If the Tx power must increase, it may also mean an increase in noise power density, adding now to the required RRF.

If the 2-port feed system must operate CP, then the effective OMT coupling will decrease from approx 35db to closer to 20db depending on the axial ratio of the overall feed assembly. This will then demand a corresponding increase in both TRF and RRF.

In some instances, HPA noise power density is measured directly, this value can be used to replace the 1st term in equation (5.3.4)

5.4 Passive Intermodulation in Antennas 5.4.1 Brief History Ever since the choice of certain frequency plans for multiple-carrier small-signal communication links, such as the 7/8 GHz band, interference phenomena were observed that are self-inflicted. Single carrier operations remained clean. However, when more than one carrier was introduced, the received signal path was disturbed with spurious signals that were related to the transmit signals in a particular pattern called intermodulation products. The mechanism appears to be a multi-paction" or "micro-arcing" process in the feed and antenna structure. The level of these self-inflicted interferences was such that the received low level signals from a target satellite were completely swamped. Observations have revealed several things: 1. Spurious signals are seen when transmit and receive signals occupy the same signal path [8]. 2. The spurious in the receive path are harmonically related to the transmit frequencies. 3. If the receive frequency band is selected to contain these harmonics, serious interference will result. 4. As the power level of the transmit signals in the feed/antenna system increases by 1db, the resulting disturbance in the receive band increases by a factor of approximately 3db. 5. Below a threshold transmit power level, no significant spurious is detected 6. Random spurious bursts in addition to the expected intermodulation products [9]. 5.4.2 Theory Analysis of the transfer characteristics of a non-linear passive device shows that for (2) equal amplitude signals with frequencies 1 and 2 at the input, an additional set of spurious frequencies will also appear as an unacceptable self-induced interference at the output. The largest in amplitude among these spurious

frequencies are the components with frequencies equal to 212 ff and 122 ff known as "third-order"

intermodulation products. The degree of non-linearity will determine the amplitude of 212 ff and

122 ff . For perfect linearity, the amplitudes of 212 ff and 122 ff will equal zero.

If a signal path exhibits non-linearities of a non-active nature (not involving amplification), then passive intermodulation or PIM is generated. An ordinary waveguide run consisting of several sections connected with standard flanges, will demonstrate PIMs.



200

\The multi-carrier amplitude transfer characteristic of a non-linear device can be represented by the polynomial

...55

44

33

221 SaSaSaSaSaaS iiioo (5.4.1)

where

oS = output voltage of the amplifier

iS = input voltage = ]2cos[1

tfvn

iii

na = constants associated with the waveguide device

if frequency

For a linear device, 0na for .1n

The components iS with exponents 1m represent intermodulation products of order m seen in the

output signal oS .

2nd Order PIM - 2 equal amplitude transmit carriers

For 2 equal amplitude transmit carriers to the device, tfvtfvSi 2111 2cos2cos

For 2m , called 2nd order intermodulation products or IM, will be represented by

2211122 2cos()2cos( tfvtfvaSa i

2nd Order PIM tftftftfva 22

21122

12 2cos2cos2cos22cos (5.4.2)

Evaluating this expression for single frequency elements,

2nd order PIM tfftfftftfva )(2cos)(2cos2cos2cos 212122

122

12 (5.4.3)

The transmit carrier frequencies are 1f and 2f . 21 ff and 12 ff will lie outside the transmit band and

can be blocked by appropriate rejection filters. We can conclude that even order PIMs are not going to affect a multi-carrier system. Let’s look at odd-order PIMs. 3rd Order PIM – 2 equal amplitude transmit carriers

For 3m , called 3rd order PIM, we have the components 32111 2cos2cos tfvtfvSi .

3rd order PIM will be given as

)2cos()2cos(2cos2cos2cos22cos 2122

21123

122 tftftftftftfvaSa i

tfftfftfftfftftf

tftfva

)2(2cos)2(2cos)2(2cos)2(2cos2cos2cos

2cos2cos

1212212121

2123

23

13

413

13

... (5.4.4)

The only contributors to 3rd order PIMs will be the terms 212 ff and 122 ff .

Among the possible intermodulation products, 3rd order PIM will possess the largest amplitude. As the frequency separation between transmit carriers decreases, higher order PIM frequencies will possess

increasingly larger amplitudes. For a given frequency pair 21 , ff and a given frequency Rxf in the receive

band, the order of the PIM can be calculated as

21

212

ff

fffm Rx

. (5.4.5)



201

3rd Order PIM – 3 equal amplitude transmit carriers For 3m , and operating with 3 carriers, we will have 3rd order PIM given by

3312111 2cos2cos2cos tfvtfvtfvSi

3rd order PIM 33213

22 )2cos(cos)2cos()2cos( tftftfvaSa i . (5.4.6) Resolving this expression into single cosine terms (in a manner similar to that done above) leads to 3rd order frequency terms

212 ff , 312 ff , 122 ff , 322 ff , 132 ff , 232 ff ,

212 ff , 312 ff , 122 ff , 322 ff , 132 ff , 232 ff ,

321 fff , 321 fff , 321 fff , and 321 fff

The following trigonometric identities are useful for these derivations

212121

21 coscoscoscos

2cos1cos 212

For a given frequency pair 21 , ff and a particular frequency Rxf in the receive band, the order of the PIM

can be calculated as 1232

1

ff

ffm Rx

. (5.4.7)

Specific cases of PIM frequencies Some operational frequency bands which can suffer from 3rd and higher order PIMs are: 1. For the military X-band frequency plan discussed in the preceding sections, the PIM frequencies that will occur are shown in Table 5.4-1. Operational power levels are considered as 1.25 kW for each of two carriers. Table 5.4-1 For the transmit frequencies marked along the left side and top of the table, the corresponding 2-carrier 3rd order PIM frequencies are highlighted in yellow. The lower table shows the 3-carrier 3rd order PIM frequencies marked in yellow.

0.050.05 7.90 7.95 8.00 8.05 8.10 8.15 8.20 8.25 8.30 8.35 8.407.90 7.90 8.00 8.10 8.20 8.30 8.40 8.50 8.60 8.70 8.80 8.907.95 7.85 7.95 8.05 8.15 8.25 8.35 8.45 8.55 8.65 8.75 8.858.00 7.80 7.90 8.00 8.10 8.20 8.30 8.40 8.50 8.60 8.70 8.808.05 7.75 7.85 7.95 8.05 8.15 8.25 8.35 8.45 8.55 8.65 8.758.10 7.70 7.80 7.90 8.00 8.10 8.20 8.30 8.40 8.50 8.60 8.708.15 7.65 7.75 7.85 7.95 8.05 8.15 8.25 8.35 8.45 8.55 8.658.20 7.60 7.70 7.80 7.90 8.00 8.10 8.20 8.30 8.40 8.50 8.608.25 7.55 7.65 7.75 7.85 7.95 8.05 8.15 8.25 8.35 8.45 8.558.30 7.50 7.60 7.70 7.80 7.90 8.00 8.10 8.20 8.30 8.40 8.508.35 7.45 7.55 7.65 7.75 7.85 7.95 8.05 8.15 8.25 8.35 8.458.40 7.40 7.50 7.60 7.70 7.80 7.90 8.00 8.10 8.20 8.30 8.40

f 1 frequencies - GHz

f 2 fr

equ

enci

es

- G

Hz

Two Carrier 3rd Order PIM frequencies - GHz

0.01 7.91 7.92 7.93 7.94 7.95 7.96 7.97 7.98 7.99 8.00 8.01

0.05 7.90 7.95 8.00 8.05 8.10 8.15 8.20 8.25 8.30 8.35 8.407.90 7.91 7.97 8.03 8.09 8.15 8.21 8.27 8.33 8.39 8.45 8.517.95 7.86 7.92 7.98 8.04 8.10 8.16 8.22 8.28 8.34 8.40 8.468.00 7.81 7.87 7.93 7.99 8.05 8.11 8.17 8.23 8.29 8.35 8.418.05 7.76 7.82 7.88 7.94 8.00 8.06 8.12 8.18 8.24 8.30 8.368.10 7.71 7.77 7.83 7.89 7.95 8.01 8.07 8.13 8.19 8.25 8.318.15 7.66 7.72 7.78 7.84 7.90 7.96 8.02 8.08 8.14 8.20 8.268.20 7.61 7.67 7.73 7.79 7.85 7.91 7.97 8.03 8.09 8.15 8.218.25 7.56 7.62 7.68 7.74 7.80 7.86 7.92 7.98 8.04 8.10 8.168.30 7.51 7.57 7.63 7.69 7.75 7.81 7.87 7.93 7.99 8.05 8.118.35 7.46 7.52 7.58 7.64 7.70 7.76 7.82 7.88 7.94 8.00 8.068.40 7.41 7.47 7.53 7.59 7.65 7.71 7.77 7.83 7.89 7.95 8.01f 2

fre

qu

enci

es

- G

Hz

Three Carrier 3rd Order PIM Frequencies - GHz





202

2. Ku/dbs band Rx = 10.7 - 12.75 and Tx1 = 13.75 - 14.5 GHz and Tx2 = 17.3 - 18.4 GHz. In this case, operating single carriers in each of Tx1 and Tx2 simultaneously can lead to PIMs detectable in the Rx band. Here the PIM frequency crops up as shown in Table 5.4-2. “dbs” refers to direct broadcast satellite service. Table 5.4-2 PIM frequencies for the three band Ku/dbs frequency plan. Only when 18 and 14 GHz signals are operated simultaneously, that the PIM issue becomes apparent.

0.0750.1 13.75 13.83 13.90 13.98 14.05 14.13 14.20 14.28 14.35 14.43 14.50

17.30 10.20 10.35 10.50 10.65 10.80 10.95 11.10 11.25 11.40 11.55 11.7017.40 10.10 10.25 10.40 10.55 10.70 10.85 11.00 11.15 11.30 11.45 11.6017.50 10.00 10.15 10.30 10.45 10.60 10.75 10.90 11.05 11.20 11.35 11.5017.60 9.90 10.05 10.20 10.35 10.50 10.65 10.80 10.95 11.10 11.25 11.4017.70 9.80 9.95 10.10 10.25 10.40 10.55 10.70 10.85 11.00 11.15 11.3017.80 9.70 9.85 10.00 10.15 10.30 10.45 10.60 10.75 10.90 11.05 11.2017.90 9.60 9.75 9.90 10.05 10.20 10.35 10.50 10.65 10.80 10.95 11.1018.00 9.50 9.65 9.80 9.95 10.10 10.25 10.40 10.55 10.70 10.85 11.0018.10 9.40 9.55 9.70 9.85 10.00 10.15 10.30 10.45 10.60 10.75 10.9018.20 9.30 9.45 9.60 9.75 9.90 10.05 10.20 10.35 10.50 10.65 10.8018.30 9.20 9.35 9.50 9.65 9.80 9.95 10.10 10.25 10.40 10.55 10.70


f 2 f

requ

enci

es

-

GH

z

Two Carrier 3rd Order PIM frequencies - GHz 3. L/S bands: Rx1 = 1.67 – 1.70 GHz and Rx2 = 2.24 – 2.25 GHz; Tx1 = 2.06 – 2.072 GHz and Tx2 = 2.1 – 2.11 GHz. The unusual aspect of this frequency plan is the interleaving of Tx bands between two receive bands. In this case, the higher order PIMs will emerge with quite high amplitudes, as shown in Figure 5.4-1.

Figure 5.4-1 Measured PIMs in a 13m L/S antenna system in which the PIM issue initially was not considered. Because of the close proximity of the Tx carriers, 5th, 7th, and 9th order PIMs are clearly visible. What is not shown is the 19th order PIM interference in the L-band. (Used with permission of General Dynamics SATCOM Technologies Inc.) Amplitude of PIMs If no suppression of PIMs is undertaken in the design of the feed and the reflector assembly, the magnitude of the PIMs that can be expected at the input to the LNA will be in the order of -20 to -40dbm in the presence of two 200 Watt carriers. In principle, an acceptable level of 3rd order PIMs is -170 dbm under the conditions of transmitting two 100 watt carriers as measured at the feed terminals. Some operational conditions require higher transmit power levels. And as shown in Figure 5.4-2 below, as input Tx power is increased by 1db, output PIM levels increase by approximately 3db. This then is approximately equivalent to a specification of -145 dbm under



203

the conditions of transmitting two 700 watt carriers, or -135 dbm with two 1400 watt carriers. A particular military requirement reads -135 dbm with two 1250 watt carriers. For other applications involving lower power levels, the PIM levels are often relaxed. A typical specification may read -145dbm with two 200 Watt carriers. However, regardless of such a specification, effort should be given to reaching -170 dbm, and not just -145 dbm, since conditions and circumstances may change for the worse with time. What is magic about -170 dbm ?? This just represents the practical noise floor in the measurement process. In principle, it would be better to try and reach even lower PIM levels. The sizing of filters should follow the routine as outlined in Section 5.3 and suggested in (5.3.2), (5.3.3), (5.3.4). The manufacturing techniques to guarantee such low PIM performance requires modifications to the standard antenna structure, special manufacturing methods for the feed system, as well as confirmation tests for PIM performance. There, the price for antennas with such requirements is more than antennas with no PIM specification. Causes of PIM in antennas A partial listing of such discontinuities includes: - Battery action caused by the contact between dissimilar metals. - Diode action in non-metallic junctions - for example in corroded junctions. - Any mechanism which causes current path leakage - for example flanges which are not completely tightened. - Any imperfect metal-to-metal contacts in the signal path in the aperture of the antenna such as represented by poor welds, panel rivets, or reflector panels that may be touching each other due to poor alignment. More details and some analysis is given in [7]. - If the transmit signal path leaks power in a manner that the antenna aperture can capture, the various discontinuities in the path will cause PIMs to be detectable. - If the Rx path before reaching the LNA leaks, any stray Tx power will have the chance to enter the LNA, prompting PIMs to interfere. Therefore, the design and manufacture of antennas for the purposes of being able to accommodate multi-carrier operations in closely spaced Rx and Tx bands becomes critical for the suppression of passive PIMs. The design entails the removal from direct illumination of all metal-to-metal contacts, as well as controlling the manufacture of absolutely clean feed system components with no discontinuities anywhere. And in order to reduce any residual active PIMs from the power amplifier and passive PIMs from the interconnecting waveguide, the feed system must include high rejection filtering to prevent such self-induced interference at the input to the LNA. 5.4.3 Some Interesting Observations 1. Fabrication must reveal complete continuity of the current path inside the various waveguide components. 2. Any necessary flanges require special treatment to ensure perfect closure. 3. Parts must be totally clean - devoid of any machining residues or particulate matter. 4. Transmitter generated PIMs need to be "killed" at the transmitter output with special bandpass filters. 5. Leakage of RF power into the space surrounding the antenna must be suppressed. 6. Any metal-to-metal contacts in the immediate RF path must be eliminated. For example: - reflector panels touching each other - mounting hardware for subreflector, quadrupod, feed fixtures, etc - dirt in the reflector - high metallic structures on the near local horizon 7. Large amounts of water will mask PIM generators of the type indicated in [8]. This phenomenon can be utilized to locate discrete sources of PIM, particularly in large reflector structures. 8. Small amounts of water can induce PIM generators into activitiy, as exemplified by the small effects of rain mixing with particulate in the immediate RF path of the antenna.



204

9. A general relationship between Tx carrier power levels 21 , ffP and the resulting 3rd order PIM level has

been established, expressed as

dbff

dbPIM PinchangeKPinchange 21 , (5.4.1)

where K can take on values in the range 2.0 < K < 3.0 For example: Tx power = 25 Watts per carrier, required PIMs = -142dbm at the input to the LNA. If the transmit power is changed to 50 Watts, this represents a change in power equal to 3db higher level. The expected PIM level for this higher power level will be at least 3 x 3 = 9db or Pimp = -133dbm at the input to the LNA. As seen in Figure 5.4-2, as the input power level increases, the value for K decreases to nearly 2.

PIM levels as a Function of Input Power Levels

y = -0.1246x2 + 9.5463x - 271.27

-160

-150

-140

-130

-120

-110

-100

-90

-80

10 15 20 25 30 35 40

Sum of two equal Tx carriers - dbW

Res

ult

ing

PIM

Lev

els

- d

bm

f = 7600 MHz

Poly. (f = 7600 MHz)

Figure 5.4-2 High power PIM characteristics measured in the Lab on a feed with a particular PIM characteristic showing a non-linear K relationship between input power level and resultant PIM level. For unequal carrier levels, the PIM problem is reduced, but should not be neglected. Figure 5.4-3 shows the result of unequal carrier levels.

PIM Response for Unbalanced Tx Carriers

Tx1 f1 = 7.9 GHz P1 = 1250 Watts

Tx2 f2 = 8.2 GHz

(a) P2 = 250 Watts (b) P2 = 500 Watts

(c) P3 = 750 Watts (d) P4 = 1250 Watts

-156

-154

-152

-150

-148

-146

-144

-142

22 24 26 28 30 32

Input Power Level - dbW

PIM

Re

sp

on

se

at

76

00

MH

z -

db

m

PIM levels at f = 7600 MHz

Figure 5.4-3 As one carrier level is reduced while holding the second constant, PIM levels are reduced, and K increases to 3.



205

Measurement of PIMs The measurement of PIMs requires a test setup as shown in Figure 5.4-4. The important features are 1. Two separate signal sources and power amplifiers with filters to eliminate significant active IMs. 2. The feed looking into an environment which will not introduce PIMs 3. A means to monitor input power 4. A means to monitor PIM levels at the input to the LNA.

Power meterto monitor input

power to the feed

Spectrum Analyzer to monitor PIMs

LNA

Fee

d S

yste

m

Cross-guide Coupler

Ban

dsto

p F

ilter

Diplexer

90o

Hybrid90o

HybridFilter

Filter

Termination

TWTA nr.2

TWTA nr.1Synthesized

Signal Generator

SynthesizedSignal

Generator

Tx

Wav

egui

de In

terc

onne

ct

Zenith Sky

Roof

RF Dev Labs

Figure 5.4-4 Test setup to measure PIM on a feed system. The same configuration is used to check for PIM in a reflector type antenna. The diplexer is intended to suppress active PIMs generated in the TWTAs. The bandstop filter is required to eliminate out-of-band Tx power from reaching the LNAs.



206

5.5 Link Analysis Sections 4.2.1, 5.2.7, and 5.2.8 detailed some fundamental aspects of a satellite link. The following paragraphs will consider some new link concepts and the relationship between eirp, gain, sidelobe envelope, and G/T. 5.5.1 Uplink Analysis For an uplink from an e.s. antenna of gain Ge.s. to a satellite, the carrier level to be expected at the satellite antenna of gain Gsat is given by:

satpl

seinputu G

GPC

..

(5.5.1)

Where inputP power in to e.s. antenna of gain Ges

pl path loss over slant range R from e.s. to satellite

at frequency

(c

f = wavelength)

The derivation of path loss is a little tricky, taken from basic field expressions. The electric and magnetic field expressions carry the form

14k

RE

(field potential function)

24k

RH

(field potential function)

in which it can be seen that the field strength decreases with increasing distance R (expressed in wavelengths).

The power HEP (analogous to IV in dc circuits)

2

4

1

R

P

The interpretation of

24

R

is therefore as an attenuation commonly referred to as “path loss". Now we

can write:

sates

satesi

u GR

eirpG

R

GPC

2244

(5.5.2)

where uC uplink carrier power level received at the satellite

inputi PP at the e.s. antenna

eseirp “effective isotropic radiated power” from the e.s. antenna

The definition of “power flux density” is the spread of power over a unit area of the sphere of radius R. The surface area of a sphere is given as:

S = 24 R



207

Therefore, 222

4

44

R

eirp

R

eirpP eses

d (5.5.3)

Substituting this last expression in the equation for uC

sates

satdu GR

eirpGPC

2

244

1

(5.5.4)

Where:

222 444 R

GP

R

GP

R

eirpP esiesies

d

(5.5.5)

and Pi can be written as the power input to the antenna to achieve a prescribed “Power flux density” Pd.

Pi = 24 RG

P

es

d (5.5.6)

Every link will be bounded by the noise floor of the uplink satellite antenna system. The noise floor will be given by:

BkTN satu (5.5.7)

Where, k Boltzmann constant = 1.380658 x 10-23 W/Hz/K

satT Satellite antenna system noise temperature (K) while looking at the 300K earth

B Bandwidth of the satellite receiver

Now the dynamic range of the useable signal as received at the spacecraft receiver is:

kBT

GP

BkTG

R

eirp

N

C

sat

d

satsat

es

u

14

1

42

2

(5.5.8)

Case Study 1 Given an e.s. antenna of 9.0m size, operating into a satellite system characterized by a (G/T)sat = -15 dbK, and a transponder amplifier which saturates when exposed to a power flux density (pfd) of -80 dbW/m2 in a bandwidth of 36 MHz (an analogue TV channel). The operational frequency is 14.25 GHz. The slant range e.s. to satellite is specified by an elevation angle of 10o and a range of 36000 km.

Earth surface

10o

Local horizon

Ges

R = 36000 kmsatellitesaturated pfd

= -80dbW/m2

(G/T)u = -15 dbK

Tx

IFL loss = 3db

Pi

Figure 5.5-1 Description of the satellite link for Case Study 1



208

cmGHzf

c

o

11.225.14

30

dbiD

mGes 7.6065.)0.9(2

antenna efficiency = 0.65

2/80 mdbWpfdsaturatedPd

k 1.38044 x 10-23 W/K/Hz = 228.6 dbW/K/Hz

B 40 MHz

dbKT

G

sat

15

Question: What is the input power at the 9.0m e.s. antenna required to produce saturation at the satellite?

dbdbimdbWRG

PP

es

di 1.1627.60/804 22

= 21.4 dbW or 138 Watts If we consider that the e.s. power amplifier (PA) is located at some distance from the antenna, the losses associated with the interconnecting IFL (interfacility link) must be added into the uplink budget. A typical IFL loss is about 3 db. Therefore, PA power output required is 21.4 dbW + 3 db = 24.4 db = 275 Watts. If we further consider that the PA must operate in the linear range, the power must be backed off by about 4 to 6 db. Therefore, the PA must be rated at 21.4 dbW + 3 db + 6 db = 30.4 dbW or 1100 Watts. The dynamic range of the uplink at the satellite transponder i/p is now:

kBT

GP

N

C

sat

d

u

14

2

0.766.2280.1553.44/80 2 dbmdbW

dP 2

4

satT

G

k B

= 13.0 db 5.5.2 Downlink Analysis Let us examine the downlink of this same signal to another e.s. antenna. The carrier signal level is given by:

espl

satd G

eirpC

(5.5.9)

Where sateirp “effective isotropic radiated power” from the satellite antenna

And, s

essat

d kBTG

R

eirp

N

C 1

42



209

kBT

G

R

eirp

N

C

s

essat

d

1

42

(5.5.10)

Case Study 2 Given an e.s. antenna of 4.5m, operating with a downlink frequency of 11.0 GHz with a bandwidth of 40 MHz, the downlink configuration is shown in Figure 5-5.2.

db

20o

R = 36000 km

Satellite

eirp = 50dbW

G/T

4.5m antennaEarth surface

Figure 5.5-2 Description of the satellite link for Case Study 2

dbD

Ges 4.5265.2

KelevTa 60)20( KTLNA 80

KKTs 5.211408060

dbKT

G9.30

0.76)6.228(9.304.20450 dbWN

C

d

eirp PL esT

G

k B

= 29.3 db If there is more than one downlink of equal bandwidth, then some form of power division must take place at the output of the LNA. For a satellite of 24 transponders, and an e.s. with corresponding receivers, a

minimum of 14 db power split loss must be included, causing the effective dN

C

to be reduced to 15.2 db.

For an IFL loss of 2 db, the dN

C

is reduced even further to 13.2 db.

The total system

du

du

NCNCN

C

/

1

/

11

,

(5.5.11)



210

208.100479.00501.0

1

db1.10

It is generally taken that the value of N

C should always be larger than 10 db for acceptable analogue TV

performance. 5.5.3 EIRP and Power Density Consider now the requirement to minimize interference of an uplink from an e.s. antenna into neighboring satellites. A typical radiation pattern for a 2.4m antenna at 14 GHz is shown Figure 5.5-3, with an allowed

uplink eirp of 76 dbW. The input power is given by:

gaineirpP 1 76 – 50 = 26 dbW

and the eirp at 1o off-axis is 55 dbW

0db

29-25log(t) dbi


10

20

30

40

50

76dbW 56dbW

66

56

46

36

266

16

26

36

46

On-axis eirp dbW/40kHz in 100 slots over 4MHz modulation bandwidth

Ant

enna

Gai

n -

dbW

Re

lativ

e p

ower

-

50dbi

40dbi

30dbi

20

10

0 dbi1 2 4 6 70

Pow

er

Den

sity

dbW

/40

kHz

eirp

- d

bW

Figure 5.5-3 Example 14 GHz pattern for a 2.4m antenna showing the amplitude scale in terms of antenna gain, the ITU 580 sidelobe envelope, corresponding eirp, and radiated power density. When the input power is modulated, the 76 dbW eirp will be spread over the modulation bandwidth.

Typically, the bandwidth slots are 4 kHz at 6 GHz or 40 kHz at 14 GHz [ITU 524-4 and IESS-601]. If we choose as reference 76 dbW/40 kHz power density, then for an 80 kHz bandwidth, there are two 40 kHz slots, and therefore, the resultant power density will be 76 dbW – 10 log (80/40) = 73 dbW. This means that as bandwidth is increased, the effective spectral power density (power per unit freq.) is decreased.

40 kHz

P

1.0

P

0.5

40 kHz 40 kHz Figure 5.5-4 Power density spreading with frequency



211

If we spread 76 dbW over 4 MHz in 40 kHz slots, the 76 dbW is effectively reduced by 10 log (4 MHz/40 kHz) = 20 db to 76 – 20 = 56 dbW/40 kHz. The effective eirp is now 56 dbW. Now a new scale can be added to the antenna pattern – on-axis

eirp dbW/40 kHz.

Therefore, the power density at 1o off-axis is 35 dbW/40 kHz. Now the 29-25 log (t) sidelobe envelope (SLE) corresponds to the 35-25 log (t) dbW/40 kHz off-axis eirp

envelope. The general expression for this is:

SLEgainbwslot

bwmodulationeirpaxisOneirpaxisOff

log10

from which

BgaineirpaxisOneirpaxisOffSLE log10

Example: eirpaxisOff 35-25 log (t)

eirpaxisOn 76 dbW

gain 50 dbi

B 4 MHz/40kHz = 100

SLE 35 – 76 + 50 + 20 = 29-25 log(t)

Power input for this is 76 – 50 = 26 dbW or 400 Watts This also says that in order to maintain the 35-25 log (t) dbW/40 kHz off-axis eirp characteristic, and it is

desired to increase eirp to 80 dbW, then the SLE must be lowered to 25-25 log (t).

Note: If the modulation bandwidth is not given, then the connection between off-axis eirp density and SLE

cannot be established. If an antenna with a sidelobe envelope lower than 29-25 log (t) is available, this becomes very attractive for an operator because he will now be permitted to operate with more input power, and therefore, smaller antennas at the signal receiving points, with greater C/N or signal quality in the total link.



212

References: [1] J. Dijk, C. T. W. van Diepenbeek, et al., "The polarization losses of offset paraboloid antennas", IEEE Trans. AP-22, July 1974, pp 513-520 [2] T. Chu, R. H. Turrin, "Depolarization properties of offset reflector antennas", IEEE Trans. AP-21, May 1973, pp 339-345 [3] B. K. Watson, A. W. Rudge, N. Adatia, “Dual-polarized mode generator for cross-polar compensation in offset parabolic reflector antennas”. 8th European Microwave Conference, Paris, France, Sept. 1978. [4] V. Blake, “Antennas”, Artech House, Inc. 1984 [5] H. Schrank, “Antenna Noise Temperature", IEEE - AP Newsletters, Dec 1984. [6] The ITU Report 720 dated 1978 [7] E. K. Smith, J. W. Waters, “Microwave attenuation and Brightness temperature due to the Gaseous Atmosphere – A Comparison of JPL and CCIR Values”, JPL Publication 81-81 for NASA, 15 August 1981. [8] R. C. Chapman, J. V. Rootsey, T. Polidi, W.W. Davison, "Hidden threat - Multicarrier passive component IM generation", American Institute of Aeronautics and Astronautics - AIAA/CAST Montreal, CA, No. 76, 1976. [9] W. H. Higa, "Spurious signals generated by electron tunneling on large reflector antennas", IEEE Proceedings, vol. 63, No. 2, Feb 1975

Chapter 6 – Tracking Feed Systems

MICROWAVE REFLECTOR ANTENNA DESIGN CONCE:PTS AND TECHNIQUES Roland Schwerdtfeger

213

Chapter 6 - Tracking Feed Systems 6.1 Introduction 6.2 Maximum Signal “Search and Track” Methods 6.2.1 Step Track 6.2.2 Conical Scan 6.2.3 Electronic Conical Scan 6.3 Zero Signal Track Methods 6.3.1 Phase-amplitude Monopulse 6.3.2 TE21 mode Coupler Design Concepts 6.4 Array Monopulse Feeds 6.4.1 4-horn “cross” Array 6.4.2 4-horn “corner” Array 6.4.3 The Integrated 5-horn Array 6.4.4 Polarization Requirements for Monopulse Functions 6.4.5 Monopulse Detection Methods 6.5 Array Analysis and Design 6.1 Introduction Ideally, any antenna pointed toward a target satellite should remain pointed for reception of maximum signal level. At the same time, the transmit (uplink) signal should also be pointing the beam maximum toward the satellite. However, in practice, the satellite is not completely stationary. Furthermore, the earth station antenna is not stationary either, since it will be subjected to wind loads, causing the reflector system to rotate and/or deform. For low look-angle operations, the atmosphere itself may introduce non-linearities that can cause beam squint. In order to accommodate such relative movements between e.s. antenna pointing and the target satellite, several things must be considered. In order for the RF link to be maintained within a prescribed 0.5 db variation, the antenna pattern beamwidth must be related to the magnitude of the angular pointing error. Mechanically, this is achieved by controlling the optimum position using

a. manual tracking b. automatic target following or tracking c. If the satellite is slightly inclined to the geostationary arc, use a form of program track d. If the satellite is in a highly inclined or even polar orbit, need to consider a special positioner

with precision track. For small antennas, the main beam half-power beamwidth will be much larger than the relative target displacement for operations with a nominal geostationary satellite. Case Study 1. Consider a 4.5m antenna operating at 4 GHz: The half power beamwidth will be approximately 1.1o. Geostationary satellites are usually kept on station to 0.05o or less. The signal variation due to a 0.05o movement of the satellite from beam axis of the e.s. antenna is determined using (2.5.1) as

2

21

33

nn PP



214

dbPn 025.0)1.1(

05.03

2

21

If, in addition, the e.s. antenna stiffness under normal wind loads (30 gusting 45mph) is maintained to less than 0.025o, the total angular excursion will be 0.075, and the total signal variation will be about

db055.055.0

025.005.03

2

, well within the allowed 0.5 db. See Figure 6.1-1.

Therefore, it can be said that this 4.5m antenna just needs to be parked looking toward the centered satellite look angle, and the signal link will remain within limits. And therefore, no automatic tracking system is needed to maintain station. It can be further said that no motor control even is necessary if a manual satellite acquisition mechanism is supplied – that is az, el hand crank, compass and precision calibrated inclinometer.

0db

0.03db

0.06db

0.05o

0.075o

3db

3 = 1.1o

Direction of satellite under conditions of satellite drift from center plus wind load/deformation effects.

In summary called "pointing accuracy"

Figure 6.1-1 Pointing characteristics of the 4.5m at 4 GHz. The antenna beam is sufficiently wide to encompass small satellite movement in geostationary orbit.

As a rule of thumb, acceptable pointing accuracy is 101 of the half power beamwidth or less. In this case we

have 0.075/1.1 or about 7%. Now, let’s look at the transmit conditions for the antenna at 6 GHz. Half power beamwidth is

.deg8.0450

5703 Now, the 0.075 deg pointing error will be about 10% of .3 The variation in the

uplink signal which the satellite receiver will see is db12.04.0

075.03

2

- happily still within the bounds

of 0.5 db allowed, but getting closer. Can we say now that the antenna needs no tracking? Answer: Yes. Case Study 2. Consider now a 4.5m antenna operating 11/14 GHz. Can we still say that the antenna pointing at the same satellite needs no target following or tracking device? The antenna under worst case conditions will deflect from nominal target direction by .075 deg. At 11 GHz, 3 = 0.424 deg. 10% 3 = 0.04 deg., and we see that we are likely to be out of bounds. The signal level represented by 0.075 deg. will be Pn = 0.4 db. At the same time, the 14 GHz uplink signal

variation will be ,63.0~16.0

075.03

2

db

exceeding the 0.5 db limit.



215

Therefore, some device now needs to be considered to offer a modicum of station keeping, so that when the satellite drifts, and a steady state wind blows the antenna even further off target, the antenna can be driven back into target position. Several means to do this present themselves; and, we will examine each in a little detail. 6.2 Maximum Signal “Search and Track” Methods 6.2.1 Step Track This is a simple idea that goes as follows: When the antenna is pointed at the target satellite, the Rx beacon (a single frequency) cw signal level is measured. Is the signal maximum? On a preset, timed basis, the antenna is driven away from its present position clockwise (cw) in azimuth (az). If the signal amplitude decreases, move the antenna the same small angular increment ccw. If again the signal decreases, move the antenna back to its original position and perform the same trick in elevation (el). If the starting position in az and el represents the maximum (optimum) position, then stop and wait for the next check period. The dwell time between check periods can be adjusted, as can the angular az, el segments for effective tracking accuracy.

0db

0o

az

el

-Ve

e

Satellite

On targetRx signal is maximum

Antenna beam off-targetRx signal has decreased

Figure 6.2-1 The step track philosophy Typical values might be: dwell time ~ 10 to 30 minutes. Az, El angle increments → dependent on receiver sensitivity. Can 0.03o be accurately sensed by the angle measurement devices on the az, el axes? And, can 0.1 db signal variation be reliably detected? A typical value might be 0.01 deg. for the 4.5m at 11 GHz. If the antenna moves only at 0.01 deg./sec., then a complete cycle may take 8 sec., neglecting start-stop times in between each increment. In the practical case, so called steady-state winds may suddenly die down, or become gusty in a matter of 1 or 2 seconds. Therefore, a smoothing function needs to be considered so that the tracking system does not become confused and search continuously. Variations in this model exist, but are being supplanted by “smart” antenna controller software routines that consider more parameters and react in an optimum target-following routine.



216

6.2.2 Conical Scan Consider the Cassegrain antenna configurations shown here:

F1

F2

F1

F2Target

Rotating tilted subreflector axis traces a conical path causing the antenna beam to scan a conical pattern around the target

Cone tilt angle For the nominal target direction, the beacon signal remains invariant as the tilted subreflector is rotated.

Note: The max signal level is slightly reduced.

Nominal target direction

Cone tilt angle

Nominal target direction

o 1 o 1

P1Po

Off axis target direction

Figure 9.2-2

Target

[a] [b]

[c] [d]

Figure 6.2-2 The con-scan principle For the off-axis target, the signal level received when the scanned beam is closer to the to time position of the rotating subreflector is larger than P1, received when the scanned beam is closer to the t1 time position. The received signal difference is processed in conjunction with the subreflector rotation position, and used to derive a voltage for the antenna az, el drive motors to reposition the antenna until the signal remains at a constant level during a complete subreflector rotation. This tracking device has been in use for precision tracking on relatively fast moving targets for many years, particularly by the military. Interestingly, the very first earth station in England (Goonhilly 1, a 25m prime focus antenna) used this tracking system to observe the first Intelsat 1 spacecraft – a medium earth orbit satellite, not in geostationary orbit. But because it involves relatively large moving parts which are out of reach for “in service” maintenance, this scheme is not a desirable system, effective though it may be.



217

6.2.3 Electronic Conical Scan Imagine now that instead of mechanically moving the subreflector in a conical scan mode, the feed were in effect moved as shown:

F1

F2

F1

F2Target

Rotating the feed around an offset axis causes the antenna beam to scan a conical pattern around the target

Target

Figure 6.2-3 The conical scan implemented for the Cassegrain reflector system However, moving a large feed could be a mechanical nightmare. Therefore, the question comes to mind – can we design a device in the feed that will tilt or scan the beam without moving the horn at all? Consider a simple feed assembly operating with the TE11

o mode. In order to cause the aperture field of the horn to be squinted, additional modes must be added into the throat of the horn. For example, the use of the TM01, TE21 and TE01 modes when combined with TE11 with the appropriate amplitude and phase, will cause the beam maximum to squint. The higher mode TM01 is generated by asymmetry in the supporting waveguide. The mode coupler consists of circular waveguide coupled with four short-circuited square waveguides. Each coupled square waveguide consists of a beacon frequency selecting filler and a PIN diode. The coupling slots are transverse to the central guide, and the amplitude of the generated TM01 is governed by the length of the

coupled square waveguide – a maximum being attained for a length of 4gn

.

In a similar fashion, the use of TE11 and TE21 leads to similar beam squinting features, as does the combination of TE11 with TE01.



218

TE11 TE21

TE11TE01

+

+ =

=

TE11TM01

+ =

Upward squinted aperture

Sideways squinted aperture

Figure 6.2-4 Circular waveguide modes to support asymmetrical fields associated with a squinted beam The PIN diode is placed in the waveguide in such a way that when switched (reverse biased) to act as a short circuit, it alters the length of the coupled waveguide. This results in the generation of TM01 mode. The phased placement of the mode coupler junction with respect to the TE11 mode provides the squinted aperture field. The band pass filter protects the PIN diode from transmit signal power. The diode switching unit sequences the reverse bias on the diodes, causing the co-pol beam to scan in a conical pattern.

Horn

Bandpass filter

Short circuited w/g with PIN diode switch

OMT

H

V

Rx

LNA

d/c

RcvrACU

azim, elev motor control

elev

azim

drives

nlg/4

Tx

DiodeSwitch

TM01 mode Coupler

Figure 6.2-5 Possible network for an electronic scanning feed system Performance example: 3db = .32o, Beam offset = 0.063o

Receiver bandwidth = 300 Hz, Scan freq. = 512 Hz Resulting acquisition range = 0.3o Tracking error resolution = 0.003o Tracking error = 0.01 to 0.03o This compares with step track performance.



219

The potential merits of the electronic scan system: Simple tracking coupler Fast electronic acquisition with PIN diodes Achievable pointing accuracy comparable with steptrack No mechanical moving parts

Possible disadvantage:

Degraded cross-pol within the pass band of the filter 6.3 Zero Signal Track Methods 6.3.1 Phase-amplitude Monopulse

Examining the electric field distribution associated with waveguide modes ,, 012101ooo TEandTETM we see

that each of them has a “zero signal” condition in the center of the aperture, on the axis.

TM 01 Mode TE21 Mode TE01 Mode

180o - 90o

= 90o270o

180o

90o

0o

180o - 270o

= -90o

= (270o)

360o - 180o

= 180o

0o

90o

180o

270o

180o

0o

Figure 6.3-1 Tracking modes in circular waveguide While pointing at the target beacon signal, the antenna will receive maximum beacon signal in the

(downlink) path. If a device which supports any of the 012101, TEandTETM modes can be included in the

feed horn assembly, then the steep amplitude vs angle characteristics with a null (or zero signal condition) on the RF axis can be used to precisely define the direction to the target satellite. If the satellite moves off-axis, or the antenna is caused to move off-target, or a combination of both effects, then the non-zero signal that results can be used to present an “error” voltage for the antenna drive system. The motor drive control logic will use the error voltage to drive the antenna back toward the null or on-axis position. Question: How does the antenna drive system identify which direction to drive? Viewing the mode diagrams, it must be understood that the amplitude patterns are defined by not only amplitude but relative phase angle as well. Therefore, if we arbitrarily assign 0o reference phase to the “North South” principal plane, then a successive 90o phase is related to each quadrant of the aperture moving around the axis. Now, as the off-axis beacon signal is received, amplitude and phase must be measured which will correspond to a particular quadrant, and therefore, a unique direction. The phase-amplitude condition detected and processed by the receiver will then cause the drive system to move the antenna toward the zero-signal/on-target/null position. With the antenna in the null position, the error channel signal will nominally be equal to zero. In order for the receiver to maintain lock on the beacon, a signal coupled from the main communications signal path is used as a reference [0o – phase/constant amplitude] to which the separate error channel signal can be compared. The receiver is therefore a 2-channel device with a phase-amplitude discrimination capability. A simplified tracking system configuration is shown in Figure 6.3-2



220

Tracking coupler

Communications Polarizer Network

LNA

LNA

Transmit (Tx)

Tracking ErrorChannel Network

Az, ElMotor Drives

Antenna Control Unit

2-channel Receiver

Variable Attenuator

Position Detectors

Horn Coupler Receiver (Rx)

Az, El axes

Figure 6.3-2 Tracking system network Note: since the “zero signal search and track” method is very much more sensitive than any “max. signal” system, the early radar systems preferred this type of tracking scheme. Early target range and position identification radar used gated pulses, and measured their returns. Because the system relied on this measurement of single return pulses, it became known as “monopulse” radar – this name remaining today in systems which do not use pulse radar, but which utilize the same waveguide technology.

Tracking modes in circular apertures

90o0o

270o

180o

NNE quadrant time

phase = 90ocw

SE quadrant time

phase = -90o ccw

NW quadrant

time phase = -90o

SW quadrant

time phase = +90o

E

SW

NW NE

SESW

-90o → 0o

0o - (-90o) = 90o

-90o → 180o

180o - (-90o) - 90o

=180o

+90o → +180o

+90o → 0o

(0 - 90o) - (-90o) = 0o

0o

90o

0o

270o

180o

TE01 + TM01 mode pattern TE21 mode pattern

These two modes are sensitive to all polarization angle - applicable to LP and CP sense.

Here the curved field lines are contributing a spatial phase orientation of the field vector. This characteristic places limits on the use of this mode, depending on the orientation of the LP polarization vector.

(180o - 90o) -180 = -90o

Figure 6.3-3 Tracking modes in circular waveguide TM01 + TE01 mode pattern These two modes are sensitive to all polarization angles – applicable to LP and CP senses. This makes this approach attractive. However, to generate TM01 and TE01 modes requires two separate devices, which induces an inherent bandwidth limitation. Therefore, the single TE21 mode is the preferred approach.



221

TE21 mode pattern Here the curved field lines are contributing a spatial phase component to the time phase orientation of the field vector. This characteristic places limits on the use of this mode, depending on the orientation of the LP polarization vector. For LP signals aligned with the principal planes, the fields are aligned with the TE21 fields in the aperture. For LP signals aligned at 45o, the TE21 mode fields are orthogonal, and therefore, will not be seen. Therefore, the patterns associated with this mode are as shown in Figure 6.3-4.

0db

45o plane pattern for LP angles

psi = ± 45o planes

0db

3db

CP pattern for all polarization planes

Figure 6.3-4 Amplitude sensitivity between linear and circular polarization For CP signals, left or right hand, the TE21 mode fields are always aligned with one or the other of the orthogonal components of the CP wave, and the peaks are then 3 db lower than for the principal plane LP patterns. To overcome this anomaly, an additional 45o rotated TE21 mode is introduced into the aperture. In this case, the LP patterns for all polarization angles ( = 0, 45o, 90o) will be of equal peak magnitudes. For in-

between polarization planes, the peak amplitudes will be variable. For the CP patterns, peak amplitudes will be smoothed to nearly equal level around the off-axis beam peak. 6.3.2 TE21 mode Coupler Design Concepts Question: How do you generate these error signal modes, and how is the error signal extracted from the fundamental mode communication downlink path? The answer lies in recognizing the physical conditions needed to support the fundamental TE11 mode and TE21 mode. The basic characteristics of these modes were discussed in Section 3.9, and are repeated here.

c =

d1

6.92d1

GHz

TE21

c = 11.47

d1

GHz

b

a

c =

TE10TE11

2a

11.81GHz

Figure 6.3-5 Cut-off conditions for TE11 and TE21 modes compared with the cut-off for rectangular waveguide Example: Tracking is required for a C-band antenna system receiving 3.625 - 4.2 GHz, and transmitting 5.85 - 6.425 GHz.



222

For the Rx function, circular waveguide at the throat of the horn has diameter d = 2.125 in. For the TE11

mode cutoff is 11cf = 3.26 GHz, which is about 11% below the start of the Rx band. For the same size

waveguide, the TE21 mode is in cutoff - 21cf = 5.40 GHz. Only when the waveguide is opened up from d1 =

2.125 in. to d3 = 3.425 in. is the 21cf = 3.35 GHz. Both modes, if generated, can now co-exist for the Rx

band in this guide. The TE21 mode with its particular field distribution is now generated by introducing four orthogonal coupling slots in the 3.425 in. diameter guide and combining them as shown with magic-tees (180o hybrid).

Incoming LP (H and V pol) error signalIncoming CP error signal 3db lower level

Error signal terminal

rectangular waveguide coupling junctions

magic tee power combiner

circular waveguide

MT

MT

MT

Figure 6.3-6 The simplest TE21 coupler network using three magic-tees to derive the difference mode for monopulse tracking When a second 45o rotated TE21 error signal coupler is added, then 8 coupling slots are used and combined, as shown, for an incoming LP signal with any polarization angle.

H0o

V-45o

H-135o

+45

o

V+45o

H-45o

+31

5o

V180o

0o

180o

90o

V135o

H45o

+22

5o

H180o

+180o

270o

V0o

H-90o

V0o

H-90o

V0o

+90o

V-135o

H+135o

+13

5o

H0o

V90o

V0o

H-90o

H0o

V90o

90o

Hybrid

a

bLP error signal

a

b

H-90o

V 0o

H-90o

V 0o

H 0o

V 90o

V-90o

H+180o

a

b

V 0o

V 0o

H-90o

H-90o

Vector diagram

Vector diagram

H180o V-90o H0o V90o

+270o

= 0

See vector diagram

MT

MT

MT

MT

MT

MT

Figure 6.3-7 Linear polarization phase relationships in the TE21 tracking coupler



223

This is a configuration adequate to collect all the available LP error signal, with no polarization matching losses. Physically, the tracking coupler assembly is as shown in Figure 6.3-8.

beacon signal input from horn

Coupling slots

8 terminations

Rectangular waveguide a x b

To combiner network0o reference

phase position

Figure 6.3-8 Tracking coupler structure details. The TE21 mode is coupled from the central guide into the surrounding rectangular waveguide array. The 0o Ref. position defines the coordinate system which is usually set parallel with the antenna elevation plane. If the polarization angle of the incoming LP beacon signal is not in the principal plane (az. or el. plane), then the ref. signal path must be polarization matched. This means that the ref. signal path must be corrected by a phase angle equal to the polarization angle shift from the reference 0o. This is normally accomplished in the tracking receiver subsystem. Alternatively, the tracking coupler can be rotated to match the incoming polarization angle with the predetermined 0o ref. position. But now the coordinate system must be transformed to accommodate the polarization rotation out of the coordinate (el, az) system of the antenna.

H0o

V-45o

H-135o

+45

o

V+45o

H-45o

+31

5o

V180o

0o

180o

90o

V135o

H45o

+22

5o

H180o

+180o

270o

V0o

H-90o

V0o

H-90o

V0o

+90o

V-135o

H+135o

+13

5o

H0o

V90o

V0o

H-90o

H0o

V90o

90o

Hybrid

a

b

LCP error = 0

a

b

V-45o

H-45o

V-45o

H-45o

V+45o

H+45o

V-45-90o

H-90-45o

= 0

a

b

Ha

Hb

Va

Vb

Vector diagram

Vector diagram+270o

V

H

-45o

+45o

V

H


Vb

Hb

Va

Ha

= 0

RCP error signal

-45o+45o

VH


RCP

LCP

V+45o

H+45o

V-135o

H-135o

a

b

Figure 6.3-9 Circular polarization phase relationships in the TE21 tracking coupler



224

If the incoming beacon signal is RCP, then the 90o phase shift between the associated orthogonal field vectors, and the setting of the 0o phase reference in the coupler will lead to the extraction of the relative 90o phase shifted V and H field components at terminals “a” and “b”. The 90o hybrid will now cause the selection of LCP and RCP components at the hybrid output terminals. Typically, beacon signals are single sense polarization. And hybrids function optimally if one output terminal is terminated. The “error” channel pattern, as derived from the TE21 mode 8-port coupler network, is shown with approximate levels relative to the communications “reference” channel TE21 signal level in Figure 6.3-10.

0db

3db

10db

0o- 3db/2 + 3db/2

HornRCP

beacon signal input

Termination

d3

d1

90o ph. sh.

error signal output

H

V

Communications Ref. Ch. output

OMTTransformerTE21 coupler

Figure 6.3-10 Block diagram of the TE21 tracking feed system As the horn aperture becomes larger, the main “reference” channel pattern becomes narrower, and the “error” channel pattern peaks come closer together, making the “slope” of the pattern through the axis become steeper. The error pattern needs to be interpreted as a voltage pattern. The sensitivity of the error pattern will increase as the slope into the null increases. As the target moves off-axis by a angle, V will represent the relative error voltage available for the drive system to return the antenna to the “on-target” position. Nominally, since the voltage diagram shows the error pattern passing through 0 volts at = 0o relative target direction angle, the logarithmic “db – scale” diagram should show an on-axis Null of infinite depth with respect to the 0 db reference pattern maximum. In practice, this can only be approximated.

1 Volt Reference channel pattern

0.3 volt

+ve phase

1st sidelobe

-ve phaseError ch. pattern

V

-3/2 +3/20 volt

slope = V

- 0.3 volt

volts/degree

Figure 6.3-11 The tracking slope voltage diagram Asymmetries as represented by frequency and polarization voltage and phase errors in the combiners of the error network and the TE21 coupling junction will cause the null to shift off-axis and even “fill.” Typically, the on axis value of the null will reach an indicated depth of only 40 or 50 db below the error pattern peak



225

level. This is also approaching the noise floor of many measurement test beds, and the effects are seen in Figure 6.3-12.

0db

3db

10db

0o- 3db/2 + 3db/2

error

SumReference 0db

3db

10db

0o- 3db/2 + 3db/2

error

SumReference

Effectivedynamicrange

Variation with frequency and/or polarization

Figure 6.3-12 Influence on tracking accuracy by system noise and difference pattern polarization and phase errors In the presence of noise, the error pattern will not have a clearly defined null, leading to a pointing uncertainty called "tracking jitter". The TE21 tracking coupler junction has terminations at the end of the coupled arms. The terminations at ambient temperature generate noise of approximately 300K. If the coupling factor is unity (1.0) or 0db, this noise power will be coupled completely into the body of the coupler. Only the insertion loss effects of the error channel network (w/g or coax) will contribute noise together with the antenna pattern noise and the LNA. However, in reality, the coupling factor is about 10 db, causing the terminations to present at least 270K plus the effects of the pattern and the combiner insertion loss to the error channel terminal and attached LNA. Case Study Let’s look at a typical 4 GHz “monopulse” network.

For optimum coupling between oTE21 and the coupled rectangular 10TE waveguide, the guide wave

length g for both waveguides must be equal at the operating frequency of .

For the circular waveguide of diameter d3:

2

3

221

47.1111

o

o

c

o

og

o

fd

f

c

TE

(cm) (6.3.1)

of freq. (GHz)

c speed of light = 3 x 108 m/sec

3d diameter (inches)



226

For the rectangular waveguide:

2210

211

o

o

c

o

og

fa

c

f

c

TE

(6.3.2)

a = waveguide broadwall width For equality:

3

47.11

2 da

c with 30c (6.3.3)

)(5149.0)(47.112 33 inchesdxcmd

x

ca (6.3.4)

For 3d 3.425 in. (diameter of coupler body)

a 1.76 in., and b 0.88 in. (dimensions of rectangular waveguide – nonstandard)

Question: The coupling junction – one coupling hole or many, as in a directional coupler? The configuration and networking of the coupler slots is such that only the TE21 mode can be generated. The TE11 mode will not couple out. The TE11 mode for the Rx signal will not couple out; the TE11 mode for the Tx signal, if the frequency is not out of the "frequency range" of the coupler, will not couple out. Typically, the coupling bandwidth of the coupler is nearly 2:1. The coupler is in fact a "directional coupler" for the TE21 mode. Following the general principles of directional coupler design discussed in Section 1 and Figure 1.4-12, the length of the coupler and the size of the coupling slots are chosen to achieve a directivity of about 30db. The idea here is to minimize secondary coupling back into the body of the coupler. The TE21 coupling should be as large as possible for two reasons: to maximize the error voltage and therefore, the on-axis error signal slope to reduce noise temperature caused by the terminations A one-hole coupler has very little coupling and practically no directivity, and in practice, one needs at least a coupling of about 10 db. A directivity of 30 db will assure a negligible insertion loss. This also means that if only 10db of the available TE21 mode is actually coupled out from the circular guide, then the remaining TE21 mode will be free to move on down the line, together with the TE11 communications signal. At some point, the waveguide will need to reduce in diameter to mate up with the OMT. Here the TE21 mode will reach a cut-off condition, and be returned to the throat of the horn. Therefore, it will also need to be able to exit through the corrugated horn throat. Bear in mind that the "horn throat" might also include a QJ (quadrature junction). The corrugation geometry here will need to be designed to present a low VSWR for the TE21 as well as for the TE11 modes. If this is not done, then the TE21 mode will become trapped in the coupler, and cause unwanted discontinuities. If now the antenna must also transmit in the frequency band 5850 – 6425 MHz, this signal path will include the TE21 tracking coupler. The transmit signal will be moded as TE11 and launched in waveguide size approximately 1.37 inches diameter. The transition from 1.37 to 3.425 inches diameter must occur with symmetry and in a manner that does not generate any additional modes.

Consider the modes in circular waveguide that may exist at Lf = 5850 MHz and Hf = 6425 MHz in the

coupler body. So long as discontinuities are small, TM01 and TE01 will not be generated. However, small asymmetries can excite the modes TE31, TM21, TE41 and TE12. These will result in cross-polarized field



227

components. Therefore, the dimensions of the coupler body must be chosen carefully to keep the cross-polar frequencies out of the band of interest. For example, if a TE21 coupler body diameter is chosen as 3.400 in., the cross-polar components of TM21, TE41 and TE12 can exist, causing spikes in the frequency response at 5675, 5876, 5891 MHz respectively. See Table 6.3.1. A coupler body diameter of 3.425 inches moves these possible trouble spots out of the band. Table 6.3.1 Table of circular waveguide higher order modes for diameters 3.400 and 3.425 inches which can cause troublesome mode spikes in the transmit band.

Waveguide Mode Table

Waveguide Diameter = 3.400 inches

TE Cutoff Freq TM Cutoff FreqMode No. m n MHz m n MHz

1 1 1 20342 0 1 26573 2 1 33754 1 1 42345 0 1 42346 3 1 46427 2 1 56758 4 1 58769 1 2 5891

10 0 2 610011 3 1 7050

Waveguide Mode Table

Waveguide Diameter = 3.425 inches

TE Cutoff Freq TM Cutoff FreqMode No. m n MHz m n MHz

1 1 1 20202 0 1 26383 2 1 33504 1 1 42035 0 1 42036 3 1 46087 2 1 56338 4 1 58339 1 2 584810 0 2 605511 3 1 6999

Coupler characteristics at 4 GHz are not significantly different between diameters 3.400 in. and 3.425 in.. As a consequence of the foregoing discussion, the complete design of tracking couplers is only possible with a full understanding of all operational frequencies, both receive and transmit. The above mentioned modes must be checked as part of design procedures. A System Performance Study: Let us consider an example of an 11m antenna operating on a 4 GHz beacon signal:

Reference Ch. Comms Network

Error Ch Combiner Network

FeedHorn

Taref = 40K

Term 300 K

Taerror = 40 K

Phase Shifter

Tlna = 40 KGain = 60 db

C1 = 20db

C2 = 10db Block Downconverter

NF = 10db(2700 K)

IFL and Tracking Receiver

TE21 Tracking CouplerLNA

LNA

Rx

Figure 6.3-13 Simplified TE21 tracking system block diagram Reference Ch. Parameter Error Ch. Parameters eirpsat = 10 dbw Antenna gain = 35 dbi (TE21 mode) Path loss = 196 db at 4 GHz e.s. ant. gain = 51 dbi

feed loss = 11db (included in gain) [feed loss includes coupling factor of TE21 coupler (10db) and insertion loss of combining network.

feed loss = 0.3 db (incl in gain) LNA gain = 60 db c1 = 20 db LNA noise temp = 40 K = 0 db Antenna noise temp = 273 K at 10o elev Downconverter NF = 12 db Antenna noise temp = 40 K at 10o elev Ref temp. = ambient temp. = 27oC = 300K LNA noise temp = 40 K



228

The methods of Section 5.2 allow the determination of (a) the beacon signal level and (b) the noise power at the input to the Ref. Ch. and Error Ch. LNAs. Reference Channel Path Ref. Ch. Beacon signal level C at i/p to the LNA:

gainantennalosspatheirpC sat -105 dbm

Ref. Ch. Noise temp components as seen at i/p to the LNA:

antT 40 K, lnaT 40 K, 1c = 20db = coupling

KTgainLNA

ccT refLNApost 3300

10

11010

16

221

1

KcgainLNA

Trec 3.010/10

2700

/

270026

1

Total system noise temperature at i/p to the LNA:

dbKKTTTTT RxLNApostLNAas 2.193.833.0304040

Noise power skTN = -198.6 + 19.2 = -179.4 dbm/Hz

oN

C= 74.4 db

for bandwidth = 1 kHz, N

C = 44.4 db

Error Ch. Path Error Ch. Noise temperature components at i/p to the LNA: Antenna pattern noise = 49 K at 10o elev

KTant 6.6530010

110

1010

49

101

101

101

1010

Termination noise = 300 K26110

11

1010

ST 65.6 + 261 + 40 = 366.6 K → 25.6dbK

Noise Power oN -198.6 + 25.6 = -172.9dbm

Total noise power at the input to the downconverter: Ref Ch: -179.4 + 60 – 20 = -139.4 dbm Error Ch: -172.9 + 60 – 10 = -122.9 dbm Total = -122.8dbm Total signal (beacon) at input to receiver downconverter: C -105 + 60 – 20 = -65 dbm

oN

C = 58.6 db;



229

For bandwidth = 1 kHz

N

C = 28.6 db

Let us consider the error channel pattern peak pointed toward the target satellite; receiving the beacon signal. The beacon signal level at the input to the LNA on the off-axis peak is determined as:

emodTEgainantennalosspatheirpC sat 21

= 10 dbW - 196 + 35 dbi + 30 = -121 dbm The noise power level (from previous page) = -172.9dbm

oN

C = 52.7 db;

and for bandwidth = 1 kHz,

N

C = 22.7 db

1 Volt

1st sidelobe

V

-0.24o +0.24o

0 volt

slope = V

- 0.16 volt

0db

3db

16db

0o-0.24o

error

SumReference

Pn = Noise floor

n

C/N = 22.7db

+0.24o

90o

+0.16 volt

Figure 6.3-14 The monopulse error channel voltage pattern and slope in the null. This indicates that the dynamic range in the error ch. path is 22.7 db, and peak signal level = -121 dbm. Signal level in the Ref. Ch. = -105 dbm.

If the null depth in the error ch. pattern is larger than 22.7 db, a small angular range n will represent

pointing uncertainty and is called “noise jitter angle” error.

n is now a contributor to monopulse tracking error. Generally, this angle segment can be found,

assuming the error pattern is represented by a sine function.

)90(sin

)sin(

1)(Re

x

voltf

Vn (6.3.5)

Ne

C

volt

Vx n

20

1

10arcsin1

arcsin



230

The angle ratio

32

121

90

n

x

90

10arcsin 201

321

21

NeC

n

(6.3.6)

For the case being considered here eN

C = 22.7 db. (BW = 1 kHz)

nV 0.0733 Volts

3 Half power beamwidth for the 11m at 4 GHz = 70D

= 0.48 deg

.deg0112.021 n

This is the connection between dynamic range and noise jitter angle.

If the error ch. eNC / were 30 db, the noise jitter angle becomes:

.deg0048.021 n

and the tracking slope is given by

.deg/5.60112.0

0733.0

21

voltV

n

n

When compared to the reference voltage, the “system tracking slope” will be affected by several factors:

a) The nominal level difference between the TE11 and the TE21 pattern peaks of approx. 16 db b) The gain differential between reference and error channel patterns as found in the reflector system,

typically about 11 db including the network losses c) If the beacon is LP, and the error channel network is configured to receive CP signals, an additional

3 db must be applied. For the case under consideration, the effective “system tracking slope” will be 16 db degraded, or 6.31 times smaller – namely, 1.0 Volt/(ref. volt)/ deg. or

tracking slope = n

nV

21

/(effective voltage gain difference between sum and error signals) (6.3.7)

Note: The tracking slope can be "artificially" increased by including a low noise amplifier into the error path to reduce the level difference between the TE11 and TE21 pattern peaks. As the error voltage is increased, the slope through the null will increase.



231

6.4 Array Monopulse Feeds 6.4.1 4-horn “cross” Array We have seen previously that a horn can have an associated power pattern. The beamwidth will be related to the aperture size "a". Consider now two such horns arranged as in Figure 6.4-1(a) and (b). When the two horns are connected in phase to a combiner (e.g., magic tee), the pattern seen at the Σ (sum) terminal will correspond to the effective size of the aperture in the x-z plane A ~ a + d. The resulting beamwidth in the pattern will be correspondingly decreased. This is shown in (c). The pattern seen at the Δ (difference) terminal will have a null or "zero" signal on the axis, as seen in (d). Note here also that, as would be expected, the Δ-pattern peaks will lie 3db below the Σ-pattern peak. If we replot this pattern as shown in (j), on a voltage scale, the result of the "difference" mechanism in the Δ-terminal of the magic tee will be zero volts on the pattern axis. With reference to a 1 volt peak on the Σ-pattern, we will see 0.5 volt on the -pattern peaks. Figure 6.4-1(f), (g), (h), shows the form of these patterns when looking from the "top down", showing the designated az and el angle directions. Clearly seen in (h) is the fact that a difference pattern exists in the nominal az plane, but no signal at all in the el plane.

3

aØ

Pdb

h1 h2

One horn Two horn arrangement

h1 h2

Two horn array

P1 P2 P3 3

h1 h2

P3 3

Σ

d

Σa b c d

e f g hTop view of power pattern Top view of power pattern associated with 2-horn array

Ele

v pl

ane

Azim plane

0db 0db

0db

0db

3

6db

3db

3db

Figure 6.4-1 The 2-horn array and principal features of the array sum and difference patterns. (a) single element horn and pattern; (b) independent twin elements; (c) sum of twin elements; (d) sum and difference of twin elements; (e) to (h) “top view” of elemental patterns; on page 232 (i) voltage pattern of sum and difference.



232

1 Volt Reference ch. pattern

+ve phase

1st sidelobe

-ve phase

Error ch. pattern

V

-3/2 +3/20 volt

slope = V

t

- 0.5 volt

volts/degree

0.5 volt

j Figure 6.4-1(i) The 2-horn array and principal features of the array sum and difference voltage patterns Consider this array pointing toward a target signal source. The signal available at the Σ-terminal would offer evidence that the target was there – one could even "step track" the target. At the same time, the Δ-terminal shows a "zero" signal toward the target. Moving the target in azimuth will instantly be registered with a difference voltage signal - either "+" or "-", depending on which direction the target has moved. Therefore, the measured voltage seen in the Δ-signal can then be detected, demodulated, amplified, and used to power a mechanical system to move the array back to a "zero" signal condition, meaning pointing the antenna exactly at the target again. The magnitude of the Δ-voltage will correspond to how far off target the array is pointing. The identification as to whether the Δ-voltage is +ve or -ve indicates in which direction the antenna must be moved. The sensitivity with which the array can react to any movement of the target can be seen in the measurement of the Δ-voltage vs off-axis angle . The ratio /v is referred as tracking slope. The larger this ratio, the more sensitive the array will be to target movement. We observed earlier that the 2-horn array in the azimuth plane will not show a Δ-signal voltage in the elevation plane. Therefore, for this antenna to be useful in the 3-dimensional world, a second pair of horns will be needed in the elevation plane, to perform, independently, the same function just described, but now in the elevation plane. Seen from the top, the array of horns will look as in Figure 6.4-2. The sum signal is given by (1+2 + 3+4); the azimuth error signal = (1-2); the elevation error signal = (3-4).

el

azΣaz,el

Az-plane

El-p

laneZ

1

2

3

4

(3-4)(1+3)+(2+4)(1-2)

1st sidelobes

elev

azim

Sum PatternDifference Pattern

1

2

3

4

+

-

+

- azim

elev

(a) (b) (c) Figure 6.4-2 The 4-horn “cross” array and associated sum and difference patterns



233

6.4.2 4-horn “corner” Array An alternative 4-horn array network is considered here. In this network, the two array pairs are combined as shown in Figure 6.4-3.:

[(4-3) + (1-2)] azim

(4-3

) -

(1-2

) =

0

1 2

34

(1+2) - (3+4) elev

Σ(1+2+3+4)

1 - 2 1 + 2

4 - 3 3 + 4

Az plane

Ele

v pl

ane

magic tee

mag

ic te

e

mag

ic te

e

magic tee

Figure 6.4-3 The 4-horn “corner” array. The connections from the magic tees are all in the same direction, denoting vertical polarization. (Photo used with permission of General Dynamics SATCOM Technologies). In azimuth, (1 + 4) represents a new array element, as also (2 + 3); similarly (1 + 2) and (4 + 3) represent an array elements in elevation. When these paired elements are combined, then the Δ-pattern gain can be increased, thereby increasing tracking slope when compared to the crossed 4-horn array discussed in Section 6.4.2. The sum pattern remains the same. 6.4.3 The Integrated 5-horn Array Monopulse tracking functions are typically installed in large antennas. Small antennas can effectively step track a target satellite. The Σ-pattern in the monopulse networks discussed so far is required to carry the "communication path" (basic Rx and Tx functions), and the Δ-pattern provides the necessary tracking information. The Σ-pattern of the 4-horn array is not an efficient feed for large reflector antennas. The general observation is that when the Δ-pattern of the 4-horn array is optimum to illuminate the reflector system, the Σ-pattern is too narrow, resulting in low illumination efficiency, and therefore low gain. The solution to this dilemma is to incorporate a 5th horn serving only to handle the Σ-channel Rx and Tx functions. See Figure 6.4-4. Two very important features of the array and its associated difference pattern to note: As the separation in the array elements increases to incorporate the 5th horn (a) the sum pattern main beam narrows down, corresponding to an increase in gain. (b) the difference pattern peaks come closer together, to increase the tracking slope. (c) the peak level (or gain) of the difference pattern decreases, tending to reduce the effective tracking slope. More on this in Section 6.5. This becomes an issue in monopulse tracking feed design when a decision is made to use a 5-horn array in a prime focus, or in a dual reflector antenna system. If the central horn design becomes too large, the spacing in the array may produce difference patterns which are too narrow to illuminate the primary reflector, reducing performance to an unacceptable level.



234

azim

1 2

34

elev

Σ(Reference)

1 - 2 1+ 2

4 - 3 3 + 4

Az plane

Ele

v pl

ane

(1+2) + (3+4)

(1+2) - (3+4)

(1+4) - (2+3)magic tee

mag

ic te

e

mag

ic te

e

Figure 6.4-4 The 5-horn “corner” array Figure 6.4-5 attempts to portray a comparison between the TE21 tracking coupler, the “crossed” array, and the “corner” array monopulse tracking networks. Figure 6.4-6 similarly shows the features of the 4-horn and 5-horn arrays. When to use which arrangement:

The TE21 mode tracking coupler is the most efficient tracking coupler. The sum main beam can be tailored to the reflector geometry, and the difference tracking beam provides the highest illumination efficiency.

Practically, the crossed array will not be used, except in a multiband configuration requiring two 4-

horn arrays, each designed to handle a different frequency band. For example, L, C, and X. X would be equipt with TE21 coupler, and L and C tracking would be in a twin array – C band in a “corner” array couched in a “crossed” array for L band.

For example: S-band communications and tracking in a 4 horn array, mounted around the 5th

central Ku-band tracking and communications horn. The 4-horn array will only be used if a TE21 tracking coupler cannot be implemented in a multi-

band tracking application. For example: S-band communications and tracking in a 4-horn array, mounted around the 5th

central Ku-band tracking and communication horn. The 5-horn array in a single-band application will only be used if there is no physical space for a

TE21 tracking coupler.



235

The corrugated hybrid mode horn configuration with TE21 mode coupler for sum and difference patterns

Common horn aperture for both "sum" and "difference" signals

TE21 tracking coupler

10db

20db

0db

6db

15db

Reflector aperture angle

Difference pattern

Sum pattern

Angular position of target

Null

Off-axis target position

Phase determines

target position from Ref 0o

180o

90o

270o

Amplitude determines angular position off-axis

View of pattern looking into feed aperture

Elev axis

Az plane

(c - d)Azimuth

difference

(a - b)Elevationdifference

(a + b + c + d)Sum

Terminated

El p

lane

"A" x "A" can be seen as the size of the array aperture

"A"

"A"

b

c d

a

4-element "cross" array for sum and difference patterns

Off-axis target



0db

6db4db

10db

20db

15db

TE21 mode monopulse pattern characteristics


El p

lane

View of (separated) Azim. And Elev. Feed patterns

Cross array sum and difference patterns in azimuth and elevation planes

Magic tee

Mag

ic t

ee

Mag

ic t

ee

Ref = 0o phase

Az plane

Ref

lect

or a

pert

ure

angl

e

Null plane

Nul

l pla

ne

(a) (b) Figure 6.4-5 Comparison between (a) TE21 tracking feed pattern features, and (b) 4-horn “crossed” array feed.



236

(a + c) - b + d)Azimuth

difference

(a + b) - (c + d)Elevationdifference

(a + b) + (c + d)Sum

Te

rmin

ate

d

"A" x "A" can be seen as the size of the array aperture

"A"

b

c d

a

4-element "corner" array for sum and difference patterns

Magic tee

Mag

ic te

e

Mag

ic te

e

Magic tee

b

c d

a

"Corner" array for difference patterns,

and central 5th horn for sum patterns

central 5th horn

4 array elements for difference pattern only

Ele

v p

lan

e

Azim plane

Off-axis targetposition



0db

10db

20db

15db

Corner array sum and difference patterns in azimuth and elevation planes

3db

Off-axis targetposition



0db

10db

20db

15db

Corner array sum and difference patterns in azimuth and elevation planes

3db


El p

lan

e

View of (separated) Azim. and Elev. feed patterns

Az plane

Nul

l pla

ne

Azimuth error angle to target

Elevation error angle to target

Azim plane

Ele

v p

lan

e

Elevation target error

Azimuth target error

Null plane

View of Azim. and Elev. feed patterns for 5 horn array

Sum pattern main beam

"A" x "A" can be seen as the size of the array aperture "A" x "A" can be seen as the size of the array aperture

(a) (b) Figure 6.4-6 Comparison between (a) 4-horn array pattern features, and (b) “corner” array with 5th horn feed.



237

6.4.4 Polarization Requirements for Monopulse Functions The previous sections have discussed networks that are linearly polarized. An essential requirement for the configuration is the need to align the az/el planes of the array to be aligned with the az/el coordinate system of the antenna. This means that if the incoming polarization from the target satellite is not aligned with the az/el planes of the monopulse network, then a polarization correction mechanism will need to be installed in both Δaz,el and Σ paths. In order to overcome this difficulty, the most frequent approach is to generate a CP monopulse network. The network then must accommodate horizontal and vertical polarization components and the required 90o

differential phase shift.

azim

1 2

34

elev

Σ(Reference)

(1- 2)v (1+ 2)v

(4 - 3)v (3 + 4)v

Azim plane

Ele

vpl

ane

h

h

v v

h

vv

h

(2 - 3)h(1- 4)h

(1+ 4)h (2+3)h

(1- 2)v + (4 - 3)v = (1+ 4)v - (2 + 3)v = elv

(1+ 4)h - (2 + 3)h = azh

(1+ 4)h + (2 + 3)h = Σelh

(1+2)v - (3+4)v =

(1+4)v - (2+3)v = azv

(1+2)v + (3+4)v = Σelv90o

Hybrid

90o

Hybrid

90o

Hybrid

(1- 4)h + (2- 3)h = (1+ 2)h - (4 + 3)h = elh

RCP

LCP

RCP

LCP

RCP

LCP

Σv

Σh

v

h

90o

Hybrid

v

Σh

RCP

LCP

Σref

magic tee

mag

ic te

e

mag

ic t

ee

magic tee

5th horn reference

Array sum reference

magic tee

mag

ic t

ee

magic tee

mag

ic t

ee

Figure 6.4-7 Dual polarized configuration of the 4-horn array. Notice that 90o hybrids are used for circular polarization. Horn structures for monopulse arrays discussed here can be of various configurations. (a) Cavity-backed crossed-dipoles connected with the appropriate combiners - usually coax. (b) Waveguide horns (corrugated or smooth walled, circular or square section), each fitted with a circular polarizer and waveguide magic tee combiners. If only a single sense CP monopulse error/tracking network is required (as is generally the case), then the network of Figure 6.4-4 can be considered. If however, both polarization senses are required, as for tracking a satellite being launched into orbit with the possibility of polarization senses to be switched, then the more comprehensive network of Figure 6.4-7 must be considered. 6.4.5 Monopulse Detection Methods “Pseudo monopulse” or single channel tracking How is the Az, El difference pattern signal processed ?? Basically, the separate and independent error signals Az and El are added to a sample of the sum reference, and the resulting modulated sum signal is detected, converted to phase reference voltages, and used by the servo to drive the antenna movement. This scheme requires two tracking receivers – one to handle the Az error signal path, the other the El error signal path.



238

If the tracking requirements do not demand a high speed response, as is the case in most commercial satellite systems, then the cost of the two channel scheme described above can be reduced by adopting a routine of sequentially detecting Az and El error signals, and processing them with a single receiver. This routine is called “Pseudo Monopulse” tracking. A diagrammatic explanation for this process is shown in Figure 6.4-8. The 5-horn monopulse array is shown at the center left. The communications sum reference signal path is through the central (5th) horn, which in this case includes a CP polarizer (90 deg differential phase shifter and OMT) and the diplexer to separate the receive and transmit functions. The 4-horn array and combiner network provides the Az and El error signals. Assume for the moment that the antenna is pointing at the target satellite. The Az and El signals are zero. This condition is shown at Inset #1. The sum relative power pattern is red is seen at the input to the LNA. The difference relative power pattern is seen at the output of the error channel combiner at the points marked “a” and “b”. Now imagine the antenna is purposefully moved off target by a small angle t in the elevation plane only. This means El delivers a signal. The scanner is basically just a time-sequenced dual-line switch. The switching is accomplished by latching a ferrite phase shifter. The 0o or 180o phase shift allows the EL signal to be guided from “a” to “c” terminal, or thrown into the termination. At one instant in time t1, the signal at “a” is switched to the output “c”. At time t2 the signal at “b” is switched to arrive at “c”. At t3, the signal from “a” is switched 180 deg in phase. At t4 the signal at “b” is reversed in phase. At “c” the error signal is coupled with the sum signal, resulting in a modulated signal that can be detected and demodulated to represent a voltage for the servo system. This modulation scheme is implemented to aid in detecting the small change in the sum signal level that results from the error signal generated by the off-axis condition. The modulation rate is given in terms of a switching rate of approximately 100 msec. A view of the modulated reference signal is shown in Inset #2. As noted earlier, the antenna is off-target in elevation only, and therefore the zero voltage condition, while the scanner is looking at the signal from the azimuth error terminal at times t2 and t4. The phase reversals for this sequence are performed by the two ferrite phase shifters in the scanner assembly which can be switched between two phase conditions – 0 and 180o – as shown in Inset #4. The box immediately to the right of the scanner detail shows the four modulation states of the error signals sent to “c”. These states are reflected in Inset #5. An important alignment condition: The phasing sections in both the sum and difference signal paths must be set such that both are in phase at the input to the LNA. Inset #6 shows a plot of the modulated error voltage for various off-axis angles in elevation. This diagram is called the MOD (modulation) slope diagram for the tracking system. To be noticed is the slope of this error voltage, which can be related to the slope of the difference pattern discussed earlier. The larger the gain of the 4-horn array, the steeper the difference pattern slope, and therefore the larger the MOD slope. Furthermore, since the target offset was only in elevation, the corresponding MOD slope plot for the azimuth plane is zero. If for some reason, an Az error signal is seen at “a” while the antenna is moved in elevation, a mis-pointing or a combiner phase problem has occured. This phenomenon is termed error channel “cross-talk”. Inset #7 shows the corresponding change in the MOD slope diagram. The impact of the presence of a Az cross-talk signal: The antenna will be commanded to drive in Az in spite of the fact that it is already on target in this axis. The antenna thus circles around the target direction, without actually ever getting there. Figure 6.4-9 attempts to show the error phenomenon in terms of what is happening in the antenna pattern.



239

→ ΔEl / 0o state 1

→ ΔEl / 180o state 2

→ ΔAz / 0o state 3

→ ΔAz / 180o state 4

J1 J2

J3 J4

0o

180o

0o180o

Ferrite electrically latched phase shifters

Scanner

Scanner driverPulses sent in pairs

sequentiallyPulse width = 10μsecPilse rate = 100msec(minimum = 4msec)

Scanner detail

a

b

b

aoutput

c

cError ch.Network

Combiner 9db coupler

Termination

OMTDifferential

Phase ShifterΣ-Horn

Monopulse 4-horn array

- Δaz, Δel

1, 2

3, 4

phasing section

magic tee

magic tee

Angle off-axis

Σ-pattern Δ-pattern

Operational setting = 0.25db

volta

ge

1

0

Σ

Δ

Σ + Δ

Note: For this voltage addition to be correct, Σ + Δ paths need to be phased. This is done with adjustable flex w/g sections in the error path.

Angle - degrees

Elevation error signal in from

Azimuth error signal in from

Scanner output phase states

phasing sections

LNA

TxRx Rej Filter

Tx Rej Filter

Re

lativ

e P

ow

er

- db

1 2

3 4

Error voltage states as delivered by the scanner output while looking at the off-axis target satellite

volta

ge

+ve

-ve

w/g switch Rx

0o

Actual angle off-axis az, or el - degrees

Cha

nge

of s

tate

vol

tage

0

+ve

-ve

+ve-ve

Δ el

expected Δ Az cross-talk(referred to as X-el)

Note: Expected is a line at 45o, (assuming equal angle scales)

This is known as the MOD slope perfomance of the tracking system.The slope is a measure of the tracking sensitivity

The mod slope is also expressed as a change in angular position with respect to an expected change in angular postion.

Exp

ecte

d ch

ang

e in

off

-axi

s an

gle

-

degr

ees

Direction to target satellite

J1 J2 J3 J4

+ve

-ve

Figure 6.4-8 Pseudo monopulse tracking explained



240

Azimuth Plane

Ele

vati

on

Pla

ne

First sidelobes

Main lobe

Apparent elevation sum pattern cut

Apparent azimuth sum pattern cut

Apparent elevation difference pattern cut

Apparent azimuth difference pattern cut

On-axis View of Difference Pattern On-axis View of Sum Pattern

Ele

vati

on

Pla

ne

Azimuth Plane

Elevation 1st sidelobes lower in elevation plane compared to those seen in the azimuth plane

Nominal azimuth difference pattern null filled with signal from elevation plane difference pattern

Nominal elevation difference pattern null filled with signal from azimuth plane difference pattern. Asymmetry caused by skewed pattern cut as a result of elevation motion not orthogonal to azimuth axis

Notes:

Notes:

Figure 6.4-9 Head-on views of Sum and Difference patterns as they apply to 4-horn monopulse tracking systems. If the error pattern null is disturbed by a high noise floor, an angular range of uncertainty called “jitter angle” will become evident. This is shown in the diagram Figure 6.4-10. In this case, the modulated error voltage amplitude will be masked by the noise. It may be possible to still detect the error voltage by averaging the noise, but this will take time, and the target acquisition time will be increased.

1 Volt

1st sidelobe

0 volt

Tracking slope

V

0db

3db

10db

0o

error

SumReference

P n = Noise floor

Difference signal C/N

V n

n

=

V

Power pattern

Voltage pattern

Noise floor P n determined by bandwidthNominal values realizable = 35 to 50db below Sum reference 0db peak

n

V n

V

V

V n

+--

ccw off-axis cw off-axis

Antenna position

+

--

In the presence of noise, the tracking receiver will detect changes in average noise voltage from + to -

n

In the absence of noise, the tracking voltages can provide immediate signals for the antenna drives

on

axi

s

Vol

tage

Figure 6.4-10 Monopulse tracking in the presence of noise. In the absence of noise, the tracking receiver can immediately provide the antenna drive system with directional information. In the presence of noise, the noise voltage will need to be averaged over time before an off-axis tracking signal can be provided for the antenna drives.



241

6.5 Array Analysis and Design Consider the 4-horn array shown in Figure 6.5-1. To calculate the array pattern, two basic pieces of information are required: 1. The pattern characteristics of each of the elements 2. The geometry of the arrangement of the array elements, leading to the array factor which characterizes the array. The pattern for the array is the product of the element pattern and the array factor. Assume the pattern of each element is the same, and given by

uge in the E-plane and ugh in the H-plane

where

sin2

au

a aperture size in the plane under consideration;

angle in the E and H planes

Further, for the 45 deg plane, the pattern will be given by ugug he

The final pattern of the array must take into account the Huygens source pattern

2

cos1 C

The far field patterns of the array in the principal planes are:

In the 0 deg (E-plane) Cugg e 00

In the 90 deg (H-plane) Cugg h 90 (6.5.1)

In the 45 deg plane Cugugg ee 45

The array factor determines the pattern of the array of isotropic sources. If the four isotropic sources are in the xy plane, then the far field at point P depends on the relative phase of the sources amongst themselves and on the differential distance of point P from the various sources. The unit vector from the origin towards P is

cossinsinsincos0 zyx iiir

and the vectors pointing from the origin to the four sources 1,2,3,4 are

xibr 1

yibr 2 (6.5.2)

xibr 3

yibr 4

The electrical phase difference between the sources and the origin as seen from P will be

sincos

2101 brr

sinsin

2202 brr (6.5.3)

1303 sincos2 brr 2204 sinsin

2 brr



242

14

3 2

P

r o

b

Z

Y

X

r4 r2

r1r3

O

Figure 6.5-1 Geometry of four isotropic element array. The sum of the array elements The sum mode occurs when all the sources are excited in phase as (1+2+3+4). The array factor

4231, jjjjS eeeeA

sinsin

2cossincos

2cos2, bbAS (6.5.4)

In the three planes of interest

o0

1sin

2cos200

bAS

o45

sin2

cos445 bAS (6.5.5)

o90 SS AbA 0090 sin2

cos12

The difference between array element pairs In the difference mode, the sources (1-3) and (2-4) are in 180 deg phase relative to each other, and therefore the expression of the array function will be

21 sinsin2, 4231 jeeeeA jjjjD

In this expression, j could be omitted because it only shows that the difference signal is in 90o phase

relative to the sum signal. Substituting the expressions for 1 and 2

sinsin

2sinsincos

2sin2, bbAD (6.5.6)

In the three principal planes

o0

sin2

sin200 bAD

o45

sin2

sin445 bAD (6.5.7)



243

o90 DD AbA 0090 sin2

sin2

If all four sources are used to obtain the difference signal, the 45o plane can be considered as the tracking plane – see Figure 6.5-2. On the other hand, it we use only 1 and 3 in the 0 deg plane, and 3 and 4 in the

90 deg plane, we will have 090 DA and 000

DA respectively.

The patterns of the array f are calculated by multiplying the individual horn patterns g by the appropriate

array function A . These basic compositions of isotropic sources can be developed to design monopulse arrays involving even pairs of elements. The most interesting configurations are the cross and corner arrangements. The cross array - Figure 6.5-2 The sum patterns

SS Agf 000000 SS Agf 454545 SS Agf 909090 (6.5.8)

where g is the element pattern for the 0o, 45o, and 90o planes respectively.

The difference patterns

E-plane tracking: DD Agf 000000 DD Agf 454521

45 090 Df

H-plane tracking 000 Df DD Agf 454521

45 DD Agf 009090 (6.5.9)

1

24

3

+

+

0o

45o

90o

Y

Xo,o

Ele

v pl

ane

Azim plane

Figure 6.5-2 The cross array (a), showing the position of isotropic sources for the 4-horn sum and 2-horn difference patterns. Note that rotating this configuration, one ends up with the 4-horn corner array The corner array - Figure 6.5-3 The sum patterns

SS Agf 0000x

00 SS Agf 4545x

45 SS Agf 9090x

90 (6.5.10)

The difference patterns

E-plane tracking: DD Agf 4500x

00 DD Agf 0045x

45 0x90 Df

H-plane tracking 0x00 Df DD Agf 0045

x45 DD Agf 0090

x90 (6.5.11)



244

1 2

34

0o

45o

90o

Y

Xo,o

Azim plane

Ele

v pl

ane

Figure 6.5-3 The corner array, showing the position of isotropic sources for the 4-horn sum and 4-horn difference patterns A comparison between the corner and cross arrays is shown in Figure 6.5-4. The particular arrangement here is for the illumination of a Prime Focus reflector.

A

B

a

t

bs

4-Element Cross Array Sum and Difference Patterns

-40

-35

-30

-25

-20

-15

-10

-5

0

0 20 40 60 80 100 120 140 160 180

Angle Off-axis - degrees

Am

plit

ud

e -

db

H-plane SUM

E-plane SUM

H-plane DIFF

E-plane DIFF

(a) (b)

A

B

a

tb

d

s

4-Element Corner Array Sum and Difference Patterns

-40

-35

-30

-25

-20

-15

-10

-5

0

0 20 40 60 80 100 120 140 160 180


Am

plit

ud

e -

db

H-plane SUM

E-plane SUM

H-plane DIFF

E-plane DIFF

(c) (d) Figure 6.5-4 A comparison between the patterns for cross and corner arrays. (a) shows the cross array consisting of 4 rectangular apertures. (b) The cross array Sum and Difference patterns. (c) The corner array configuration. (d) The corner array Sum and Difference patterns. Note the increase in Difference pattern gain (by about 5db) for the corner array compared to that for the cross array. All four elements are contributing to the difference pattern. This is the feature which makes the corner array attractive for monopulse applications. The principal features of a planar array as discussed here are: (a) as the array spacing increases, the main beam width of the array decreases (b) the number of sidelobes increases (c) the sidelobe envelope rapidly increases in level



245

These are all tendencies that rapidly lead to poor illumination of a reflector system, even to the point of becoming completely useless. As the main beam width decreases, the increasing first sidelobe (which is out of phase with the main beam) will start to illuminate the reflector, in effect cancelling the illumination by the main beam. The optimization of the array pattern is to be interpreted as designing for beam symmetry for both sum and difference patterns. Optimization is best achieved with array elements that themselves have symmetrical patterns. When the array elements are rectangular waveguide, the positioning of the elements contributes toward array pattern symmetry. However, this may not always be a free parameter. The five-horn monopulse array Consider the need for including a central horn as intimated in the arrays of Figure 6.5-4. This (5th) central horn frequently is needed for an unrelated function; for example a second frequency band. The central horn will dictate the element spacing. If the element spacing becomes too large, the main beam of the array pattern will become too narrow for the reflector aperture. When laying out the array, it becomes useful to get an idea of the physical layout, particularly when a 5th central horn is involved. Consider the design example in Figure 6.5-5 (a), (b), and (c). Given: d = diameter of the array element b = distance from principal axis s = separation between one element and the central horn a = diameter of the central horn The dimensions for the array will be sadD 22

dsda

t

22 (6.5.12)

2

tdb

tdC 2

"b"

Configuration of 4-element array

"c""

"d"

"a"

"s"

"t""D"

Calculation of "b" for given "a", "d", and separation "s"1 - wavelength apertureelement diameter - "d" 3.5 inchescentral horn dia. - "a" 5 inches

separation - "s" 0 inchesseparation - "t" 2.510 inches

NOTE: "t" must be positive"b" 3.005 inches

7.633 cm

square width - "c" 9.510 inchesdiagonal width 12.00 inches

(a) (b) Figure 6.5-5 Dimensional design of a 4 or 5 horn monopulse array. (a) shows the necessary dimensional parameters, and (b) a sample design case.



246

4-Element Sum Pattern

-50

-45

-40

-35

-30

-25

-20

-15

-10

-5

0

0 10 20 30 40 50 60 70 80

Angle Off-axis - deg

Re

lati

ve

Po

we

r -

db

0-90 ptrn22-67 ptrn45 ptrnElement PatternSeries5Series6

Figure 6.5-5(c) Sample design of an array of 4 horns in a corner configuration, showing both sum and difference patterns in three planes. The spacing of the horn elements is such that a Cassegrain reflector system with a 20 degree look angle from feed to subreflector would fit for good illumination efficiency for both sum and difference patterns. The element pattern (light blue pattern) is a sample pattern measured on a cavity-backed dipole feed horn with a one-wavelength aperture. The principal feature of this element pattern is axial symmetry. Notice that the sum pattern is significantly narrower than the difference pattern. If the array spacing is limited by the size of the central horn, the sum pattern may become so narrow as to not be able to illuminate the reflector. In which case, the central horn must offer the sum reference pattern, and the array only the difference pattern, all at the same frequency. What dictates the size of the elements ?? Cost, dimensional constraints, performance. Performance means loss, noise in the difference pattern null, and if a Tx function is to be included, power handling. Dimensional constraints refer to the space available for the array and its combiner network. If only minimum of space exists to satisfy feed system packaging issues, a coax combiner may be necessary. Consider the feed shown in Figure 6.5-6. It offers sum and patterns with selectable LP or CP function. The combiner network includes rotary points in each array element to permit linear polarization rotation. Each element is a cavity backed crossed dipole assembly, in which both wings of each dipole are separately excited. The cavity backed dipole is discussed in Section 3.10.3. Figure 6.5-6 shows a five horn array in which the central 5th horn serves as the sum reference channel at a higher frequency, and the array is dimensioned to provide sum and difference (monopulse) patterns, as well as offering selectivity between circular and linear polarization. Since the monopulse array cannot rotate in polarization - this would cause azimuth and elevation axis references to be confused – each dual polarized element in the array will need to be rotated synchronously. This is done with the aid of a chain drive. Figure 6.5-7 shows a block diagram of the configuration.



247

Figure 6.5-6 4-horn CP/LP array handling both sum and difference functions. Polarization adjustment is by means of the chain drive synchronously rotating the array elements. (Photo used with permission of General Dynamics SATCOM Technologies Inc.) The most practical approach for small antennas is to make this an all-coax combiner network. The use of the cavity backed dipole – to be able to launch linear H and V fields in a mechanically compact manner, and achieve symmetric patterns – demands a 1 wavelength aperture.

1

2

3

4

V

H

V

H

V

H

V

H

RJ

RJ

RJ

RJ RJ

RJ

RJ

RJ

Σ

Σ

Σ

Σ

Σ

Σ

Σ

Σ

(1 - 2)v

(1 + 2)v

(1 - 2)h

(1 + 2)h

(4 - 3)v

(4 + 3)v

(4 - 3)h

(4 + 3)h

(1-2)h+(4-3)h = (1+4)h-(2+3)h = Elh

(1+2)h-(4+3)h = Azh

(1+2)v-(4+3)h = Azv

(1-2)v+(4-3)v = (1+4)v-(2+3)v = Elv

Az H

El

RCP/Hor

LCP/Vert

LCPVert

H

RCP/Hor

Sw

Sw

Sw

Sw

Hor

Hor

Vert

Vert

Pol axis

Pol axis

Pol axis

Pol axis

Individual element synchronized Pol

angle adjust

Polarization sense select

Figure 6.5-7 Block diagram of the dual polarized CP/LP selectable monopulse array



248

On the other hand, single CP can be accomplished with 0.6 wavelength diameter waveguide elements as shown in Figure 6.5-8. The smallest of element apertures can be a = 0.5 wavelength for rectangular waveguide, and about d = 0.6 wavelength for circular w/g elements. As an example of an optimized 5 horn design, Figure 6.5-8 shows an X-band feed in which the array apertures have been reduced to 0.6 wavelengths in order to minimize the array size and maximize the central sum horn aperture.

Figure 6.5-8 Example of a 5-horn monopulse feed horn system, in which the 4-horn array handles only the difference pattern, and the central 5th horn handles the sum reference pattern. (Photo used with permission of General Dynamics SATCOM Technologies Inc.) The principal objectives for this design were to accommodate a particular reflector geometry shown in Figure 6.5-9.

Single pol CP monopulse feed network

Dielectric subreflector

support cone

Feed shadow in the main reflector to be

smaller than subreflector blockage shadow Short focal length

subreflector

Main reflector

Conical feed support structure

F1

F2

4-horn array for difference patterns

Sum horn

Figure 6.5-9 The short focal length subreflector allows a small sum horn and an adequate array spacing for best sum and difference aperture illumination. The array elements must be small in size to get the required spacing. One wavelength apertures cannot be adapted to this requirement. A sample antenna pattern for the antenna described in Figure 6.5-9 is shown in Figure 6.5-10.



249

Figure 6.5-10 The sum and difference patterns for an 18m antenna. References: 1. Y. H. Choung, K. R. Goudey, L. G. Bryans, "Theory and Design of a Ku-band TE21-Mode Coupler", IEEE Trans Microwave Theory and Techniques, vol. 30, No.11, Nov 1982, pp 1862 - 1866.

Chapter 7 – Special Application Antennas


250

Chapter 7 Special Application Antennas 7.1 Antennas with Simultaneous Multi-band Feeds 7.1.1 Single Aperture Feed Horn 7.1.2 Wideband Feed Horn 7.1.3 Concentric Aperture Feed Horns 7.1.4 Dual Aperture Feeds with FSS 7.2 Selectable Multi-feed Systems 7.3 Beam-waveguide 7.3.1 Introduction 7.3.2 Large Antenna Beam Waveguide 7.3.3 The Quasi Beam Waveguide 7.4 Multi-beam Antennas 7.4.1 Introduction 7.4.2 The Torus 7.1 Antennas with Simultaneous Multi-band Feeds Several satellite systems, in order to increase traffic capacity, utilize 2 or more frequency bands for the uplink, and consequently, 2 or more downlinks. A case in point is Intelsat which employs both C-band and Ku-bands. The military system, having long ago reserved X-band for its dedicated services, has pursued the use of commercial bands in order to satisfy its thirst for frequency bandwidth. Combinations of S and Ku, X and Ku, X and Ka, C+ Ku + Ka, and even C, X, and Ku, are currently in operation. Inmarsat has services using L and C bands, and scientific remote sensing activities employ S and X, and S and Ka bands. Station operators are running out of real estate and forced to employ antennas capable of handling a variety of satellite functions which do not demand simultaneity. To this end, existing antennas are being converted for multi-function applications. 7.1.1 Single Aperture Feed Horn The general horn as used in feed systems attempts to transition from standard waveguide dimensions to a larger aperture in such a manner that the pattern can be used to efficiently illuminate the reflector system. In the case of the wideband corrugated horn, we can make use of the variable cutoff conditions in the conical structure of the horn throat to accommodate more than one frequency band. The highest frequency is able to propagate all the way to the smallest diameter of the horn throat; lower frequencies reach cutoff conditions closer to the aperture. At these points, signal can be coupled in or out of the horn with appropriately matched slots cut through the corrugations. Four slots are cut symmetrically and exactly orthogonal to each other, to capture horizontal and vertical polarization components respectively. See Figure 7.1-1. These slotted junctions are referred to as "Quadrature Junctions". The horizontal and vertical polarization component pairs are separately combined in magic tee junctions. Quadrature junctions can be stacked providing that each junction carries corrugations that are supported by each of the higher frequencies to be supported in the system.



251

Dual frequency (horn) input terminal

High frequency output terminal

4 low frequency output terminals

Figure 7.1-1 Quadrature Junction as part of the throat section of a horn Harking back to Section 3.6 in the discussions on the corrugated horn, it was found that the periodic groove structure could simultaneously support multiple frequency bands, depending on the groove depth. Given the following conditions:

2, 4, 6, ... > (center frequency band 2)/(center frequency band 1) > 3, 5, 7, ... band widths < 2:1 n*/4 < groove depth < n*/2 n = 1, 3, 5, ...

a corrugation geometry can be found that will provide the expected pattern beam symmetry, and the associated low cross-pol characteristics. Interestingly, the pattern beamwidths will also be similar - with the higher frequency patterns being only slightly narrower. Frequency bands which do not conform to these conditions are excluded from any horn and QJ design considerations. Any other depth would prevent the desirable symmetrical pattern and low cross-pol characteristic of the corrugated horn. As can be seen in Figure 7.1-2, only select frequency bands can be combined into a common horn. For example, the band 3.4 to 4.8 GHz can be combined with 10.7 to 12.75 GHz to function in a single corrugated horn design.



252

Corrugated Horn Groove Depth (inches) vs Frequency (GHz)

0.0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1.0

1.1

1.2

1.3

1.4

1.5

1.6

1.7

1.8

1.9

2.0

2.1

2.2

2.3

2.4

2.5

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45

Frequency - GHz

Gro

ove

dept

hs -

inc

hes

C-b

and Ku-band Ka-bandX-band Q-bandKa-band

Exclusion zones

Exc

lusi

on z

ones

Hor

nQ

J

QJ

Hor

n

S-b

and

L-ba

nd

Kt-b

and

Figure 7.1-2 Graphical determination of applicable groove depths for corrugated horns for multi-frequency band applications. In these cases, it will be important to ensure that the QJ coupling junction can be accommodated. The low frequency can only be coupled out through adequately shallow grooves which will at the same time support the high frequency. If there is no match here, the horn/QJ combination will not function. There are three examples shown here. (a) Ka and Q bands - A single groove depth = 0.22 in. horn is adequate to support both bands into a diplexer separating Ka and Q bands (b) C and Ku bands - C-band is coupled out in a QJ with grooves 0.26 in. which also supports Ku band. The horn with grooves 1.35 in. deep will support C and Ku bands. (c) S and X bands - In a manner similar to the concept for C/Ku, the QJ coupling out S-band will support X band. The horn has a groove depth of 2.1 in. which supports both S and X bands. If the grooves were 0.88 inch deep, both C and Ku frequencies will be supported. However, C cannot couple very well through 0.88 inch deep grooves, and Ku does not behave well entering the 1.35 deep groove structure. Therefore, the shallow 0.22 inch groove transition for the Ku path to the horn. What will also be evident - there is no groove geometry to support the standard C-band up and down links (3.4-4.2 and 5.85-6.65 GHz) and simultaneously the standard up and downlinks for Ku band (10.7-12.75 and 13.75-14.5 GHz). According to Figure 7.1-2, there is no choice of groove depth which does not cause the chosen frequency band to extend into an "exclusion zone", and therefore not practically workable. As an example, for the C/Ku (receive-only) combination, Ku band would be dimensioned to be available in the circular diameter of the horn throat. C-band would be coupled out through a "QJ". The QJ would be fitted with corrugations supporting Ku band. The rest of the horn would be fitted with corrugations that support C and Ku bands. The groove depth for the throat and the QJ will be approximately 0.28 inches for



253

Ku-band, and the groove depth for the rest of the horn will be approximately 1.35 inches to support the C-band.

Figure 7.1-3 Photograph of a C/Ku linearly polarized receive only feed assembly with twin QJ and single aperture horn technology. (Photo used with permission of General Dynamics SATCOM Technologies Inc.) Limitations in the application of this design lie in the need for a minimum number of grooves for the corrugated horn to function adequately. Typically, a horn design with a gain of about 17 to 22 dbi, as would be required for a Cassegrain application, will have a geometry as shown in Table 7.1-1. Such a horn design will demand a minimum of about 3 grooves per wavelength and at least 10 grooves total. The principal design difficulty is centered on the coupling junction, to ensure low loss coupling and low return loss (VSWR) for both signal paths. Table 7.1-1 Conceptual horn design for Cassegrain feeds Rudimentary Feed Horn DesignDate: March 2006

Conical Feed Horn ParametersFeed operating frequency GHz 20.000 20.00 25.00 27.00 31.00

cm 1.50 1.50 1.20 1.11 0.97Free space wavelength inches 0.59 0.59 0.47 0.44 0.38

Sub edge-taper db 18 17 20 20 20Subref half angle degrees 20.0 20.0 20.0 20.0 20.0Feed horn gain dbi 21.9 21.7 22.4 22.4 22.4Select mode in horn mode te21 te11 te11 te11 te11Horn half-flare angle degrees 14.5 14.5 14.5 14.5 14.5Horn throat diameter iinches 0.61 0.37 0.29 0.27 0.24Horn length inches 3.4 3.7 3.3 3.0 2.6

Feed horn aperture diameter inches 2.34 2.28 1.98 1.83 1.59

Guide wavelength in the aperture inches 0.62 0.62 0.49 0.46 0.40(TM11 + TE11 mode) cm 1.58 1.58 1.25 1.16 1.01

d+delta lambda 0.1791 0.1769 0.1472 0.1363 0.1187

Horn aperture - PC distance inches 1.87 1.79 1.62 1.50 1.31

mode TE11 TM01 TE21 TM11 TE016.92 9.03 11.47 14.39 14.39

Adjustable 180o differential phase shifter for C-band

pol. rotation

QJ2

QJ1 Adjustable 180o differential phase shifter for Ku-band

pol. rotation

QJ1 to QJ2 interconnects

C-band OMT

Ku-band OMT



254

This scheme will be difficult to apply to low gain horn designs (e.g., for prime focus applications), since the necessary small aperture horn will not have sufficient space to accommodate the necessary number of corrugations. The approach using a cylindrical waveguide with corrugated flange (shown in Figure 3.10-1) can be usefully applied in this case. 7.1.2 Wideband Feed Horn Another way of accommodating several frequency bands in a single aperture is to consider a wideband horn - one that can operate over several octaves. Wide bandwidth can be achieved with the use of ridged waveguide. Rectangular ridged waveguide can be designed to operate over several octaves, and similarly with circular waveguide. An example of such a scheme is shown in Figure 7.1-3.

Figure 7.1-4 Circular waveguide wideband quad-ridge horn. (Photo used with permission of General Dynamics SATCOM Technologies Inc.) Generally, the larger the dimensions of the ridge, the broader the bandwidth. However, absorptive losses increase quite rapidly. In practice, signal is coupled from a coax network into the quadridge horn as shown in Figure 7.1-4(a), thereby avoiding the difficulties of attempting to design a broadband waveguide network. Generally, this design approach is reserved for low frequency applications - less than 10 GHz. Radio astronomy is particularly interested in being able to conduct observations at specific frequencies which are widely spaced in the spectrum. Antennas have been equipt with multiple selectable feed systems. For some purposes, this is not convenient, and a number of useful applications exist that could make use of a frequency range of several octaves. For example 300 MHz to 40 GHz equals 7 octaves; 100 MHz to 26 GHz = 8 octaves. Even satellite communications now stretch across the range 1 GHz to 45 GHz = 5 octaves. The principal design difficulties in these broadband horns lie in the area of asymmetric pattern and low cross-pol. 7.1.3 Concentric Aperture Feed Horns As noted in Section 7.1, there are frequency combinations that cannot be combined with the corrugated horn-QJ. These situations can be partially covered with the use of concentric apertures, as shown in Figure 7.1-5. In effect, we now have to deal with "coaxial waveguide" modes for all signal paths involved except the inner circular waveguide. The form of these modes is shown in Section 1.9. The inner waveguide of this coaxial structure will tend to impede the signal flow in the outer path, and any significant diameter here will have a consequent impact on performance. This can be ameliorated with the use of dielectric loading, as described in Section 1.3.

Coax terminal

(a) (b



255

Now the physical size of the inner waveguide can be reduced, but the electrical size of the inner aperture is increased with the dielectric material by the factor rtconsdielectricrelative tan .

Figure 7.1-5 C/Ku concentric aperture feed system showing the large C-band horn and the concentrically located Ku-band waveguide aperture with dielectric loading. (Photo used with permission of General Dynamics SATCOM Technologies Inc.) In order to comply with low cross-pol performance, multiple modes need to be introduced. This is easily done for the large outer horn with the aid of corrugations and/or multiple flare changes. For the inner horn, the dielectric rod loading can be tailored to generate hybrid modes (combinations of several modes) that behave in a manner similar to that of a corrugated horn. Therefore the pattern of the inner aperture can be controlled to more or less equal the beamwidth of the outer aperture. For all practical purposes, beamwidth equality can be reached for use in a reflector system with an aperture half-angle of about 25 to 65 degrees. This makes this type of feed horn system applicable for feeding Cassegrain/Gregorian or prime focus reflector configurations.

C-band horn

Ku-band dielectic loaded horn

Ku OMT

C-band output terminals

Figure 7.1-6 Concentric aperture feed block diagram layout showing the C and Ku output terminals A variation of the concentric aperture feed involves the use of lenses in the various apertures instead of dielectric rods to aid in optimizing the illumination of the reflector system. The advantage in this approach is that now more than two signal paths can be accommodated concentrically, as shown in Figure 7.1-6. However, adequate control of pattern beamwidth becomes rapidly more difficult as the number of concentric signal paths increases.



256

7.1.4 Dual Aperture Feeds with FSS The attempt to combine different frequency band functions through one single horn aperture can, as explained earlier, suffer from difficulties in the design of the horn. A particular example is the C/Ku Rx/Tx feed system. A solution to this dilemma lies in the design of an FSS (frequency selective surface), mounted as shown in Figure 7.1-7. A simple C-band Rx/Tx feed is mounted into the secondary focus F2 of the Cassegrain reflector system. Mounted in front of the C band aperture is a device (the FSS) which is transparent to C frequencies. Further, the FSS is reflective to Ku signals. So following the ray tracings for the Ku signal path over the FSS and the flat metallic reflector, we end up at the simple Ku Rx/Tx feed positioned in the displaced secondary focus F2'. Both feeds can be equipt with monopulse tracking when this scheme is applied to a large antenna. Apart from the FSS, this represents an inexpensive method for combining two important frequency bands.

10

20

30

7560 9050403020100 100 110 120 130 140 15070 80

12 inch Ku feed tube

24 inch C feed tube 10

20

30

22 in

ch

Shaped Cassegrain Main Reflector Vertex

PC

15o

F2F1

Main Reflector Focus

FSS

Flat Reflector

C-band Horn

Ku-band Horn

Shaped Subreflector

FSS

Ku Reflector

Shadowing of the main reflector by the subreflector, FSS, and Ku flat reflector, as seen from the front of the antenna.

Subreflector

Ku Reflector

Subreflector

FSS Reflector

Main Reflector = 354 inches diameter

Subreflector = 52 inches diameter

Figure 7.1-7 The C/Ku feed configuration for simultaneous receive and transmit functions in both bands offers an inexpensive approach with the use of separate feeds coupled into the RF axis of the reflector with a frequency selective surface acting as a separating filter. This configuration cannot be realized with a single aperture corrugated horn. 7.2 Selectable Multi-feed Systems For some applications, the antenna system does not require simultaneous frequency functions, but rather to be able to quickly switch from one frequency and polarization condition to another. Several approaches to this problem are discussed here. (a) mechanical selection of feeds, in which feeds are physically moved into an operational condition (b) electrical selection of feeds, in which only an RF component such as an auxiliary reflector is moved into/out of play. The mechanics of moving feeds in and out of an operational position is not an issue. Rather the complications of the “flexible” interconnects to the Tx and/or Rx equipment behind the feeds creates expensive design challenges – see Figure 7.2-1 (gun barrel), and Figure 7.2-2 (multi-feed table, subreflector – prome focus feed rotation). In each case, a feed conglomerate is physically moved. Further, the feeds are all mounted in a relatively inaccessible position, which from a maintenance point of view has its detractions.



257

S-feed

C-feed

X-feed

Ku-feedRotation of all feeds around offset axis "a"

a

Subr

efle

ctor

Mai

n re

flect

or

Feed housing

Feed phase center

Main reflector

Ku-horn

X-horn

C-horn

S-horn

Feed assembly housing

Center of rotation for the feed assembly

antenna axis

antenna hub

antenna axis

Figure 7.2-1 The "revolver" design for selecting individual feed systems. The fact that the feeds physically must move (rotate) will constrain the application to large antennas to take advantage of available hub space for necessary amplifiers and moving equipment.

S-feed

C-feed

X-feed

Ku-feed

Subreflector rotationto provide L/S-band

operations

Mai

nre

flect

or

Feed phase center

Main reflector

Ku-horn

X-horn

C-horn

S-horn

antenna axis

antenna axis

Movement of the feed package

antenna hub

Rotatble"tea-tray" Turntable

Turntable axisF1

F2

Figure 7.2-2 The rotatable “tea-tray” and subreflector “flip” mechanism These designs can be ameliorated somewhat instead by rotating subsidiary reflector elements into place. See Figure 7.2-3. In particular, Figure 7.2-3 has the advantage in that all feeds are accessible from the comforts of an enclosed equipment room, in contrast to the feed(s) behind the subreflector of Figure 7.2-2. Figure 7.2-3 shows a diagrammatic layout of an antenna system with selectable feeds. The full motion antenna system with Cassegrain optics and quasi beam waveguide parabolic reflectors is designed for frequencies up to Ka-Band and higher. See Figure 7.2-4. A tiltable parabolic reflector is installed in the elevation axis which guides the RF beam to the feed systems. The various feed systems are located in the elevation axis in two cabins, one on the left, one on the right side of the mirror. Depending on the selected operating frequencies, the corresponding feed is illuminated by additional movable flat reflectors. The equipment cabins are only rotating around the azimuth axis and so easy access is provided to service the feeds and receive/tracking electronics in all operating positions. The reflector system is mounted on a two-axis pedestal with elevation over azimuth axis configuration.



258

L-ba

nd

S-ba

nd

C-bandKu+Ka bands

Left Side Equipment Cabin Right Side Equipment Cabin

Entry Entry

Rotatable 3rd Reflector

Elev

atio

n Bu

ll G

ear a

nd D

rive

Elevation Axis

13m Main reflector

5m 5m

3.5m3.5m

F1

F2 F2

Subreflector

Cassegrain Reflector Geometry

Equ

ipm

ent R

acks

Equi

pmen

t Rac

ks

M2 M1 M3

Figure 7.2-3 This drawing represents a floor-plan view of the stable equipment rooms. Signals are received by the parabolic main and parabolic subreflector Cassegrain system from a target satellite. Parabolic reflector M1 diverts the signal path into the right hand UER (Upper Equipment Room). Flat reflector M3 is used to select between S and C-band feeds. When reflector M1 is rotated to divert received signals to the left hand UER, flat reflector M2 can be rotated to select between the L-band feed and the combined Ku/Ka feed. (Used with permission of General Dynamics SATCOM Technologies Inc.) Figure 7.2-4 12m Multi-feed quasi beam waveguide antenna configuration, in which all feed systems are located in both elevated equipment rooms on the elevation axis. A single parabolic reflector in the reflector vertex can be oriented toward either room. (Used with permission of General Dynamics SATCOM Technologies Inc.)

Right side stable equipment room

Left side stable equipment room

Rotable 3rd reflector looking either left or right



259

7.3 Beam-waveguide 7.3.1 Introduction The beam-waveguide configuration was developed in the late 1970s to accommodate a demand by station operators for increased comfort. Commercial satellites at this time were eirp limited, and the downlink required large high-gain antennas on the ground. Typical antenna sizes were 30 meters for C-band operations. Ku-band satellites had not yet been introduced. The physical effort to reach the Cassegrain feed, for operational and maintenance purposes, was significant. Helium cooled LNAs were, at the time, not trouble free. The idea was to bring the feed down to ground level and somehow transfer an image of the feed to where it had been, so that the antenna would still function as before. The use of a multimode oversized waveguide connection was out of the question, because of the serious danger of mode spikes, and loss due to currents in the walls. Then a re-arrangement of an idea that had been investigated a little earlier was considered. The idea, shown in Figure 7.3-1, was called a beam-waveguide. It provided the means for transferring the image of a feed from one end of the guide to the other by means of an ordered series of reflectors.

Elliptical reflectors

Oversized waveguide

F1

F3

F4

F5

F6

Source horn

Receive horn

Parabolic reflectors

Oversized waveguide

F2 F3

Source horn

Receive horn

F2

F7

F1

F4

Variation in beam waveguide configurations

Figure 7.3-1 Initial idea for the beam waveguide for a lossless transfer of RF power with use of elliptical and parabolic reflectors. Other variations are possible with hyperbolic reflectors, and an appropriate mix of reflector types. Note that the focal points are all located on a straight connecting line. 7.3.2 Large Antenna Beam Waveguide Large antenna designs were targeted to bring the feed down to ground level through a series of offset reflectors that would optically image the feed into the Cassegrain position. At the same time, the reflector system had to accommodate for the elevation and azimuth motion of the antenna. The resulting reflector configuration is shown in Figure 7.3-2. The distinct advantage is that the feed is easily accessed, and protected from the elements.



260

F 3p

45o

F 1p

F 2

M1M2

M3 M4

Feed system

Main reflector

Subreflector

Azimuth rotation

Elevation axis

Beam waveguide shroud

Elevation rotation

Notes:P = parabolic reflectorM = beam waveguide reflector = Cassegrain focal points

Elevation bearings

Elevation bearings

Figure 7.3-2 The configuration for a Cassegrain beam waveguide antenna system However, this reflector configuration possesses several unexpected complications. 1. Because of the use of offset reflector elements, beam asymmetries can be expected, which contribute to cross-polarization losses. Long focal length reflectors are required to minimize cross-pol. 2. Rule to assure outgoing pattern from the beam waveguide is by designing for F1, F2, and F3 to lie on a straight line. This is shown in Figure 7.3-3 and Figure 7.3-4 for several different reflector geometries. 3. Polarization sense changes occur as the reflector system is rotated in both azimuth as well as in elevation. This situation is incurred by the fact that the reflector system rotates with respect to the fixed feed polarization condition. Orthogonality between H and V polarizations is preserved. But it forces the feed system polarization to rotate in a 1:1 correspondence with the azimuth and elevation motion.



261

F 3p

45o

F 1p

F 2

M1M2

M3 M4M4

M1

M3

M2

Horizontal polarization

Incoming vertical polarization


Incoming horizontal polarization

Vertical polarization

Incoming vertical polarization


Elevation angle

Azimuth angle

Azimuth angle

Ground level Ground level

M4

M1

M3

M2



Elevation angle = 0 deg

Azimuth angle

Ground level

Incoming horizontal polarization

Feed phase center

Elevation angle = 90 deg

Inco

min

g ve

rtic

al

pola

rizat

ion

Inco

min

g ho

rizon

tal

pola

rizat

ion

Fixed feed system

(a) (b) (c) Figure 7.3-3 As the bw/g antenna rotates in both elevation and azimuth, the incoming polarization sense changes in a one-for-one correspondence. For the reference position shown in (a), an incoming H-pol wave arrives at the feed as shown. If the antenna is rotated in Az to the position shown in (b), the incoming H-pol turns into the V-pol position in the feed. If the antenna is now rotated in elevation as in (c), the incoming H-pol again rotates to a position 180 degrees from the original orientation in the feed. The nomenclature is = field vector coming out of the page and = field vector going into the page.



262

F 3

F 1

F 2

h

e45o

F 3

F 1

F 2

e

h45oM4

M1

M1

M2

M2

M3 M3 M4

(a) (b)

F 3

F 2

h

e

45o

F 1

F 3e45o

F 1e

F 2

M2 M1

M3

M1M2

M4

M3

M4

(c) (d) Figure 7.3-4 Several different applicable reflector geometries are shown here that will assure appropriate beam waveguide performance. The layout shown in Figure 7.3-3 is a fifth option. The nomenclature used in the diagram is: e = elliptical reflector; h = hyperbolic reflector; p = parabolic reflector; F = curved reflector focal points. To be noted: F1 = focus of M2; F3 = focus of M3; F2 = common focus of M2 and M3. Configurations (a), (b), and (d) are options for unequal feed and output beamwidths. (c) represents an option for equal beamwidths. Two offset geometries are considered. The parabolic offset, and the ellipsoidal offset. These two geometries are shown in the ray diagram of Figure 7.3-4(c) and 7.3-3(a). The fundamental principle in the design of the offset reflectors is driven by the requirement for low cross-pol performance. As indicated in Section 2.4.1 and Table 2.4-1, cross-pol effects are reduced as focal length is increased. As a corollary, cross-pol levels are reduced as radius of curvature of the offset reflector is increased. Therefore, in order for the cross-pol from the complete offset reflector chain to remain low, the F/D of the offset reflectors will need to be made as large as possible.



263

Looking at the "parabolic" configuration, an F/D >= 1.1 for which an off-axis cross-pol of >35db can be expected. In this geometry, the ray tracings of the field distributions between upper and lower parabolic offsets show that the cross-pol characteristics can be partially cancelled. This can prompt the use of smaller focal length reflectors when space is limited, as for example in smaller antennas. In the case of the "elliptic" reflector system, the ray tracings of the field distributions between upper and lower offset reflectors (M2 and M3) show an effective re-enforcement of cross-pol fields in the upper offset. The only method of reducing this effect is with the use of a third curved (small ellipticity) reflector (M4) in Figure 7.3-4(c). The ray diagrams shown here are a little mis-leading, since the upper and lower offset reflectors (M2 and M3) will be "looking at each other" in the near-field. The nature of the near-field patterns is such that there is no clear cross-over, but rather a narrowing of the field distribution along the vertical path. The net result is that the cross-pol characteristic of all schemes is about the same. However, when the antenna is rotated in elevation, one can see that the orientation of the top flat reflector M1 changes with respect to M2 - an asymmetry is introduced into the reflector set. As a result, cross-pol becomes slightly degraded as elevation angle approaches 90 degrees (meaning as the antenna turns to zenith) In order to protect the beam-waveguide system from external sources of interference, all four reflectors are shrouded in a cylindrical housing. The diameter of the housing is chosen in such a manner as to minimize the spill-over currents in the walls of the housing - this to keep noise temperature contributions to a minimum. The alignment of the beam-waveguide reflector system presents additional problems, particularly for very large antennas. Figure 7.3-5 shows approximate dimensions for a 25m bw/g antenna operating at S-band. They are quite large, and present a challenge to successful mechanical/optical alignment.



264

K t -

S-

M 6Elliptic

M 5Elliptic

M 1Flat

M 4Flat

M 3Parabolic

M 2Parabolic

250

200

150

100

0

50

50

100

150

200

250

300

0 50 100 150 200 250 300 350 450 550 650 750 850 950 1050 1150

350

F2

F2aF3a

F4

F5

F6

12 deg

18o

12o

Shielded Feed Room

Subreflector

Main reflector

550

500

450

400

350

300

14m

13m

12m

10m

11m

9m

Beam waveguide shroud

Elevation axisElevation axis

M 6Elliptic

Inches

meters

Inches

Rotatable

reflector M6

Azim

uth bearing

Azimuth axis

Figure 7.3-5 Beam waveguide reflector layout to accommodate two or more feeds. Each feed can be sequentially addressed by rotating M5 around the azimuth axis as shown at the bottom of the assembly. This design has been laid out to operate at S-band and higher frequencies.



265

As an extension to the discussion in Section 7.2 about selectable feed antennas, the beam-waveguide can be fitted with multiple feeds, each selected by means of a single moveable/rotatable reflector, as shown in Figure 7.3-5. And in the event simultaneous frequency band operations are required, effective use of FSS reflectors is easily implemented. And all these special functional additions remain in the protection of the equipment room in the pedestal of the antenna as seen in Figure 7.3-6.

M7

FSS

M8

Flat Reflector

M5

Elliptical Reflector

F4

F5

F6a

F6b

High Frequency

Feed

Low Frequency

Feed

To beam waveguide

Figure 7.3-6 The addition of a second Frequency Selective Surface reflector M7. The FSS permits the reflection of low frequencies from focus F6b, and the passage of high frequencies from F6a. These are both funneled up to focus F5 and thence into the main portion of the beam waveguide shown in Figure 7.3-5. 7.3.3 The Quasi Beam Waveguide As operational frequencies increase to Ka band and beyond, antenna design must incorporate systems issues. At these frequencies, the power available on the ground begins to decrease, atmospheric losses increase, weather influences become significant, available power on board the satellite are limited, and general link G/T becomes noise limiting. Several tactics are employed in these situations: 1. The earth station transmitter is located as close to the antenna as possible to minimize Tx signal path losses. 2. Reflector errors are reduced by special design. 3. To counter weather effects, signal link diversity is employed with the use of more than one antenna, each located 20 to 50 miles apart. Ideally, the transmitter located in the hub will reduce the waveguide losses in the connection to the Tx terminals of the feed. Transmitters producing several hundred Watts of RF power also produce considerable heat, which must be dissipated. Transmitters are bulky instruments, generally tending to completely fill the hub with little room for other equipment, such as LNAs and converters. The difficulties encountered for the maintenance staff can only be imagined. Another more convenient approach is to consider the configuration of Figure 7.3-7. For the circumstances outlined above, the 9m antenna is an ideal candidate for the implementation of a modified beam waveguide.



266

Redundant HPA

Feed

Feed

DNCs and Track Rx

Redundant HPA

Hub

Elevation axis

Azim

uth

Axis

Rotational Coupling

Elevation Jackscrew

Quasi Beam Waveguide

Rx

Tx

LNAs

Elevated Platform

Turning HeadPedestal

Stairs

TOP VIEW9m Cassegrain with Quasi Beam Waveguide

SIDE VIEW9m Cassegrain with Quasi Beam Waveguide

Beam Waveguide Tube

Figure 7.3-7 A modified or quasi Ka band beam waveguide system in a 9m antenna. At 20/30 GHz, the size of the beam waveguide need only be about 18 inches in diameter, can be built in the lab or factory and tested in its finally aligned condition, and then installed without further ado to fit in the elevation axis. The feed is mounted on the elevated platform with only a very short waveguide interconnect to the transmitter output. The LNA assembly is also located in the same equipment cabinet with no losses. The beam waveguide losses are in the order of 0.08 to 0.1db at 30 GHz. Maintenance and repair work can be performed in comfort, and if expansion in capability is needed at some point in the future, the equipment rack on the platform can easily be modified. Hub access difficulties are always exacerbated when the feed contains moving parts such as with polarization adjustment mechanisms and switches. So the general idea of attempting to mount all the feed and front-end amplifier equipment (both Rx and Tx) into the hub to save money becomes a debatable issue.



267

7.4 Multi-beam Antennas 7.4.1 Introduction The GEO arc contains a multitude of satellites, often closely spaced. A number of organizations are interested in being able to view more than one satellite simultaneously. One way of doing this is to use the appropriate number of single beam antennas. Another approach is to design a single reflector system with a multiple of feeds. The conventional Cassegrain can be fitted with more than one feed, but all except one would be in a defocused condition, with marginal or even unacceptable performance. Besides, to view more than 2 or 3 satellites will be difficult. The problem is seen in Figure 7.4-1.

140 E

210 E

35 N

North Pole

HA = 76.9o

East

S1

S35

Alignment axis for Torus

= Satellite declination

Antennabeam

South Pole

Equatorial plane

Circular scan angle

Figure 7.4-1 The geometry of the Torus antenna in its observation of a series of stationary satellites in the orbital arc In order to accommodate observing large segments of the orbital arc, the geometry for the reflector system is based on the "declination-over-hour angle" configuration, sometimes referred to as the "polar mount" as used by astronomers. In this arrangement, a single beam antenna, when rotated around the "hour angle" axis, will be able to view simultaneously several targets in the orbital arc; this in contrast to the "elevation-over-azimuth" configuration, which demands adjustment in both elevation and azimuth. The declination-over-hour angle arrangement is found by laying the "elevation-over-azimuth" antenna over onto its back so that the azimuth axis is always parallel to the earth's axis. At the North Pole, the antenna will stand up in the normal manner with the azimuth axis perpendicular to the ground. At the equator, the antenna pedestal - the azimuth axis - would lie on the ground. See Figure 7.4-2.



268

= declination AngleTilt angle for the antennato see target satellite inGEO position

HA = Hour AngleRotation parallel to the earth's axis to see a targetsatellite away from the e.s. meridian

Equatorial Plane

Note:For the antena pointing towarda taregt infinitely far away in the equatorial plane, = 0o.For the antenna to point to satellitein GEO, it must be tilted "down" byan amount called "decliniation".

= 0o

= - 5.0o

= - 8.6o

HA

HA

HA

North Pole

Equator

Center of the earth

30o latitude

To target satellitein GEO position

Figure 7.4-2 Definition of the declination-over-hour angle antenna positioner At the equator, the orbital arc is directly overhead, and as the antenna is rotated around the azimuth axis, a single beam will sweep along the orbital arc. At the North Pole, since the orbital arc is not infinitely far away, the satellites are below the local horizon. An antenna at the North Pole cannot see geostationary satellites. If the earth were transparent, tilting the antenna down in elevation by about -8.6 degrees would permit the antenna at the pole to see the orbital arc. For any other in-between geographic latitude, the change in elevation angle just mentioned is called "declination". The change in azimuth angle to see the arc is called "hour angle", because it is parallel to the longitudinal position of the antenna, and determination of longitude is based on time from Greenwich. For any in-between geographic location, expressed by its latitude, the declination will be less than -8.6 degrees, until it reaches 0 at the equator. Hour angle is measured from the local longitudinal plane - ccw rotation is designated negative in angle; cw positive. Declination is measured down from the equatorial plane, and is negative. Example: The view of the GEO arc from 35N, 240E is calculated in Table 7.4-1 for a FoV (field of view) = 70 degrees. The hour angle varies over approximately 77 deg, and the declination by approximately 0.5 deg. Interestingly, for the antenna at the equator, and at the North Pole, the variation in declination delta d = 0. The manner of variation for in-between latitudes is shown in Figure 7.4-3. Note: The useful FoV = 70 deg corresponds to a maximum in range in elevation above the horizon. At 2 deg spacing, this corresponds to 35 satellites.



269

Table 7.4-1 Look angles from the e.s. site toward the selected field of view of satellites

Satellite Position ComputationStatione.s. latitude 35 deg = e-la be.s. longitude 240 deg = e-loe.s. elevation 10 meters = e-el

Satellite Longitude 240 deg = s-lo 0

satellite boresight latitude 0 deg = sb-la satellite boresight longitude 240 deg = sb-lo +ve = north, -ve = southsatellite polarization angle 1 deg = s-pol +ve = east, -ve = west

Note:Declination is defined as tilt from the equatorial plane at the local positional latitude Hour Angle is defined as rotation around the earth's axis at the local meridian of longitude

alpha e Pt delta Satellite longitude Azimuth Elevation Range Pol Twist HA Declin

deg deg deg km deg deg deg 238 east 183.48 49.30 37120.82 -4.43 2.28 -5.65240 east 180.00 49.35 37117.21 -1.00 0.00 -5.65242 east 176.52 49.30 37120.82 2.42 -2.28 -5.65244 east 173.05 49.13 37131.63 5.82 -4.56 -5.64246 east 169.62 48.85 37149.64 9.19 -6.84 -5.64248 east 166.23 48.46 37174.81 12.51 -9.12 -5.64250 east 162.91 47.97 37207.09 15.77 -11.39 -5.63252 east 159.67 47.38 37246.43 18.96 -13.67 -5.63254 east 156.51 46.69 37292.75 22.06 -15.94 -5.62256 east 153.44 45.91 37345.97 25.06 -18.21 -5.61258 east 150.47 45.05 37406.00 27.98 -20.47 -5.60260 east 147.60 44.10 37472.74 30.79 -22.73 -5.59262 east 144.84 43.09 37546.06 33.49 -24.98 -5.58264 east 142.18 42.00 37625.84 36.10 -27.23 -5.57266 east 139.62 40.85 37711.94 38.60 -29.48 -5.56268 east 137.17 39.65 37804.22 41.01 -31.71 -5.54270 east 134.81 38.39 37902.51 43.31 -33.95 -5.53272 east 132.55 37.08 38006.65 45.53 -36.17 -5.51274 east 130.38 35.73 38116.46 47.66 -38.39 -5.50276 east 128.29 34.34 38231.77 49.70 -40.60 -5.48278 east 126.28 32.92 38352.38 51.66 -42.80 -5.46280 east 124.36 31.46 38478.11 53.55 -45.00 -5.45282 east 122.50 29.98 38608.73 55.37 -47.19 -5.43284 east 120.71 28.47 38744.06 57.13 -49.37 -5.41286 east 118.98 26.94 38883.87 58.82 -51.54 -5.39288 east 117.31 25.40 39027.95 60.46 -53.70 -5.37290 east 115.70 23.83 39176.07 62.04 -55.85 -5.35292 east 114.14 22.25 39328.01 63.58 -58.00 -5.33294 east 112.62 20.66 39483.55 65.07 -60.14 -5.31296 east 111.15 19.05 39642.45 66.52 -62.26 -5.29298 east 109.72 17.44 39804.48 67.93 -64.38 -5.26300 east 108.32 15.82 39969.40 69.31 -66.49 -5.24302 east 106.96 14.20 40136.98 70.66 -68.59 -5.22304 east 105.63 12.57 40306.98 71.98 -70.68 -5.20306 east 104.33 10.93 40479.17 73.27 -72.76 -5.18308 east 103.05 9.30 40653.32 74.54 -74.83 -5.15310 east 101.79 7.66 40829.17 75.79 -76.89 -5.13312 east 100.56 6.02 41006.51 77.02 -78.95 -5.11

The variation in declination for a fixed location is max at latitude 35.8 deg. This also happens to be the "center of interest” for multi-beam antennas in major continents around the world. At 35.8 N, close to the "line of maximum population" through the USA, the declination is -5.5 deg, and over 70 deg FoV above the horizon, varies +/- 0.25 deg.



270

0

5

15

25

45

60

8090

0

-1

-2

-3

-4

-5

-6

-7

-8

-9

-10

Antenna Declination vs Geographic Latitude

Dec

linat

ion

- deg

Satellite Position - Longitude - deg0 40 80 120 160 200 240 280 320 360

Latit

ude

- d

eg

North Pole

Equator

0.10o

0.29o

0.37o

0.53o

0.42o

0.16o

Sat 1

Sat 235.85

Average declination = - 5.5 deg

310240Field of View

0.50o

Diff

eren

ce in

dec

linat

ion

in 7

0 de

g Fi

eld

Figure 7.4-3 The variation of declination versus field of view for several geographic latitudes 7.4.2 The Torus An antenna has been designed for this particular "interest"; it is called the torus. The basic circular torus is defined as a surface of revolution generated by revolving a circle about an offset coplanar axis, as shown in Figure 7.4-4. The parabolic torus is generated when a parabolic profile (in the elevation plane) is swept in a circular arc in azimuth, as shown in Figure 7.4-5, on a radius approximately twice the focal length of the parabola. The offset parabola is chosen to eliminate feed blockage.

Figure 7.4-4 The torus The focus of the parabola also sweeps a circle. Multiple beams are generated by positioning feeds on a tray along the focal arc of the antenna as shown in Figure 7.4-5. If we now tilt this antenna structure back in elevation so that the multiple beams look into the orbital arc, then with appropriate settings of the feeds, each beam can be directed toward a specific fixed satellite. Individual feeds can be placed on the feed tray to view satellites with 2 deg spacing.



271

S1

S2

S3

Vertex

X

Y

Z

Feeds

Figure 7.4-5. Illumination of the Torus reflector by separate feeds. Signal from feed F1 will be directed towards satellite S1, from F2 to satellite S2. For the case of hybrid satellites, for example operating both C and Ku frequency bands, the feeds must be represented by concentric aperture configurations (see Figure 7.1-5) that operate both bands simultaneously. For any given latitude, and required FoV, the orientation of the antenna will be unique, and possibly in a manner as shown in Figure 7.4-6.

140 E210 E

35 NGEO arc

North Pole

decl = -5.13o

HA = 76.9o

decl = -5 65o

East

S1S35

decl = -5.13o

Feed settingdecl = -0 26o

140o

210o

Local Horizon

View from behind the reflector looking south

140o

210o

Feed 1

Feed 2

West South

Local Horizon

East

decl = -5 65o

View from behind the reflector looking east

Feed 2 settingdecl = +0 26o

a

b c

Orbital arc

Orb

ital a

rc

Figure 7.4-6 The physical layout for the system would appear as shown here. The antenna is tilted in an unusual position. (a) represents the view from beyond the orbital arc. (b) is the view of the Torus from behind the reflector assembly looking toward the orbital arc. (c) is the view from the side of the Torus looking east. The declination difficulty and off-axis feed settings The idea is to utilize a fixed antenna design, and have it accommodate for all declination conditions.



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One method of achieving this is to tilt the entire reflector around the vertex of the parabola to specific declination values. This is shown in Figure 7.4-7. This will tilt the beam in the declination; however, the view of the orbital arc is seen as variable with the change in hour angle, as indicated by the curve of the projection of the arc in an aperture whose center line is straight. The implication here is that the feeds mounted on the focal circle will need to be displaced to follow the arc. An example of this is shown in Figure 7.4-8 below.

z

y

x

F

F*

y*

Parabolic reflector

Conventional torus tilted around vertex V of parabola

CRV

F*

F

Projection of orbital arc onto reflector center line

View of the reflector from along the z-axis

x

Figure 7.4-7 Declination beam tilt by rotating the torus around the parabolic vertex

Y

Front view of reflector with set of feeds

X

Line of feeds with adjustment for built-in declination compensation

-1.43 inch

+1.43 inch

Figure 7.4-8 shows the relative positions of the various feeds which have been scanned (moved) away from the nominal focused position in the reflector in order to ensure it's antenna beam is pointed toward the designated target satellite. Note that only the feeds located on the straight line are not defocused, and therefore the signal links associated with these feeds will not suffer any loss in antenna gain. A second method is to tilt the plane of the torus as shown in Figure 7.4-9. The effect of this is to shift the parabola up, thereby tilting the beam in declination downwards. The result is to present a view of the orbital arc to the feeds on the focal circle that follows the natural curve of the orbital arc. That is, the feeds will all lie equally on the feed circle without the need for displacement.



273

z

y

x F

F*

y*

Parabolic reflector

Conventional torus tilted around center of torus circle C makes up the modified torus

R C

R

V

F*F

Projection of orbital arc onto reflector center line

View of the reflector from along the z-axis

x

Figure 7.4-9 Declination beam shift by tilting the circular plane of the torus A third method of beam tilting is to scan or move the feeds upwards out of the focus in the y-direction. This can be tolerated with minimal loss in gain and pattern sidelobe performance, provided the scanning distance is kept reasonably small. This is depicted in Figure 7.4-10.

Parabolic reflector

Feed phasecenter

x

z

d

B

FVertex

D

Cen

ter o

f ref

lect

or c

ircle

R

Figure 7.4-10 Beam tilt by vertical displacement of the feed from the focus Apart from a number of errors due to aberrations, a displacement of the feed by an amount d results in tilting or scanning the beam by an angle B . B is less than the feed offset angle Fd /arctan by a factor BDF called Beam Deviation Factor [1].

FdBDF B

/arctan

(7.4.1) BDF is generally approximately 0.7 to 0.9 [1]. The displacement d can be calculated from

D

F

BDF

d B

3

1

(7.4.2) where wavelength

` 3 half power beamwidth for the aperture D of the parabola A useful maximum value for d is that which supports 35 B without causing major first sidelobe issues of more than 15db.



274

For a 7m Torus reflector with DF / 1.0, a BDF 0.716, and operating at

4.2 GHz, 3 0.71 deg; B 3.57 deg; and d 49.87cm or 19.64 inches

12.75 GHz, 3 0.235 deg; B 1.18 deg; and d 16.43 cm or 6.47 inches This means if the antenna is to operate at both C and Ku frequencies, the Ku beam cannot be scanned as far as the C beam. From this it can be seen that to tilt the beam to _5.5 deg declination will not be advisable just by scanning the feed without incurring pattern performance problems. Therefore a fixed tilt in the reflector system of +5.5o is included in the design [2]. See Figure 7.4-9. As can be seen in Figure 7.4-11, the declination angle varies for all the target satellites in a 70 deg FoV, the range being -5.13 to -5.65 degrees, a variation of 0.26 deg. Therefore, each of the feeds will need to be adjusted to specific off-focus positions. To reach 0.26 deg declination, the feed will need to be set vertically away from the focus by

B

AnglenInclinatiodd

1 (7.4.3)

and for Inclination Angle = 0.26, 1d 1.43 inches. In order to avoid this difficulty, while tilting the conventional torus by -5.5 deg in declination, tilt the plane of the circle containing the curve of the reflector by 5.5 deg. This action will tilt the feed focus by 5.5 deg. The result - the feeds will be located on a line parallel with the center-line through the reflector. Thus, for the modified torus, 1d 0.

Earth Station Torus Antenna Pointing CharacteristicsHour Angle and Declination vs Satellite Position

-90

-80

-70

-60

-50

-40

-30

-20

-10

0

10

20

30

40

50

60

70

80

90

150 200 250 300 350

Satellite Position - Longitude - deg

Hou

r Ang

le -

deg

-9.00

-8.00

-7.00

-6.00

-5.00

-4.00

-3.00

-2.00

-1.00

0.00

Dec

linat

ion

Ang

le -

deg

Satellite Longitude 240 dege.s. latitude 35 dege.s. longitude 240 degHour Angle to SatelliteDeclination to Satellite

e.s. Latitude

e.s. Longitude

Declination Sat 1

Declination Sat 2

Field of View

Sat 2

Sat 1

Figure 7.4-11 For the given e.s. location, the viewable satellite arc is from 240E to 310E. This requires the reflector aperture to have an Hour Angle of 77 deg. The number of viewable satellites between and including S1 and S2 is 35. Phase aberrations in the feed horn. Spherical aberration takes place in circular or spherical reflectors in which the rays from different areas of the reflector converge at different points along the axis of the feed as seen in Figure 7.4-12. This is the reason why no good focal point can be defined in the plane of the torus. Ideally, all rays should converge



275

on the feed phase center. Since they do not, a phase error exists in the aperture plane of the torus. The parabolic reflector segment of the torus serves to minimize the gain loss due to spherical aberration. The magnitude of this phase error is dependent on R, the radius used to generate the torus. The larger the radius R, the smaller the phase error; the larger the ratio F/D, the smaller the phase error. But cost will drive the size.

Vertex

Z*

Reflector is formed by rotation ofparabolic profile "P" around Y* axis.

Vertical plane of reflector is parabolic.Horizontal plane of reflector is circular.Parabolic focus is at "F". Center ofcircle is at "O". Axis of circle Y* is tilted by = - 5.5 degrees around theX axis of the coordinate system

Parabola

F

Y*

X

Focus forrays in plane of Torus - circular section of reflector

O

Fp

R

Rotation around tilted axis gener-ating the torus

Feed

Focus forrays in plane circular plane perpendicular to Torus - focus of parabola

Torus

Fc

Figure 7.4-12(a) The nature of spherical aberration in the plane perpendicular to the parabola in the Torus.

Cylindrical reflector has no point focus; only a line focus.

Line focus in the horn represents phase error

Nominal phase center of the horn

Figure 7.4-12(b) Torus reflector and feed showing the defocussing effects of spherical aberration The focal circle Fp is only well defined in the plane of the parabola carrying the axis of the illuminating feed pattern. For off-axis segments of the feed pattern in the circular plane perpendicular to the parabola, the focus shifts to Fc, causing a "smeared" focal line. An average focus with phase errors may be defined, and will be discussed later. Siting the torus to other latitudes Declination angles at sites at 20 to 50 deg latitude range from about -3.5 to -7.5 deg. Now the feed locations must accommodate declinations variable from +2 to -2.0 deg. In fact, at latitudes approaching 50o and less than 20o, Ku band performance will begin to deteriorate because of excessive declination angles, which cannot be accommodated by scanning the feeds. This will require feed offsets of 11 to 12 inches, accompanied by loss in gain at C-band of about 0.2db, and at Ku band about 0.5db. The patterns of Figure 7.4-15 and Figure 7.4-16 show predicted patterns and gain performance for the case of feeds scanned off-focus by 0 and 12 inches at 4 GHz and 12 GHz respectively. Notice there is no significant deterioration in the cross-pol.



276

What happens if the modified torus is installed in Singapore, very close to the equator ?? Table 7.4.2 shows the HA and declination for the 60 to 120 FoV of a conventional torus.

Table 7.4.2 Pointing angles for the orbital arc from 60 E to 120 E as seen from Singapore. The hour-angle range is 71.7 degrees, and if satellites are spaced 2 degrees apart, 35 feeds will be accommodated.

Earth Station Pointing and Polarization Angles for Satellites in the Geostationary Orbital Arc

Site: SingaporeGeographic Coordinates: Boresight of Satellite Signal on Earth:

e.s. latitude 1.42 +ve = north, -ve = south e-la satellite boresight latitude 0 sb-lae.s. longitude 103.82 +ve = east, -ve = west e-lo satellite boresight longitude 10 sb-loe.s. elevation 10 meters e-el satellite polarization angle 0.1 s-pol

Vertical pol = 0 degMean radius of the earth = 6371.64 km Hour Angle - defined as rotation around axis parallel to the polar axis

Mean height of the geostationary = 35785.55 km axis orientation = [90 - site latitude] degrees from local vertical orbit above earth surface

Declination - defined as tilt in look angle with respectto the orthogonal to the HA axis

satellite longitudesatellite east longitude Azimuth Elevation Pol Twist Range HA Declin

deg deg deg deg km deg deg50 268.96 28.54 89.06 38740.03 61.45 -0.2352 268.88 30.70 88.98 38546.78 59.28 -0.2454 268.80 32.87 88.90 38357.83 57.11 -0.2456 268.71 35.06 88.81 38173.47 54.92 -0.2458 268.62 37.25 88.72 37994.00 52.73 -0.2460 268.52 39.46 88.62 37819.71 50.52 -0.2462 268.41 41.68 88.52 37650.89 48.30 -0.2464 268.30 43.91 88.40 37487.80 46.07 -0.2466 268.17 46.15 88.28 37330.74 43.83 -0.2468 268.03 48.40 88.14 37179.96 41.57 -0.2470 267.88 50.66 87.99 37035.74 39.31 -0.2572 267.71 52.92 87.83 36898.31 37.04 -0.2574 267.52 55.20 87.64 36767.94 34.76 -0.2576 267.31 57.49 87.43 36644.84 32.47 -0.2578 267.07 59.78 87.19 36529.26 30.18 -0.2580 266.79 62.08 86.91 36421.39 27.87 -0.2582 266.46 64.39 86.58 36321.44 25.56 -0.2584 266.07 66.70 86.19 36229.61 23.24 -0.2586 265.59 69.02 85.72 36146.05 20.91 -0.2588 265.00 71.35 85.13 36070.94 18.58 -0.2590 264.25 73.67 84.38 36004.41 16.24 -0.2592 263.25 76.00 83.38 35946.60 13.90 -0.2594 261.85 78.33 81.98 35897.62 11.55 -0.2596 259.77 80.65 79.90 35857.57 9.20 -0.2598 256.34 82.95 76.47 35826.51 6.85 -0.25

100 249.64 85.20 69.77 35804.52 4.50 -0.25102 232.05 87.28 52.19 35791.64 2.14 -0.25104 172.77 88.31 -7.09 35787.89 -0.21 -0.25106 123.06 86.94 -56.80 35793.29 -2.57 -0.25108 108.73 84.80 -71.13 35807.81 -4.92 -0.25110 102.89 82.53 -76.97 35831.43 -7.28 -0.25112 99.78 80.23 -80.08 35864.11 -9.63 -0.25114 97.86 77.91 -82.00 35905.78 -11.98 -0.25116 96.55 75.58 -83.31 35956.36 -14.32 -0.25118 95.60 73.25 -84.25 36015.75 -16.66 -0.25120 94.88 70.93 -84.97 36083.83 -19.00 -0.25

The modified torus will first of all be tilted +5.5 deg. The reflector will be oriented to look to the west. The long sides will be nearly vertical. Since the declination is only 0.25 deg, with variation = 0, the feed circle will as a result behave in a manner similar to that shown in Figure 7.4-8. That is, the feeds will need to be moved off-axis in the plane of the parabola, nominally by d1 = 1.37 inches. General performance features of the torus Since the antenna is fixed, it will not be possible to measure antenna patterns or any other performance features, except G/T. The only way of determining pointing and general system alignment is to install each feed and manually position it for maximum received signal. At this stage, G/T can be ascertained with a C/N measurement performed on a known test signal or beacon. If, on the same or nearby site, another well calibrated antenna can be used to observe the same test signal, accurate gain and G/T performance for the torus can be determined. The torus concept provides performance advantages such as low noise temperature, low sidelobes, resulting in low interference from terrestrial sources, or adjacent satellites. This approach minimizes ground space requirements and improves systems reliability by not requiring the movement of a large structure to access different satellites. The 7m torus design has a nominal 7m vertical aperture, with sufficient width to provide a 70 deg FoV. This design permits simultaneous communication with - nominally - as many as 35 geosynchronous



277

satellite without movement of the main reflector. Thus, the torus could provide the same capability as 35 conventional 7m antennas, even at different frequencies, with a tremendous cost advantage. See Figures 7.4-13 and 7.4-14.

Figure 7.4-13(a) A typical Torus installation. Actual reflector orientation and overall dimensions will vary from site to site. (Used with permission of General Dynamics SATCOM Technologies Inc.)

Foundation

Bipod

Rear Braces

Tripod Feed tray support legs

Feed tray

Reflector Panels

Feed tray support cables



278

Figure 7.4-13(b). Torus Backstructure showing the steel back-beam and truss support structure. The left hand back leg is adjustable.

(a) Torus feed tray with C/Ku feeds in place (b) Close Spacing of Feeds

Figure 7.4-14 (a) A view of the C/Ku feeds mounted onto the feed tray. Feed terminals are shown temporarily short-circuited. (b) Close spacing (as close as 2° of separation) allows viewing of up to 36 satellites simultaneously. (Photos used with permission of General Dynamics SATCOM Technologies Inc.) The predicted antenna patterns have been calculated for this configuration in Singapore, and these are presented in Figure 7.4-12 and Figure 7.4-13. (a) represents the Az/El pattern with the C and Ku feeds focussed; (b) represents the Az/El pattern with the C and Ku feeds displaced (scanned) in order to accommodate the error in declination for the Singapore location. The main beam in (a) is not axi-symmetric because in the vertical plane, the reflector is parabolic, but in the horizontal plane, the reflector is circular in profile, and the resultant phase errors in the horizontal aperture contribute to a small loss in gain. The patterns associated with the scanned feeds suffer from an additional phase error and consequent loss in gain.



279

Figure 7.4-15(a) C-Band Antenna Pattern with no Feed Scan Loss

Figure 7.4-15(b) C-Band Antenna Pattern with 12 inch Feed Scan Loss



280

Figure 7.4-16(a) Ku-Band Antenna Pattern with no Feed Scan Loss

Figure 7.4-16(b) Ku-Band Antenna Pattern with 12 inch Feed Scan Loss



281

References [1] Y. T. Lo, “On the beam deviation factor of a parabolic reflector”, IRE Trans AP-8, 1960, pp 347-349 [2] G. Hyde, R. W. Kreutel, and L. V. Smith, “The unattended earth terminal multiple-beam torus antenna”, Comsat Technical Review, Vol 4, No. 2, Fall 1974

Chapter 8 – Structural and Mechanical


282

Chapter 8 Structural and Mechanical 8.1 Antenna Configurations 8.2 Antenna Axis Configurations 8.3 Reflector Support Structures 8.4 Reflector Geometries 8.5 Reflector Accuracy 8.6 Design of Reflector Panels 8.6.1 Main Reflector Fabrication 8.6.2 Subreflector Fabrication 8.7 Pointing Accuracy 8.8 Structural Alignment 8.9 Panel Alignment 8.10 Influences of Weather 8.11 Mechanical Layout Concepts for Complex Feed Systems 8.1 Antenna Configurations The essential elements of reflector type antenna designs are: Parabolic reflector illuminated by a feed Support structure for the feed Support structure to maintain the parabolic surface profile Practical experience, closely linked to a balance between capital cost, lifetime operating costs, and operating comfort, in large part dictates the choice of antenna configuration for a particular mission. These parameters are not always mutually compatible. The most technically reasonable design approach is not always within a bounded budget. And therefore compromise in performance is an additional parameter. Examples of a wide variety of antenna configurations are: Axi-symmetric Offset reflector Multi-reflector – single beam, single or multi frequency Multi-feed – single beam, multi-frequency Torus – multi-beam, multi-frequency Figures 8.1-1 to 8.1-5 show these commonly utilized reflector/feed configurations.

F2F2

F1

F1F1

(a) (b) (c) Figure 8.1-1 Axi-symmetric reflector and feed system configurations. (a) Prime focus; (b) Cassegrain; (c) Gregorian



283

F1F1

F1

F1

F2

F2Feed Support

Feed SupportFeed Support SupportFeed

(a) (b) (c) (d) Figure 8.1-2 Offset reflector and feed configurations. (a) Prime focus; (b) Cassegrain; (c) Gregorian; (d) Horn reflector, also known as the “Hogg” horn, named after the inventor.

F2F1

F2

F1

Flat

FSSF2

F1

Elev

atio

n ax

is

Azimuth axis

M1Latchable feed selecting parabolic reflector

F2

F2

Parabolic subreflector

Parabolic main reflector

"Gun barrel" feed selection mechanism.This could also be linear side-to-side or up-down movement

(a) (b) (c) (d) Figure 8.1-3 Multi feed antenna systems. (a) selectable feeds mounted on a rotating feed ring in the reflector hub; (b) front view of (a); (c) simultaneous operation with two different frequency bands using a Frequency Selective Surface to isolate one feed from the other. (d) feed selection by means of a central parabolic reflector that can redirect from side to side

F1

para

bolic

sphe

rical

Focal line F1

Top view

Side view

Torus Configuration

Figure 8.1-4 The Torus configuration as a fixed multi-beam antenna system. This antenna system is discussed in detail in Section 7.4.



284

F1

F2

F3

F4

F5

F6

M1

M2

M3

M4

Elevation Axis

Azimuth Axis

F1F2

F6

M 1

M2

M3

M4

Elevation Axis

Azimuth Axis

90o

0o

Az platform Azimuth platform

Foundation Foundation

Side ViewRear View

Stationary Feed Stationary Feed

Rotational Joint

F4

F2

F1

Elev

atio

n ax

is

Azimuth axis

View from the top onto the azimuth pedestal platform with quasi beam waveguide

M1

M2

Fixed M2 and feed on top of azimuth platform

(a) (b) (c) Figure 8.1-5 The multi-reflector beam waveguide Cassegrain that locates the feed at ground level for comfortable access and maintenance. (a) View of the antenna system looking to zenith as seen from the rear. Everything above the azimuth platform rotates in azimuth. M1 and the Cassegrian reflector system rotates in elevation on the elevation rotational joint. This reflector configuration is extensively discussed in Chapter 7.3. (b) Side view of the beamwaveguide looking to the horizon. (c) Quasi beam waveguide configuration using jut two reflectors M1 and M2 laid out flat on top of the azimuth platform. In elevation, M1 and M2 rotate with respect to each other. What is the basis for choosing one configuration over another ?? Antenna sizes are measured in terms of wavelength. As a general rule of thumb, when considering the smallest reflector in the antenna assembly - 1. aperture diameter < 10-15 wavelengths - single reflector prime focus configurations are more reasonably considered for use in low frequency missions. For example: 2m aperture at 2 GHz. 2. 10 wavelengths < aperture diameter < 150 wavelengths - Cassegrain or Gregorian configuration For example: 11m aperture at 2 GHz 3. aperture diameter > 150 wavelengths - Cassegrain/Gregorian configuration, or - Multi-reflector configuration, in which the smallest reflector can be made greater than 20 wavelengths For example: 35m aperture at 2 GHz From the point of view of operational comfort, large prime focus configurations are undesirable, since the feed is, from a maintenance point of view, in an inaccessible location. Large Cassegrain/Gregorian antennas have feeds located in the hub of the main reflector, have complex interconnects between the equipment room (transmitter and receiver) and the feed, generally a cramped space and at anything except 0 deg elevation an uncomfortable location for maintenance.



285

Large complex antennas in the beam-waveguide configuration have the feed located in the equipment room in the lower pedestal area. The feed illuminates a series of reflector elements in a quasi-optical manner to reach the Cassegrain/Gregorian reflector assembly. In essence, the image of the feed is transferred from the equipment room to the Casegrain/Gregorian region of the upper reflector system. The fact that all the equipment (including the feed) is accessible in one large comfortable (air-conditioned) space makes this an attractive configuration. Since there is no complex interconnect, the feed and its components do not move, and are easily accessible. Applications for these antenna styles – to track satellites and other targets in various locations A. Geostationary earth orbit – GEO (36,000 km) Slightly inclined GEO Medium earth orbit - MEO (approximately 6,000 to 10,000 km) Low earth inclined orbit – LEO (approximately 1,000 to 6000 km) Polar orbit Low earth equatorial orbit Aircraft/missile tracking radar Weather radar B. Fixed earth station antennas Mobile antennas Quick deploy antennas Ship- and air-borne antennas 8.2 Antenna Axis Configurations In order for the antenna to point its RF beam toward any part of the sky, movement in two orthogonal axes is required - one which tilts up and down, and a second which moves side to side. The predominant form is the Elevation-over-Azimuth positioner. A second positioner type is the so-called X-Y or Elevation-over-Cross Elevation positioner. A third mechanism is called the Declination-over-Hour Angle. Elevation-over-Azimuth General features This two axis configuration can direct the antenna axis toward any point in the sky. The nominal coordinate system is centered on the horizon – Elev = 0 deg, Azim = 0 along a local meridian of longitude. The motion of the positioner will be 0 to 90 deg in elevation; -180 to +180 deg in azimuth. Moving targets near the horizon are tracked with nominal azimuth and elevation motions. Near zenith, slowly moving targets require slow elevation and fast Az velocity. Zenith (Elev = 90 deg) is known as the “keyhole” for the Azim/Elev positioner requiring infinite Az velocity. Targets cannot be tracked while passing through the "keyhole". There is a corresponding “keyhole” (not considered for our applications) through the ground at El = -90 deg. That is, the keyhole occurs at the extensions of the azimuth axis. The analogy: The human body can turn around its vertical axis (azimuth motion), and tilt its head (elevation). Try to follow a target going nearly over head; the body has to turn very quickly with the head looking nearly straight up. Physically, the antenna can be made an “elegant” structure.



286

0o

90o

Azimuth angle 0o to 360o

Elevation axis

Azim

uth

axis

Pede

stal

Reflector and support hub

Reflector axis

Elevation angle

0o North

90o

180o

Figure 8.2-1 Elevation-over-azimuth positioner

(a) (b) Figure 8.2-2 Elevation-over-azimuth positioner, elevation drive: (a) with jack screw; (b) gear drive. To be recognized here – the gear drive offers a linear motion with angle; the jack drive offers a non-linear motion as a function of elevation angle. The jack drive mechanism is significantly less expensive than the gear drive. (Photos used with permission of General Dynamics SATCOM Technologies Inc.)

Elevation jack screw

Azimuth jack screw

Elevation gear

Azimuth drive



287

X-Y or Cross Elevation-over-Elevation General features This two axis configuration can direct the antenna axis toward any point in the sky. The nominal coordinate system is centered on the local zenith – Elev = 90 deg, Cross-Elev = 0 deg. The motion of the positioner will be 0 to 180 deg in elevation; -90 to +90 deg in cross-elevation. Moving targets near the zenith are tracked with nominal El and Cross-El motions of the positioner. However, for targets near the horizon along the El axis, the Cross-El motion rapidly becomes excessive. The horizon points at the extensions of the (upper) cross-elevation axis form two “keyholes” for the X-Y antenna. The analogy: The human head can move up and down (elevation motion), and tilt side to side (cross-elevation motion). Try to follow a target moving along the horizon; the eyes are looking to the horizon. This represents elevation = 0 deg. When the target continues to the left along the horizon, the head must tilt to the left (representing cross-elevation approaching -90 degrees). If the target continues past -90 along the horizon, the elevation must now very rapidly move to +180 degrees in elevation to capture the continuing target position. In contrast to the Az/El, the X-Y is somewhat inelegant and generally more expensive.

horizontal Y-axis

horizontal X-axis0 - 180o

0 - 180o

Reflector hub

pede

stal

Ver

tical

axi

s

Reflector axis

Z

Y

X

Figure 8.2-3 X-Y or Elevation-over-Cross Elevation positioner



288

Figure 8.2-4(a) Example of X-Y or Elevation-over-Cross Elevation antennas at the National Oceanic and Atmospheric Administration – NOAA - site at Wallops Island, VA.

Figure 8.2-4(b) Example of X-Y or Elevation-over-Cross Elevation antennas at Vertex, Kilgore, Texas. (Photos used with permission of National Oceanic and Atmospheric Administration). Declination-over-Hour Angle General features A two axis configuration set to view the geostationary arc with movement around the Hour Angle axis. The declination angle is set to accommodate the fact that the GEO orbit is only 42,000 km from the earth's center. See Figure 8.2-5. One can view the Declination-over Hour Angle positioner as representing a “bridge” between El-over-Az and X-Y, dependent on its position on the earth’s surface. At the equator, it equals the X-Y positioner, since the nominal Azimuth axis lies in the horizontal. At the geographic poles, its features are the same as the El-over-Az. See Figure 8.2-6

Elevation gear

Cross-Elevation gear

Elevation

Cross-Elevation

Cross-Elevation

Elevation

Cross-Elevation Elevation



289

Reflector axis

Hour Angle axisPedestal

Fixed declination angle = 90o - geographical latitude

Variable declination angle

Variable declination axis

Hub

± 90o Hour Angle

Figure 8.2-5 Declination-over-Hour Angle positioner

20o

40o

60o

80o

Center of the Earth

45 deg Latitude

Equator

North Pole

= _ 5.0o

= 0.0o

= _ 8.6o

Hour Angle

= Declination angleTilt angle for the antennato see the target satellite in GEO position approximately 36,000 km from the earth's surface

HA = Hour AngleRotation parallel to theearth's axis to see a target satellite in angle from the e.s. meridian, also called the Hour Angle because time is measured proprotional to angle from Greenwich

Note:For the antenna pointing toward a target infinitely far away in the equatorial plane, = 0o.

For the antenna to point to satellite, in GEO, it must be tilted "down" by an amount called "declination".

0oEquatorial plane

South Pole

Figure 8.2-6 Definitions of declination and hour angle Interestingly, each of these positioners can be realized with particular orientations of the elevation-over-azimuth positioner. Similarly, one could consider the Azimuth-over-Elevation as being a reasonable configuration. However, mechanical disadvantages associated with asymmetrical azimuth bearing loads, causes this arrangement to be less interesting. The appropriate choice for the mechanism to move the antenna will be dictated by the nature of the orbit of the target satellite. For example, to steer the antenna to a satellite in geostationary orbit - GEO - (with range approximately 36000 km), can be accomplished easily and inexpensively with an elevation-over-azimuth positioner, because the elevation angle range will be limited to less than 0 and 90 degrees, and the azimuth angle range will be limited to less than -90 and +90 degrees. low-earth orbit - LEO - (< 1000 km), will require an X-Y mount, which can cover the necessary 0 to 180 degrees range in elevation and less than -90 to +90 degrees range in cross-elevation. This satellite orbit may present overhead passes which the antenna positioner must follow.



290

The overhead (zenith) pass cannot be reached by the elevation-azimuth pedestal because at zenith the azimuth angle is not defined - the so-called "keyhole". Figure 8.2-7 shows the antenna motion for a LEO target. Even if an elevation motion of 0 to 180 degrees were provided, that would solve the problem for a direct zenith pass, but not for a slightly off-zenith pass.

Elevation angle

LEOSatellite

ZenithPass

Over-zenithPass

azim

uth

axis

azim

uth

axis

Elevation axisAzimuth axis must rotate with infinte velocity from (a) to (b).This represents zenith"Keyhole" on non-trackable target pass

[a] [b]

Azimuth rotation

satellite zenith passage

Figure 8.2-7 Antenna motion requirement for a "Keyhole" pass Point of interest: If the elevation-over-azimuth pedestal is mounted onto a third axis - to tilt the azimuth axis about a horizontal cross-axis - the position of the keyhole can be shifted away from the local zenith. See Figure 8.2-8. This presents a favourable alternative to the relative complexities of the X-Y positioner.

[c]

Shifted or tilted antenna "Keyhole"

Elevation axis

Tilted azimuth

axis

Terget at zenith

Figure 8.2-8 The tilted azimuth axis configuration as an alternative to the X-Y positioner.



291

Y - axis

X

X - axis

Z

Figure 8.2-9 The antenna motion requirement in the "Keyhole" position for the X-Y postioner Medium earth orbit - MEO - (approximately 6,000 to 10,000 km), may be covered with an elevation-azimuth or the X-Y pedestal. Generally, for (electrically) small antennas, the X-Y structure may represent an attractive alternative to the elevation-azimuth pedestal. Deep space targets, such as the planets in our solar system, an elevation-azimuth pedestal is appropriate, since all interesting points lie within the available range of motion. Stars may be tracked with one of three positioners - (a) elev-azim; (b) X-Y; or (c) hour-angle/declination. The Hour-Angle/declination positioner is more familiarly known as the "polar mount" as used in optical telescopes for astronomical observations, and represents a one-axis mechanism which is set to be parallel to the polar axis at the local geographic latitude - hence the "polar" mount. Only the hour angle motion is required to observe distant stars as they traverse the local sky with the passage of time. Since the passage of time is measured in hours, the angular motion is called "hour angle". The declination angle, once set for a particular target, is used for minor corrections incurred by the fact that observations are being made from a slightly ellipsoidal earth rather than a spherical earth. This type of mount also represents the basis for the design of the Torus antenna, discussed in Section 7.4. 8.3 Reflector Support Structures Reflectors represent large surfaces which need to be tilted into positions ranging from looking straight up to the zenith sky all the way down to the horizon. In this process, the primary objective is to build a reflector assembly that does not change its shape due to effects of gravity, wind and ice and/or snow loads, or to a weakness in the support structure. The usual approach is to design a strong and stiff hub structure that carries the elevation axis, to which a radial set of trusses are rigidly connected, in a form similar to that of a spider's web. This hub and "radials", when tilted in elevation is then sufficiently strong to not change shape. All materials will deflect under load. The challenge is to make the structure sufficiently stiff that the signal loss is minimized to a specified amount. Figure 8.3-1 shows several methods for the design of "radials" and the necessary cross bracing for stiffness.



292

(a)

(b) (c) Figure 8.3-1 The reflector supporting back structure. (a) The reflector back-structure on the Parkes 64m radio telescope. Notice the curved reflector support elements, the thin radials, and the relatively small diameter hub. The reflector can support S-band performance. The inner 15m supports Ka band; the middle 42m supports S-band; and the outer 64m mesh supports VHF frequencies. (Used with permission of CSIRO, Australia). (b) Steel truss radials providing support for stretched panels whose profile is maintained with “Zs”. (c) Noded aluminum radials providing support for self-supporting formed double-skinned honeycomb panels. (Diagrams in (b) and (c) used with permission of General Dynamics SATCOM Technologies Inc.)



293

When the nominally rigid and correctly profiled reflector elements are mounted onto the radials, they will not be stressed by the supporting structure, and the reflector assembly will retain its basic parabolic shape. To ensure the correct profile, the reflector surface elements are mounted with built-in adjustment. Optical observations of targeted mounting points on the reflector surface provide the means to map the surface and determine its profile accuracy. For large antennas, particularly those that must operate at high frequencies, the deflection of the reflector surface due to gravitational forces can produce excessive deflections that degrade the signal. If the final antenna alignment is known so that the antenna surface can be aligned in the operational position, the gravitational forces on the reflector that distort the RF signal can be eliminated. Much like the deflection in a beam can be counteracted if the supported weight is known so that the beam can be cambered by the amount of the deflection. If the operating alignment of the antenna is not known or the antenna may be positioned on different satellites during it lifetime, a study is made where gravity is applied to the reflector at different elevation angles and the antenna is aligned at the optimal elevation angle that produces an equal deflected rms value at 5 degrees elevation and 85 degrees elevation. Then the deflections due to the movement of the antenna off this optimal position will be minimized. In general, the support structure and the reflector must be designed for two conditions. The structure and reflector must be stiff enough to maintain the RF signal and the structure and reflector must be strong enough to meet the maximum environmental conditions applied to the structure during the life of the antenna. For strength considerations, the design of reflector support structure must take into account the effects of wind, snow, and ice. Seismic forces are often specified in the loading criteria but because the structure presents a large wind sail area with a relatively low weight, wind forces will almost invariably control the design over seismic forces. If the antenna operates at low frequencies and will be designed for high winds, the strength requirements may control the design. However, most designs are controlled by stiffness because of the low deflection requirements for compliant performance. For stiffness considerations, the antenna must meet deflection requirements and rms maximums in reasonable wind speeds which are specified as mean wind speeds with wind gusts. This is because wind can load the antenna over several hours. The mean wind speed can be corrected to some extent with the control system, while wind gusts must be resisted by the stiffness of the structure. Typical operational wind speeds are 30g45 and 45g60. Figure 8.3-2 shows the distortional effects of wind on a reflector. The deflections have been magnified several hundred times so the deflections can be seen. The original shape of the reflector is shown by the dashed lines. Maximum environmental winds, usually referred to as survival winds, are specified as gust wind speeds. These wind speeds are normally winds measured as 3 second gusts. Although antenna structures have shorter response times than 3 seconds, usually in the 0.5 second range, gust factors are used to correct for this fact when converting wind speed to wind pressure. Large antennas are typically anchored on large concrete foundations. The size of the foundation is controlled by the weight and size of the foundation resisting the wind forces trying to ‘overturn’ the antenna. Since concrete is inexpensive relative to the cost of an antenna, standard foundations are sized to resist hurricane force winds even when not being placed in hurricane prone areas. However those foundations may be reduced if the location of the antenna is know to be in a lower wind area. The traditional equation used by Vertex for calculating operational equivalent wind speeds

3

222 mG

meq

VVVV

(8.3.1)

where eqV equivalent steady-state wind velocity

mV mean wind velocity

GV gust wind velocity



294

Values for typical specifications: eqV 35.7 mph for winds 30g45 mph;

eqV 50.5 mph for winds 45g60 mph The EIA 411 equation for equivalent wind speeds [1],[2]

41̀

422224

33

36

mGmG

mmeq

VVVVVVV (8.3.2)

Values for typical specifications: eqV 31.2 mph for winds 30g45 mph;

eqV 45.8 mph for winds 45g60 mph Wind velocities must be converted to wind pressures for structural analysis. The standard equation for converting wind speed to pressure is P = 0.00256 V2 Where P = dynamic wind pressure in psf V = wind speed in mph

0.00256 = conversion factor based on wind density at standard temperature and pressure. Table 8.3.1 shows wind pressure values for equivalent wind velocities, as well as a value for a survival wind of 125 mph. Standard antennas are designed to survive winds of 125 mph.

Table 8.3.1 Pressure loads on an antenna for various wind conditions eqV (EIA 411) mph 31.2 45.8 125

eqP (EIA 411) lb/ft2 2.49 5.37 40.0

eqV (Vertex) mph 35.7 50.5 125

eqP (Vertex) lb/ft2 3.26 6.53 40.0 Wind applied to a smooth circular surface will produce a different force than wind applied to a flat surface and must be accounted for when applying the wind load to an antenna. The wind pressures calculated above must be modified for different wind attack angles and antenna orientations by coefficients which are called drag coefficients. Although drag coefficients are well documented for standard shapes such as pipe and flat signs, parabolic antenna shapes are a special case. Fortunately several wind tunnel tests have been documented that furnish the designer with those values. For instance the wind pressure applied directly into the convex surface of an antenna will be about 1.5 times the dynamic wind pressure whereas the wind pressure applied to the concave back surface of an antenna will be about 1.0. The drag coefficients for wind applied at several different angles is known from the test. Further considerations in the design of reflector support structures take into account the effects of wind and loading effects of snow and ice. The very large wind forces act to distort and overturn the antenna. To counteract this, antennas are typically anchored in a large concrete foundation that has been proportioned accordingly. In locations where high winds and even hurricanes (typhoons or cyclones) occur, extra safety factors and structural reinforcement is included in the design to ensure that the antenna will survive. Figure 8.3-2 shows the distortional effects of wind on a reflector. Wind velocities must be converted to wind pressures for structural analysis. An expression has been found as a result of wind tunnel tests.



295

The equation for converting wind velocities at standard temperature and pressure is:

200256.0 VPeq (8.3.3)

where eqP equivalent wind pressure in psf

V wind speed in mph

This expression for eqP corresponds to a wind approaching the antenna at approximately 120 degrees off axis.

Figure 8.3-2 The distortional effect of wind load on a reflector. The reflector aperture will be translated and rotated. The effect on the pointing of the beam is discussed in Section 8.7. [1]. Note: the deflections shown here have been magnified for visual effect. 8.4 Reflector Geometries All reflectors are surfaces of revolution of one of three conic sections with symmetry around the focal axis. Offset reflectors are segments of such surfaces of revolution. The primary reflector is usually parabolic. Relevant fundamental features of the parabola will be briefly discussed in the following segment. Although most antenna systems utilize "shaped" surfaces (discussed in Section 2.6.3), they are still basically derived from the various conic sections involved. From a structural point of view, there is very little difference between the shaped and unshaped assemblies; however from an RF performance point of view, shaped reflectors can provide considerable enhancement in performance. Figure 8.4-1 shows the dimensional differences between a shaped and unshaped Cassegrain reflector system.

120o

Wind direction



296

9.0m Cassegrain Antenna Geometry

0

20

40

60

80

100

120

140

0 50 100 150 200

Radius - inches

Mai

n R

efle

ctor

Dep

th -

inch

es

Difference in Main Reflector Profile wrt Parabola

-0.6

-0.4

-0.2

0

0.2

0.4

0.6

0.8

0 50 100 150 200

Radius - inches

Prof

ile D

iffer

ence

wrt

Par

abol

a

Figure 8.4-1 (a) show the 9m shaped Cassegrain reflector system profile. (b) indicates the dimensional difference in shape of the main reflector with respect to a true parabolic - in total approximately 0.5 inch. The subreflector shape difference is even smaller. Some essential dimensional aspects of the parabolic reflector can be determined from the following relationships: The basic parabolic profile as seen Figure 8.4-2

F

xz

4

2

(8.4.1)

where F the focal length xD 2 aperture diameter

Front aperture area S

2

2

DS (8.4.2)

Side projected area sA

F

xAs 3

3

(8.4.3)

Total surface area nA of the parabolic surface

322 843

23

FFxF

An

(8.4.4)

Parabolic arc length sL from the vertex to any point along the surface is given by

2222 4ln44

1FxxFFxx

FLs (8.4.5)

x

z

y

12

3

45

6

PanelTier #

Figure 8.4-2 Reflector coordinate system



297

8.5 Reflector Accuracy Great effort is given to the theoretical design of a microwave reflector antenna and its feed system, to guarantee the required performance. But the mechanical condition of the antenna is terribly important to support the guaranteed performance. What is meant by "reflector accuracy" ?? An analogy: look into a flat mirror at home, and if the mirror is flat, the image is unremarkable and expected. Just a small indentation will prompt a noticeable deformation in the image. The deeper the indentation, the greater the degrading effect on the image. If the number of indentations increases in a random manner, then the image will have the corresponding deformations, but by and large still recognizable. If the indentations occur regularly or systematically across the mirror, the image will appear particularly disturbing. If the indentations are small, closely spaced, and large in number, the image will still appear completely recognizable, but "smudged". At microwave frequencies, similar effects can be observed. The image distortion can not be directly seen, but can be detected in changes in the RF antenna pattern. Large deviations in reflector profile will change the main beam as well as sidelobe features. Many large deviations will alter the overall sidelobe envelope. Systematic deviations will present pattern singularities - in the form of large SLE excursions (saber-teeth sidelobes). If there are many small deviations, the sidelobe envelope will rise, and the sidelobe nulls will fill in. Since sidelobe performance is a controlled requirement, it becomes imperative to ensure that the reflector surface conforms to the design shape. Reflector deformations may occur due to faulty surface fabrication, distortions introduced by the reflector support structure, gravitational effects as the reflector is tipped in elevation angle, or due to loading effects by wind, snow, ice. When a reflector surface is deformed, what actually changes to cause degraded performance ?? The function of the parabola relies on the expression for equal path lengths from the focus to the aperture plane. If one or more of the path lengths is not equal to all others, this represents local distortions in the parabolic profile. Figure 8.5-1 shows a flat reflector. An incident ray is intercepted by the reflector at point 1. The reflected ray moves away from the reflector at an angle with respect to the normal to the surface towards point 2. The normal to the surface is n. The angle between the incident and the reflected wave is 2 - Snell's Law of reflection.

1

2n

θ θIncident ray

reflected rayn

Incident ray reflected ray

Flat reflector surfaceFlat reflector surface

[a] [b]

1

2n

θ1 θ2Incident ray

reflected ray

3

reflected rayspartially re-directed

into varied directions

Flat reflector surfacewith defective region

[d]

n

Incident ray

Flat reflector surfacewith defective region

[c] Figure 8.5-1 (a) and (b) Reflection from perfect reflectors. (c) and (d) Reflection from reflectors with embedded defects. (c) shows a discontinuity in the reflector; and (d) shows a change in profile of the nominally flat reflector.



298

If there is a deviation from the flat reflector at point 1, the reflected ray will go elsewhere, and not toward point 2. Figure 8.5-2 shows the path of signal travel for a parabolic antenna. A signal will emanate from the focus F at 1 and be intercepted by the main reflector at point 2. Here it will be reflected along a path parallel to the focal axis toward point 3 in the aperture plane. At 2, if everything is perfect, we may draw the tangent to the parabolic surface. The normal will be at right angles to the tangent. The reflected ray will leave the main reflector surface at angle to the normal towards point 3. The angle is also equal to the angle between the tangent at 2 and the Xm axis of the parabola. If a change in reflector profile occurs at 2, the consequence will be that the ray of interest will follow the path 1 to 2 to 4. Therefore this segment of the incident signal is lost.

F

Parabola

1

23

Aper

ture

pla

ne

θθ

Tang

ent a

t "2"

Normal to the surface at "2"

Xm

θ

F

Parabola

1

2

Aper

ture

pla

ne

θ2Ta

ngen

t at "

2"

Normal to the surface at "2"

Xm

4

θ1

Zm Zm

[a] [b]

Figure 8.5-2 (a) The reflection features of the perfect parabolic reflector; (b) the reflection characteristics at/near a defect in the nominal parabolic profile. Examining Figure 8.5-3, we can relate the geometry of the deformation in the reflector surface to path length error. The undeformed path length = 1 to 2 to 3. The deformed path length = 1 to 7 to 4. Path length error = [1 to 7 to 4] - [1 to 2 to 3] which when very small dimensions are considered, is very nearly equal to [2 to 7 to 8] Path length error ps

and )1cos2()2cos( 2 ssp

from which 22 cos2)1cos2( sss The deformation of the reflector surface at 2 is something that can be measured as a quantity d.

cos

ds

Now cos2d (8.5.1)



299

F

Parabola

1

2

Aper

ture

pla

ne

Xm

4

Zm

3

6

Lengths [1 to 2] + [2 to 3]= [1 to 5] + [5 to 6] = constant

Length [2 to 4] is > [2 to 3], and therefore does not fit the profile of the parabola

5

s

p

θ

θ

Normal Ape

rture

pla

ne

tangent to the undeformedreflector surface

tangent to the deformedreflector surface

d

78

2

d = measurable depth of surface deformation

3

1

9

4

[a]

[b]

Figure 8.5-3 (a) The signal path for the ray encountering the reflector defect. (b) The geometry for the resulting path length error. This can be interpreted as "path length error = 2 x depth of deformation multiplied by the cosine of the tangent angle of the parabola at the radial distance from the focal axis at which the deformation occurs". The common expression for path length error is "half path length error" which is then just the depth of the deformation. All "half path length error" events across the reflector surface can be measured and statistically evaluated in terms of a standard deviation which is represented by the root-mean square summation of all deformations, commonly called rms . Fortunately a relatively simple expression has been developed (by John Ruze) that connects reduction in antenna gain performance with the surface error deformations.

24

43429.4log10

2

eG db (8.5.2)

where = rms , = wavelength. This can be simplified to 22763.0 fG db for rms in cm and f in GHz

2200763.0 fG db for rms in mm and f in GHz

22923.4 fG db for rms in inches and f in GHz 8.6 Design of Reflector Panels From the preceding discussion it is clear that the reflector profile must be maintained at all times and for all positions of the antenna. The trick now is to devise a method whereby the reflector can be fabricated in a reasonable manner.



300

8.6.1 Main Reflector Fabrication Depending on the size of the reflector, it may be a one-piece reflector, or a set of pie-shaped segments, as shown in Figure 8.6-1 (a) and (b).

x

1 2 3

3

z

y

12

34

56

PanelTier #

x

y

(a) (b) Figure 8.6-1 Examples of panel configurations for large reflector assemblies For large reflectors, there may be several tiers of pie shaped sections. The total surface area of the parabolic reflector is given by

32

322 84

3FFx

FAn

(8.4.4)

The length along the surface of a panel is given by

2222 444

1FxxlnFxFx

FLs (8.4.5)

These two expressions offer the means to calculate the dimensions of a panel. There are several methods of preparing reflector panels. Stretched panels with “zees” Figure 8.6-2 shows a 4’ x 8’ sheet of aluminum being stretched or pulled over a tool which has the shape as calculated by the shaping analysis discussed in Section 2.3.3, and (8.4.4) and (8.4.5). Most metals can be stretched up to a yield point so that when the load is released the material will return to the original shape. When stretched beyond the yield point it enters a plastic state where permanent deformations will occur before the material fails. This property of metals is used to shape the aluminum sheets to the desired contour. This happens before it tears or is otherwise permanently damaged.

(a) (b) Figure 8.6-2 The panel stretching process at General Dynamics, Kilgore, Texas. (a) mounting the flat sheet; (b) the stretched sheet being prepare with coordinate alignment holes. (Photos used with permission of General Dynamics SATCOM Technologies Inc.)

Sheet gripping jaws

Stretch tool or form

Stretched sheet



301

The sheet is grabbed by the two jaws of the machine and pulled taught. Then the tool is pushed upward from below the sheet, thereby causing the aluminum to be subjected to equal stretch forces along the surface of the tool. When released, the sheet will no longer be flat, but rather have the shape of the tool. The newly formed sheet (or skin) is laid on to a second tool which will cut the skin into the required "pie" shape. This can be a saw, or a water jet cutter, which provides a finished edge without burrs. See Figure 8.6-3.

Figure 8.6-3 Cutting the freshly stretched panel to its required “pie-shape” is done on the water jet cutter. (Photos used with permission of General Dynamics SATCOM Technologies Inc.) The next stage involves vacuuming the prepared skin onto a third tool, like the stretch tool, which carries the precise shape of the required panel. See Figure 8.6-4.

Figure 8.6-4 Panel on the assembly tool with “zees” installed. (Photo used with permission of General Dynamics SATCOM Technologies Inc.) Here, flexible stiffeners (called "Zees") are adhesive bonded onto the back surface of the skin in both radial and circular directions, creating box like structures on the back of the skin for stiffness. The zees are fabricated by taking "Z" shaped aluminum sections and "curfing" or slotting one edge as seen in Figure 8.6-4. When the adhesive has cured (hardened), the finished panel can be lifted away from the tool, and it will hold its shape. The next stage in preparing the panel is to measure the surface profile and comparing it with the required shape as shown in Figure 8.6-5(a). The result will show any deviations in the surface and a sample mapping is presented as in Figure 8.6-5(b).

water jet tt

Reflector form



302

Figure 8.6-5 (a) Panel measurement (b) Sample surface measurement (Photo used with permission of General Dynamics SATCOM Technologies Inc.) The laser emitting instrument also receives signal from the hand-held precision sphere, which is moved over a predetermined grid on the reflector surface. (b) shows the result of mapping on a 5”x5” grid. For greater precision, a finer grid is chosen. Point of interest: Careful attention must be given to the choice of adhesive, and the configuration of "Zs". Most adhesives shrink during the curing process. Many adhesives have, after curing, a surface adhesion strength which is larger than the tensile strength of aluminum. Laying a bead of adhesive onto the top surface of the panel skin and letting it cure, will locally shrink the top surface slightly, causing the lower surface to buckle. When "Zs" are attached, the buckling effect can be seen, but the magnitude remains small. When the "Zs" are attached in a box configuration, the "hard" boundaries presented by the box-line of adhesive plus "Zs", tends to impede linear thermal expansion of the aluminum. When the post-cure ambient temperature changes, the panel skin inside the box tends to buckle inwards. The distortions in the surface can be severe, as seen in Figure 8.6-6.

(a) (b) Figure 8.6-6 The result of the effects produced by "Zs" mounted into a box structure on the back of the panel are shown in (a). Thermal differences between the time of assembly and the time of observation have distorted the panel. (b) shows a different panel design with practically no distortions. (Photos used with permission of General Dynamics SATCOM Technologies Inc.)

Laser emitter and detector Precision reflecting target

Computer control



303

If carefully made with good tools, a surface accuracy of 0.020 to 0.015 inch rms can be achieved, depending on the size of the panel. In broad terms, the smaller the size of the reflector, the smaller the achievable surface rms. Stretched panels with precision profiled radials In this variation of the stretching technique, the skins are stretched as before, and the stiffeners are made from stretched "T" or "L" shaped bars. These stiffeners are then either riveted or screwed to the skins to form the finished panels. For some applications, the stiffeners form an integral part of the radials, and the skins are then mounted without adjustment to the radials. The reflector accuracy is determined by the accuracy of the hub/radial machining and assembly, as shown in Figure 8.6-8. If carefully made with good tools, a surface accuracy of 0.005 to 0.012 inch rms can be achieved, depending a little on the size of the panel.

Figure 8.6-7 (a) Precision hub and radial interface (b) Formed interfaces for stretched panel mounting

Figure 8.6-7 (c) rear view of completed antenna (d) Front view of completed antenna. (Photos used with permission of General Dynamics SATCOM Technologies Inc.) Stretched panels with honeycomb core between two stretched panels For high precision applications, instead of sparsely located "Zs", an aluminum honeycomb material mounted between two stretched skins provides a high density reflector panel as shown in Figure 8.6-8. The attachment to the two skins is with a uniformly spread layer of adhesive. This becomes an extremely stiff panel which is relatively low weight and not easily damaged. If carefully made with good tools, a surface accuracy of 0.005 to 0.010 inch rms can be achieved. However, thermal sensibilities in the reflector when



304

subjected to direct sun illumination may require careful consideration, for example white diffusive paint to minimize surface temperature. Trapped air in the honeycomb, when heated excessively will deform the panels.

Figure 8.6-8 Example of the honeycomb material and its application in a precision reflector panel (Photos used with permission of General Dynamics SATCOM Technologies Inc.) Spinnings For small axially symmetric reflectors in low frequency applications, a fast method for making reflector assemblies is to stretch the aluminum skin against a tool while it rotates. In contrast to the previously described "area stretch" process, the aluminum sheet in this case is "point stretched" as the pressure wheel pushes the material against the tool one very small area segment of the skin at a time while the work is rotating - see Figure 8.6-9(a).. The final stage of the "spinning" process is to turn a small radius rim around the outer edge of the reflector, adding to the stiffness of the reflector. This assembly needs no back-frame or radials for added support, but can be bolted directly to the hub. Typically, this technique is reserved for antennas of 2 to 3 meters in size, and operating less than 10 GHz. If carefully made with good tools, a surface accuracy of 0.050 to 0.025 inch rms can be achieved, depending on size. Figure 8.6-9 (a) The spinning process. (b) Finished spinnings with rim. (Photos used with permission of General Dynamics SATCOM Technologies Inc.)



305

Fiberglass and carbon fiber lay-ups For small high precision applications, glass fiber or carbon fiber lay-ups with included stiffeners offers a relatively fast and accurate manufacturing method. This approach is particularly attractive for high durability service as seen in the military arena or the commercial mobile broadcast business.

(a) (b)

(c) (d) Figure 8.6-10 (a) Preparation of the tool; (b) Honeycomb internal structure; (c) Finished panel; (d) Completed reflector assembly. (Photos used with permission of General Dynamcis SATCOM Technologies Inc) If carefully made with good tools, a surface accuracy of 0.007 inch rms can be achieved. Because of the labour intensive process, this fabrication approach is very expensive. Machined panels For very high precision applications such as found in radio astronomy for high GHz and Terahertz (THz) applications, reflector assemblies consist of a large number of relatively small area panels which are machined from a single solid piece of aluminum. These individual panels are then each mounted onto adjustable supports on a back-structure of radials. In some instances, anticipating small deformational movement of the radials, each panel can be automatically adjusted to compensate for this movement, resulting in a very accurate reflector structure. This obviously requires a clever control system in which a model of the back structure and its structural characteristics is included to provide guidance for the auto-adjustment of the panels. The use of aluminum is to reduce the weight and thermal loads to a minimum. If carefully made with good tools, a surface accuracy of < 0.0003 inch rms can be achieved.



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8.6.2 Subreflector Fabrication The two reflector antenna geometries are represented by the Cassegrain (with hyperbolic subreflector), and the Gregorian (with ellipsoidal subreflector) configurations. Manufacturing methods for one-piece reflectors include: Spinning Machining - base material aluminum casting to approximate shape, or from the raw solid Fibreglass lay-up on a metal tool, then metalized Carbon fiber lay-up on a carbon fiber tool For a negligible contribution to the overall reflector system surface error budget, a good rule of thumb is for the subreflector surface rms to be subreflector rms = [main reflector rms / M] M = magnification and can have a value between 3 and 5, depending on the geometry of the reflector system. A machined subreflector for commercial applications can be made to reach an rms = < 0.002 to 0.005 inch rms, depending a little on diameter. Reflectors made with fiber-glass or carbon fiber lay-ups generally will tend to suffer from an accumulation of errors - once from the errors in the tool, and again from the lay-up process. Glass reflectors require a metalization process, which can suffer from mishandling. A number of instances have been encountered in which the metalization was damaged, not recognized under a coat of paint, until unexpected low antenna gain and unusual antenna patterns were recorded. 8.7 Pointing Accuracy The fundamental objective of the antenna is to collimate all transmitted signal toward the target satellite. If one were to represent the main beam of the antenna as a "line" with no angular extent, then it can be "pointed" toward the satellite. If an error in pointing occurs, then for a satellite in the orbital arc at about 36,000 km, the "line" will miss the target by a distance d at the satellite of R meters.

deg

180

Rd (8.7.1)

Table 8.7-1 shows the magnitude of d for a number of conditions Table 8.7-1 Satellite range mis-pointing error miss distance 36000 km 0.1 deg 63 km 0.01 deg 6.3 km 0.001 deg 630 m 0.0001 deg 63 meters For the practical antenna, as we have seen in Chapter 2, the beam has dimensions related to antenna size and frequency of operation. Therefore, for small errors in pointing, the beam will not "miss" its target, but a loss in signal will be experienced at the satellite, as indicated by the change in signal level of the pattern captured by the satellite. The question now is how much "pointing error" is permitted for the satellite link ?? If the system can tolerate a 3db drop in signal level, the following table offers representative pointing errors associated with a 9m antenna operating at a variety of frequencies.



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The practical relationship between signal level on the pattern and angle off-axis is given by

Ddb

703 (8.7.2)

or rewritten as

metersGHzdb Df

21

3 (8.7.3)

Table 8.7-2 Antenna size Frequency 3db beamwidth Angular mis-pointing 9m 2 GHz 1.167 deg 0.583 deg 9m 6 GHz 0.389 deg 0.194 deg 9m 30 GHz 0.078 deg 0.039 deg where "angular mis-pointing" refers to the angle off-axis. However, as was also pointed out in Section 5.1.2, the link signal fluctuations over a 24 hour period are constrained to 1.0 db, of which 0.5db is allocated to changes in the Tx and Rx electronics - HPA and LNA subsystems. The remaining 0.5db represents the “allowable system cross-pol” the antenna may demonstrate, see Figure 8.7-1. Table 8.7-3 shows the 35db cross-pol contour, and it lies inside the angle under the 0.5db beamwidth in the principal Az and El planes. The table shows revised pointing error values for the 9m.

1/2db = 0.068 deg

db = deg Corresponds to 1db contour

0db

0.5db

1.0db

3db

0db

6.4db

9.3db

0o

0.068o

0.096o


Figure 8.7-1 Definition of the specification, and extent of the 1db cross-pol contour in the antenna pattern The practical relationship between signal level on the pattern and angle off-axis is given by

2

33

nn

P

P or

33 P

Pnn (8.7.4)



308

and

3

70P

P

Dn

n

(8.7.5)

where for nP 0.5db and 3P 3db

metersGHzdb Df

573.8

5.0 degrees (8.7.6)

Table 8.7-3 Allowable mis-pointing for cross-pol Allowable angular

Antenna size Frequency 0.25db beamwidth mis-pointing for Xpol 9m 2 GHz 0.4763 deg 0.2381 deg 9m 6 GHz 0.1588 deg 0.0794 deg 9m 30 GHz 0.0318 deg 0.0159 deg

So the net allowable pointing error is 25.0 db

or less. This is about 20% of the 3db beamwidth.

So far we have considered the reflector simply being "mis-pointed", but still retaining its theoretical shape. In practice, an antenna will be subject to uncertainties in pointing by several external mechanisms:

Errors in the position encoders giving the Az and El angle readouts, in part due to errors in the alignment of the Az and El axes

Deformation of the reflector system by gravity, which will also be dependent on El position Thermal and wind loads on the structure

The minimum reasonable acceptable pointing error for GEO satellite operations is 10% of the 3db beamwidth. Table below shows the pointing error angles for the case of the 9m antenna working at various frequencies, and as it turns out, 1/8th db beamwidth corresponds very nearly to 10% of the 3db beamwidth. Table 8.7-4 Allowable mis-pointing for 10% bandwidth

Allowable Antenna size Frequency 0.125db beamwidth Angular mispointing = 1/10 x 3db bw 10% of 3db beam 9m 2 GHz 0.2382 deg 0.1191 deg 9m 6 GHz 0.0794 deg 0.0397 deg 9m 30 GHz 0.0159 deg 0.0080 deg As discussed in Section 8.5, when the reflector surface is deformed, the image is changed. If we consider the ray diagram of Figure 8.5-1, the image can be viewed as being made up of rays that are redirected in the reflection process. If the reflector is perfect, the rays retrace themselves. If deformed, the rays will be directed into other directions. Let's consider the Cassegrain antenna. When the spherical illumination comes from the focus, the perfect reflector will redirect them into the rays that are circularly symmetrically distributed around, and parallel with, the reflector axis. This collection of rays will be represented by the main beam of the antenna pattern and its direction of propagation will be along the axis. If the feed is moved away from its focal position, the resultant effect on the path length errors summed across the aperture will cause the features of the pattern to change - the pattern shape is modified, antenna gain is reduced, and the main beam is directed away from the axis.



309

Several mechanisms contribute to such pointing errors. Rotation and translation of the main reflector Subreflector rotation and translation Feed rotation Asymmetrical distribution of surface errors

If the support structure of the reflector assembly is not sufficiently stiff, when the antenna is rotated in elevation:

the main reflector surface may translate and rotate (deform) the subreflector may rotate and translate the subreflector may shift axially the feed may rotate (droop)

These errors are shown diagrammatically in Figures 8.7-2 to 8.7-7. The effect on the antenna pattern by these individual error components is partially presented in Section 9. Beam deviation factor Consider the wavefront of a feed pattern beam, directed at a plane (flat) reflector. The direction of the wavefront is defined by the direction of the normal to the wavefront. By virtue of Snell's law, the angle of incidence of the wavefront at the reflector surface will equal the angle of reflection. The ratio of the angle of the reflected normal to the angle of the incident normal is k = 1. This is the case regardless of the nature of the pattern of the beam. A beam with spherical wavefront will remain spherical after reflection; a planar wavefront will remain planar. If however the reflector is parabolic, an incident beam with spherical wavefront originating in the focus is modified to become planar across the entire aperture of the reflector, and its normal points in the same direction as the axis of the reflector. If the spherical wavefront originates at some point offset from the focus, the reflected transformed wavefront will become slightly non-planar across the aperture. The normal to this new wavefront will point in a new direction. The angle of this new direction for the wavefront emanating from the reflector, as a ratio of the angle of incidence of the wavefront from the off-axis feed is called Beam Deviation Factor, and given by [2]

rotationfeed

patternk

(8.7.7)

where rotaationfeed is the angle from the axis of the incident feed pattern wavefront, and pattern is the resulting angle of rotation of the antenna pattern main beam with respect to the axis. The geometry for the beam deviation factor is shown in Figure 8.7-2. Here it can be appreciated that as F increases, feed will decrease, and k tends toward k = 1. The further away the feed is, the more the reflector looks and behaves like a flat reflector.



310

F

z

P

F+z F-z

a b

c

Prime focusFeed position

Reflector focus

x

Parabolic Main reflector

ab = Pangle abc = ac = P sin

θ

Antenna pattern beam direction

Axi

s of

mai

n re

flect

or

Note:Feed rotation +veresults in beam tilt -ve

In Azimuth plane:Feed rotation cwresults in beam tilt ccw

In Elevation plane:Feed rotation downwardresults in beam tilt upward

z

Figure 8.7-2 Ray tracing showing beam deviation in parabolic reflector when the prime focus feed is shifted away, effectively rotated, from the focus. Imagine the reflector as uniformly illuminated by the feed pattern, meaning that the field at the edge of the reflector equals that in the center, and aperture illumination efficiency = 100%. [This antenna is known as having "zero edge-taper"]. This situation represents the most effective transformation of spherical waves to planar wavefronts. On the other hand, imagine a reflector aperture illuminated by a narrow angle feed pattern. In this case, the reflector will be under-illuminated and having a large "edge-taper", meaning also that the effective size of the aperture is smaller than the physical size, and illumination efficiency is small. As discussed in Section 2.2.1, this means lower gain. If the effective D is smaller, this means that F/D is larger, and therefore k will increase toward the value k = 1 as the edge taper is increased. A typical value for k is approximately 0.85. The associated path length error across the aperture is given by [3] rotationfeedP cossin (8.7.8)

where P is the corresponding lateral shift of the feed phase center from the antenna z-axis. is the angle to a sample point on the main reflector. The equi-phase front across the antenna aperture will be tilted with decreasing phase errors to the left, and increasing phase errors to the right. Sign convention: 1. Movement to the right in azimuth and rotation cw as seen from the coordinate system origin (or the antenna hub) = positive 2. Movement up in elevation and rotation cw as seen from the coordinate system origin (or the antenna hub) = positive Beam tilt due to main reflector translation It is assumed here that the reflector is translated with respect to the x-z coordinate system, and the feed remains fixed on the z-axis. For very small P, the angle θ is given as P/F radians. The direction for the antenna pattern beam is now [3]

reesdegF

PkkpatternPt

180

(8.7.9)

where P = translation of the main reflector F = focal length k = beam deviation factor defined in (8.7.7)



311

F

z

θt


Reflector focus

x


Axi

s of

tran

s-la

ted

refle

ctor

P t


Aperture plane

F1Note:Reflector translation -veresults in beam tilt -ve

In Azimuth plane:Reflector translation leftresults in beam tilt ccw left

In Elevation plane:Reflector translation upwardresults in beam tilt upward

Figure 8.7-3 Beam shift for the case of the feed translated laterally from the focus by an amount Pt Beam tilt due to main reflector rotation Here it is assumed that the main reflector and the feed is rotated as an assembly around the parabolic vertex, as shown in Figure 8.7-4. The beam will rotated by )1( kPrPr (8.7.10)

z

θr


Reflector focus

x


Axi

s of

rota

ted

refle

ctor

P r

Aperture plane

θp


F1

Note:Reflector rotation -veresults in beam tilt -ve

In Azimuth plane:Reflector rotation ccwresults in beam tilt ccw

In Elevation plane:Reflector rotation upwardresults in beam tilt upward

Figure 8.7-4 Beam shift due to rotated reflector



312

Beam tilt due to subreflector translation: Subreflector translation, as shown in Figure 8.7-5, in the defined negative direction, results in a pattern beam tilt in the negative or ccw direction. For a lateral shift in the position of the subreflector by a distance Ht, the expected beam tilt is given by [3]

degM

Kk

F

H tHt

180

(8.7.11)

where Ht = lateral translation of the subreflector from the z-axis F = main reflector focal length K = beam deviation factor for the equivalent parabola. [A usual value for K = 0.98 or 0.99 radians] M = the magnification of the equivalent reflector k = beam deviation factor from (8.7.7)

z

x


H t

Axis

of t

rans

late

d su

bref

lect

or

Feed phase center

Subreflector

Translatedsubreflector

F1

F2

Aperture plane

F

Note:Subreflector translation -ve

(as viewed from main reflector vertex)results in beam tilt +ve

In Azimuth plane:Subreflector translation leftresults in beam tilt cw right

In Elevation plane:Subreflector translation upwardresults in beam tilt downward

Antenna beam direction

Figure 8.7-5 Beam shift due to laterally translated subreflector Beam tilt due to subreflector rotation: Subreflector rotation as shown in Figure 8.7-6, into the defined negative direction, results in a pattern beam tilt into the positive direction, and given by [3]

reesdegF

KkacH tHr

180

(8.7.12)

In this analysis the rotation is assumed around the vertex of the subreflector. However, in practice, this may not be the case, meaning the subreflector may be rotated and translated at the same time. This will then require the determination and addition of Hr and Ht.



313

F

z

x


H rAx

is o

f rot

ated

su

bref

lect

or

Feed phase center

SubreflectorRotatedsubreflector

F2

F1

Aperture plane

Note:Subreflector rotation -ve


In Azimuth plane:Subreflector rotation leftresults in beam tilt cw right

In Elevation plane:Subreflector rotation upwardresults in beam tilt downward


Figure 8.7-6 Beam shift due to rotated subreflector. The subreflector is shown rotated around its vertex point, although in practice, it may be rotated around some point between the focus and its vertex, depending on how it is mounted. Therefore the subreflector could be rotated and translated at the same time. This will require an addition of Ht and Hr Beam tilt due to feed translation/rotation Feed rotation or translation, as shown in Figure 8.7-7, into the defined negative direction, will result in a pattern beam tilt into the positive direction, as given by [3]

MF

K feedFr

(8.7.13)

To be understood is that for any rotation and or translation of the elements of the antenna system will result in a tilted phase front - meaning a tilting of the pattern beam. The phase front across the tilted beam will not be planar, but generally convex.

F

z

x


Subreflector

Displaced feed phase center

F1

F2

Aperture plane

F


Note:Feed translation/rotation -ve


In Azimuth plane:Feed translation leftresults in beam tilt cw right

In Elevation plane:Subreflector translation upwardresults in beam tilt downward

Figure 8.7-7 Beam tilt due to feed rotation or displacement



314

Axial displacement of the feed

F

z

x


Subreflector


F1

F2

Aperture plane

F


Note:Feed defocussed away from main reflector -results in no beam tilt, but reduced gain andfilled nulls between main and first sidelobes,because of concave phase front in pattern.

Convex phase front

Optical ray trace indicating diffuse beam

F

z

x


Subreflector


F1

F2

Aperture plane

F


Note:Feed defocussed toward main reflector -results in no beam tilt, but reduced gain andfilled nulls between main and first sidelobes,because of concave phase front in pattern.

Concave phase front


(a) (b)

Figure 8.7-8 Phase error in antenna pattern due to axial feed displacement. (a) for the case of axial displacement away from the main reflector; (b) the case for axial displacement toward the main reflector. Subreflector axial displacement The virtual focus of the subreflector must be placed in the same position as the prime focus of the parabolic (main) reflector for zero path length errors. Any axial shift in position of either the main or the subreflector from these respective positions will result in path length errors. Since the symmetry of the system will not change with an axial movement, the direction of the antenna pattern beam will not change. However, a reduction in gain can be expected from the path length error. Typically, as a rule of thumb for microwave frequencies, the accuracy of subreflector adjustment for the focused condition is < 1/10th of the operating wavelength.

F

z

x


Displaced subreflector

F1

F2

Aperture plane


Note:Subreflector defocussed toward main reflector -results in no beam tilt, but reduced gain andfilled nulls between main and first sidelobes,because of concave phase front in pattern

Subreflector defocussed away from main reflector -results in no beam tilt, but reduced gain andfilled nulls between main and first sidelobes,because of convex phase front in pattern.

S

Convex phase front


Figure 8.7-9 Phase error in antenna pattern due to axial subreflector displacement



315

The structural design of the reflector system must be such that for static conditions (no wind), the reflector geometry stays within the deflection boundaries defined above. - namely, the combined effect of all k-components lies within the prescribed pointing error of 1/10th of the 3db beamwidth. Additionally, the structural design must offer an increased stiffness for wind conditions which will tend to deform the reflector system, producing beam deviations discussed above, to maintain the prescribed pointing error. 8.8 Structural Alignment When the antenna is installed, it will be aligned using optical instruments to achieve the prescribed reflector accuracy. Since every reflector structure will move slightly with differing elevation angle due to gravitational effects, the final alignment is usually made at the operational look angle. If the antenna is required to move between several satellites which may be spread over the entire viewable orbital arc, changes due to elevation angle may be sufficiently large to demand one or more of several corrective measures. Stiffer reflector support structure to minimize pointing errors Manual repointing of the antenna based on measured pointing errors vs elevation angle A control system able to compensate for pointing errors incurred by reflector deformations The influence of dynamic structural deformations can be measured on larger antennas. With the aid of a technique of measuring gain using radio stars (see Chapter 12 Section A.2), one can watch gain variations as a function of elevation angle. Normally, antenna gain is expected to remain constant. If movements in the reflector are sufficiently large, the antenna pattern can become defocused, leading to variations in gain. In some instances, this can lead to rather large gain changes, as shown in Figure 8.8-1.

27.4m Antenna Gain vs Elevation AngleDate: 15 Nov 01 Freq = 12 GHz

64.0

64.5

65.0

65.5

66.0

66.5

67.0

0 5 10 15 20 25 30 35 40 45 50


Ant

enna

Gai

n - d

bi

Date: 15 Nov 01Antenna: M2

Tau-A Star TrackFreq = 12.GHz

Pol = Linear

AIL 20 K ParampDetector = hp8563

Weather: Clear, dampInside Radome: 19 C

Partial Interference from neighbouring 125 ft Radome and 90 ft antenna

Figure 8.8-1 The Ku-band gain response of a 27m antenna with a reflector stiffness problem. The response should nominally be constant with elevation angle. For a well designed antenna, gain may vary less than 0.25db. The measurement suggests that the antenna was aligned for best response at about 15 degrees elevation.



316

Orthogonality A contributor to antenna system accuracy for large viewing angle requirements is an error in Azimuth and Elevation angle axis orthogonality as well as othogonality between Azimuth axis and the local horizon. As seen in Section 8.4, the pointing positions for satellites in the arc depend on a spherical coordinate system in which Azimuth and Elevation angles and the radials to the target satellites are orthogonal or at right angles to each other. Therefore, if the pedestal defining the Azimuth axis is not exactly vertical, then the trace swept by the antenna beam in azimuth will not be parallel to the local horizon, nor the elevation parallel to the local meridian. Therefore, moving the antenna according to the controller position reading will not result in the antenna pointing to the prescribed satellite targets. Generally, the Elevation axis is preset in the factory to be orthogonal to the Azimuth axis. It is the responsibility for the installation crew to set the "verticality" of the pedestal. An error of 0.010o in east-west pedestal tilt (meaning in the line of the elevation axis) will result in an error of +0.010o and -0.010o in the east-west plane, and a possible 0.010o between zenith and the horizon in the elevation plane. A pedestal tilt in the meridianal plane will only result in a constant elevation angle error, which is recoverable in the elevation angle reading. For a 10m pedestal as one might have for an 18m antenna, the top of the pedestal would be out of vertical by 0.069 inches. If the antenna were operating at Ku band (14 GHz uplink), there would be a loss in signal toward the satellite of about 0.17db. 3db beamwidth at 14 GHz = 21/(14*18) = 0.083 deg

33 x

x PP 3 (2 x 0.01/0.083) = 0.17db

This represents a loss in gain for the uplink system of 0.17db. For satellite monitoring services, it is important to measure the exact location of the target satellite - distance, and angular coordinates in terms of Az and El. This is important for the purposes of - understanding exactly where the satellite is in relation to surrounding satellites - being able to locate interfering signals from illegal transmissions on the ground 8.9 Panel Alignment The main reflector, subreflector and quadrupod support is assembled on the ground. The main reflector panels must then be set to prescribed shape. This is done with the aid of one of several methods. - theodolite and precision drill tape - photogrammetry and precision reference scale - an optical interferometry routine - microwave interferometry using satellite test signals Theodolite and precision drill tape panel setting The parabolic main reflector can be defined with coordinates (Radius, Depth), or with distance along the surface and angle from some fixed reference along the axis. The second routine is the preferred method, since only one instrument is required (the theodolite) to read points on the reflector surface. Distance along the surface of the reflector is measured with a precision drill tape. The alignment procedure follows these steps:

1. The theodolite is mounted onto a precision support on the axis of the hub. 2. The support carries a device (the spindle) which captures the drill tape, and allows it rotate

around the axis of the theodolite. See Figure 8.9-1. 3. The drill tape length is prepared and fitted with holes that have been located for the given

reflector shape, to be used to drill small holes into the surface of the reflector at prescribed radial distances from the axis for the purpose of inserting precision optical targets.

4. The theodolite is used to sight each of the optical targets. Theodolite angles are preset, and the panels are adjusted to raise or lower the panel into position.

5. The targets are removed. The drill tape target holes are used as guides for target holes drilled in the panels. Targets are installed.

6. Once the approximate adjustment of the panel heights for all panels is complete, the reflector assembly is lifted into position on the hub and locked down.



317

7. The reflector is tilted to the operational position in elevation 8. The panels are finally set by adjusting the support studs under the panels to the prescribed

theodolite angle readings. This represents the optimally aligned reflector. The theodolite axis represents the mechanical axis of the main reflector. The subreflector will be aligned with the axis of the theodolite, with the instrument directed toward the reference mark at the vertex of the subreflector.

Figure 8.9-1 Reflector panel installation and alignment with the use of a theodolite and target tape built to suit. (Photo used with permission of General Dynamics SATCOM Technologies Inc.) Photogrammetry and precision reference scale Photogrammetry relies on an optical measurement technique in which a three-dimensional view of the reflector surface, represented by a large number of optical targets placed onto the surface, is generated by taking high-density digital photographs of the reflector surface from several different angles, and comparing the observed dimensional differences in the images with a known reference scale. See Figure 8.9-2. This allows a holographic (3-dimensional) image to be constructed with a high degree of precision, to be compared with a theoretical dimensional model of the reflector. Deformations seen in the observations can be immediately pin-pointed, and adjusted.



318

Figure 8.9-2 The mapping of a reflector panel with a photogrammetric technique is shown here. The red bars represent dimensional references. The blue targets give an idea of the density of points being taken to establish the panel profile. The same procedure is applied to map the entire reflector, with targets placed at 6 or 8 points per panel to measure the overall reflector profile. The antenna in this case is located inside a space-frame radome. (Photo used with permission of General Dynamics SATCOM Technologies Inc.) Microwave interferometry (holography) In a manner similar to photogrammetry, but using microwave signals instead of optical wavelengths, an image of the reflector surface can be derived from a phase-amplitude analysis of the antenna pattern measured with a cw signal from a satellite. The pattern is defined by the illumination of the reflector surface. For a perfect surface, the theoretical pattern is accurately known. Phase-amplitude deviations in the reflector will prompt changes in the pattern which are related to where on the reflector surface the deviations occur. Based on these observations, a map of the reflector surface can be generated, allowing specific errors to be corrected. 8.10 Influences of Weather Antennas are located all over the world, having to operate in all manner of environmental conditions. Desert regions - high temperatures, low humidity, blowing sand Arctic regions - freezing temperatures, snow, ice, wind Ocean-side - corrosive salt atmosphere, rain, humidity, wind Tropical regions - high humidity, large rainfall Earthquake zones High wind zones - tornados, hurricanes. Such environmental conditions suggest that antennas carry protective equipment.

1. "Close-outs" or shielding around the reflector back structure, equipt with blowers to maintain a uniform distribution of ambient air across the back surface of the panels. This helps to minimize thermal gradients that can cause panel deformations.

2. Heated "Close-outs" or shielding of the reflector back structure, to keep snow and ice off the

reflector Point of interest: "Close-outs" will add weight to the reflector assembly, and extra load to the elevation drive.



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3. Corrosion protection on all surfaces, and in particular joints and hardware and places at which different metals are connected

4. Antennas installed in tropical regions typically operate with satellites at high elevation look

angles. During rainfall, the feed window cannot shed water from the horn aperture. In these instances, the feed system may need to be equipt with a rain-blower

5. High wind and earthquake conditions will demand special structurally stiff designs that are

tailored to these specific conditions, so that the antenna will survive. Antennas are not usually required to remain operational during high wind and earth-quake events.

Inevitably, these conditions will prompt larger costs for the antenna as well as a greater maintenance effort. 8.11 Mechanical Layout Concepts for Complex Feed Systems A brief summary of important feed design considerations 1. Understand the mission for the antenna and its system boundaries - must have information about antenna size and motion, operational performance objectives, frequencies, polarizations, eirp, relative location of amplifier equipment. 2. The feed system must be sufficiently small to maintain feed blockage less than subreflector blockage/shadowing in the main reflector. 3. For monopulse tracking, choice of 4-horn array to minimize error channel noise; TE21 tracking coupler approach mechanically compact, but has a higher error channel noise floor. 4. If 4-horn array is chosen, optimize error pattern efficiency while maximizing the sum pattern. 5. Low PIM operations - demands "clean" component and flange fabrication. 6. High power operations - demands appropriate means for heat dissipation. Feed design demands complete information about a. antenna geometry b. performance requirements c. available space for the feed in the antenna Sample feed design problem: A Customer wishes a 9m antenna operating at C(cp/lp), Ku(lp), and Ka(cp/lp) in a receive-only mode, monopulse tracking at Ka. What must be done to answer the feasibility question, and devise a reasonable technical solution ?? The antenna/feed designer faces two basic challenges. For a given set of operational frequencies: 1. can a feed horn be designed to adequately illuminate the chosen reflector system in an efficient manner 2. can the feed be dimensionally realized in such a way as to physically fit into the available space between the phase center and the antenna hub Note: Experience suggests for this case that mechanically, it will be difficult to fit the large C-band horn and the complete multi-band feed system into the available space in the antenna. Therefore, the choice at this time is to use a Ku/Ka horn design, and adapt a 4-horn array for C-band around the Ku/Ka horn aperture. Corrugated horn design information from Section 3.6 and Figure 3.7-2, shows that all three frequency bands may be handled in a single horn design. Steps toward a solution: 1. The geometry of an existing 9m Cassegrain reflector system shows a phase center to edge-of-subreflector angle of 18 degrees. Sections 3.6 and 3.7 will help determine the required feed horn aperture size. See Figure 8.11-1 2. The rudimentary design ideas discussed in Section 3.12 give a preliminary feel for the size of the feed horn and location of its phase center, to fulfill the first challenge.



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Using approximate physical dimensions for the required feed components as they have been discussed in Chapters 3, 4 and 7, a feed layout commensurate with the Customer's performance needs can be laid out as shown in Figure 8.11-2 to view the feasibility of the design. This layout can be used as a first model to determine the RF performance of the antenna system using accurate spherical wave expansion and physical optics programs to determine antenna gain. Possible refinements in the model will usually have only negligible impact on the mechanical design and its feasibility.

18o

354"

= 8

991.

6mm

20"

58.1"

128.89"

36

60 Hub

Mai

n re

flect

or v

erte

x pl

ane

46.0"

Figure 8.11-1 A 9m reflector geometry and subreflector illumination angle that will define the horn design

TE21 Coupler

Ka-bandTE21 Network

Combiner

QJ1 QJ2180 180

RJ RJRJ

RJ RJ OMTOMT

4-hornArray

C-band 4-hornArray

90 Ph Sh

Interconnect waveguide

Interconnect waveguide

CorrugatedHorn

Feed Tube Housing

Ku-Ka Horn

C-band Pol Drive

Ka-band Pol Drive

Ku-band Pol Drive

Ka-band Pol select

C-band Network Combiner

4dia

3dia

10 dia

24 dia

15 18 4 6 8 4 2 8 10 6

4

58

77

16

Rea

r fac

e of

the

hub

8

115

Front face of the hubInner edge of main reflector

Ka terminals

Ku terminals

C terminals

Ka trackingterminals

Figure 8.11-2 Concept of feed layout for the space between phase center and the antenna hub with approximate dimensions, based on approximate waveguide component sizes. Note that the feed will project into the hub by about 16 inches.



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Notice that the feed projects into the hub. The anticipation of this prompted using the C-band array, rather than attempting to use a tri-band horn approach. Since the C-band array will contribute significant loss to suppress the G/T, there may be merit in examining the case for using a tri-band configuration. To assist in this objective, there may be several ways of gaining more space in the hub by folding the Ku network back on itself. This is left to the reader as a practice exercise. Optional problem for solution: Generate a second feed layout using the C/Ku/Ka horn design approach - will it fit into the 9m antenna ?? References: [1] Page, Hank “Designing Earth-based Antennas for Power Losses”, General Dynamics, Kilgore, Tx Internal Memorandum dated April 2008. [2] EIA Standard, “Electrical and Mechanical Characteristics of Earth Station Antennas for Satellite Communications”, Electronic Industries Association, EIA-411-rev A, September 1986, Chapter 4. [3] Levy, Roy, “Structural Engineering of Microwave Antennas for Electrical, Mechanical, and Civil Engineers”, IEEE Press, 1996.

Chapter 9 – Proof of Performance


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Chapter 9 Proof-of-Performance 9.1 The Specification 9.2 Basic System Requirements 9.3 Factory Testing 9.3.1 Feed System and Performance Features 9.3.2 Feed System – Sample Measurements 9.3.3 Reflector System 9.3.4 Effects of Reflector Errors 9.3.5 Other Subsystems 9.3.6 Outdoor Test Range 9.4 Customer Site Preparations 9.4.1 Pedestal Alignment Check 9.4.2 Reflector and Feed System Mechanical Alignment Check 9.4.3 Ancillary Equipment Function Check - Control System, LNAs, HPAs 9.4.4 IFL Signal Path Integrity 9.4.5 Pretest Preparations 9.4.6 Test Equipment, Location, Setup, and Function Check 9.5 Preliminary RF Checks and Example Difficulties 9.5.1 Sum Patterns 9.5.2 Difference Patterns 9.5.3 Antenna Gain 9.5.4 Antenna Noise Temperature 9.5.5 Radio Star Track Check 9.5.6 IFL Signal Paths 9.6 Formal On-site RF Antenna Tests 9.6.1 Antenna Patterns - Sum, Difference, Cross-pol 9.6.2 Monopulse Tracking Sensitivity 9.6.3 Antenna Noise Temperature 9.6.4 Antenna System G/T, Noise Temperature, and Gain 9.6.6 Transmit Uplink Gain and eirp Stability 9.7 Measurement Accuracy 9.1 The Specification Initially, customers generate a requirement or specification for an earth station system. A vendor responds with a description of the antenna and associated equipment he can offer, and a compliance statement. A contractual agreement permits the vendor to design, build, install and test the system to the satisfaction of the customer. It is the obligation of the vendor to offer a satisfactory RF proof-of-performance for the antenna system.

A predicted antenna performance specification forms the reference for final proof-of-performance measurements.



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Performance, the essence of every earth station antenna project, is paramount. The most important factors related to performance are:

Antenna G/T - A figure of merit for the radio link from the satellite to the output terminals of the earth station. G expresses the antenna gain, which includes all relevant losses.

Reflector systems errors Feed system signal path loss caused by

o cross-pol components o coupling to all other ports, including those nominally terminated o reflections seen at all ports o resistance due to finite conductivity in the signal path

T is an expression for the effects of noise in the link, and includes the noise generating effects of:

The sidelobe envelope of the antenna seeing portions of the sky and the ground, depending on the elevation look angle.

Ohmic losses in the feed as well as noise generated by coupled ports and active components in the downlink chain.

Effects of the immediate environment in which the antenna must operate, including weather and the surrounding local horizon (buildings, other antennas, topography).

Uplink EIRP - transmit effective isotropic radiated power - Directly proportional to antenna gain and transmitter power, set to conform to satellite link requirements. This in turn will determine the power handling requirements for the feed.

This feature will influence the choice and design of the connection between the transmitter and the feed flanges.

Polarization - Most satellite links today are dual polarized, meaning two separate orthogonally polarized traffic paths operating in the same frequency band. Polarization discrimination must conform to a regulated value, usually >30 to 35 db. If the link is single polarized, discrimination is not critical.

Sidelobe envelope - Since the earth station is one of many communicating with one of a series of relatively tightly spaced satellites orbiting the earth, the antenna must demonstrate that pattern sidelobes in the transmit path do not interfere with neighboring satellites. This feature is also regulated by a monitoring authority such as:

Military standard MIL-STD-188-164A

Recommendation ITU-RS.580 - See Section 12.2, 3, 4 and associated documents ITU-RS-465 and 732.

Intelsat Documents IESS-207, IESS-208 and IESS-601. Essential sidelobe requirements of the Intelsat documents are identical to that of the ITU.

FCC regulations, which assume a satellite spacing of 2 degrees, as described in the regulatory document FCC document 47 CFR Ch 1 paragraph 25-209. See Section 12.5.

9.2 Basic System Requirements

In order to support such performance requirements, the most important mechanical aspects of the antenna are listed here: 1) The antenna pedestal establishes the azimuth and elevation axes which will define the position of the

RF beam. It is important that the elevation axis be horizontal and the azimuth axis be vertical.



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2) The reflector panels must conform most closely to the necessary main reflector profile to minimize the effects of surface errors that inevitably occur as a part of manufacturing.

3) The reflector assembly must be aligned and the reflector geometry checked, to ensure that the subreflector and feed have been correctly placed.

4) Ancillary hub-mounted equipment to be interfaced with the feed terminals must, as a minimum, include LNA assembly Transmit waveguide or IFL connection to the transmitter Test couplers on the Tx path with which to measure Tx power in the feed The control system must track the target satellite with a prescribed accuracy. The impact of a

poor tracking characteristic is: - A possible degraded cross-pol performance - Interference with a neighbouring satellite system - Diminished stability in up and downlink

9.3 Factory Testing The critical sub-assemblies outlined in the listing above contribute directly to the prescribed antenna performance, and must be checked prior to installation into the antenna. There are two reasons for doing so. (a) The evaluation of these components can only be performed with specialized test equipment available in the factory. Based on the results of these factory tests, it is possible to predict the final antenna performance. If the predictions do not coincide with original expectations, corrective action can be undertaken.

(b) This check process cannot be done in the final antenna installation.

In fact, it is this preliminary check process at the factory which represents the greatest contributor to project cost savings. 9.3.1 Feed System and Performance Features Feed systems are designed as a result of a performance analysis of the antenna specification. Once the antenna spec is understood, the feed system is designed according to the principles discussed in Chapters 4 and 5. In order to qualify the feed prior to the installation into the antenna, a specification against which the feed can be measured is generated. Once all the feed components are available, checked, and mechanically assembled consistent with the drawings, the feed assembly needs to be tested for basic performance requirements. Performance is defined as an understanding of the total accumulation of all losses in the system. This also means an understanding of the relative magnitudes of each loss component. As an example: Antenna specification demands the following points: VSWR = 1.3:1 Port-to-port isolation = 20db Axial ratio = 1db >>> corresponds to crosspol = 25db >>> lost signal = 0.02db Insertion loss = 0.5db These features of the feed will exist, regardless of whether the feed is in the antenna or in the lab. Question: Which component contributes the most to the total losses ??

VSWR = 1.3:1 >>> return loss = 17db >>> reflected (and therefore lost) signal = 0.06db Port isolation = 20db >>> 0.04db Axial ratio = 20db >>> discrimination = 0.04db Insertion loss = 0.5db

So the insertion loss makes by far the largest contribution, the sum of the others about 25% of the total losses, and therefore cannot be ignored.



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Performance also implies that polarization and tracking functions of the antenna are compliant with the specification. But these are not immediately relatable to what the feed by itself needs to demonstrate in order to be compliant. Therefore a separate specification for the feed system is typically created at the time of feed design. For example: Feed sum pattern illumination requirements, which are related to - required sidelobe envelope - gain requirements for the given size of antenna Tracking sensitivity, which is dependent on - antenna size and magnitude of the downlink beacon eirp. - effective coupling value between sum and difference signal paths - difference path insertion loss and noise level Cross-talk between Az and El difference pattern peak levels = > 10db Tracking pattern on-axis null depth = 35db below sum signal maximum Tracking pattern null position stability = 0.003 degrees Level difference between sum pattern maximum and difference pattern off-axis maximum = 15db How are these requirements to be interpreted when testing the applicably designed feed ?? The following listing of measurements is one that will describe the functional features of a feed system. The objective of each test is briefly described. Not all functions listed here may be applicable at one time in any given feed configuration, but the list represents a reasonably complete reference list of tests that will be necessary to qualify any given feed system. Feed Patterns Feed pattern measurements provide a means of qualifying the feed horn design. In the event of small differences when compared with paper design, the measurement will allow relatively precise calculation of final antenna gain performance

Sum pattern phase and amplitude - 0 (H-plane, Vert pol), 45, 90 (E-plane, Hor pol) polarization plane cuts

- To be measured by rotating the feed around the horn axis For linear polarization configuration - measure cross-pol level across 1db beamwidth

- To be measured by rotating the polarization of the incoming test signal. Difference patterns phase and amplitude - 0 (Azimuth plane) and 90 (Elevation) polarization plane

cuts - Observation of difference pattern off-axis maximum level with respect to sum pattern on-axis level

Translation of null shift in the feed pattern to expected null shift in the antenna pattern - Observation of position and depth of tracking null as a function of frequency and polarization angle. Antenna null shift = measured feed null shift x ratio of aperture diameters.

Phase and amplitude variation at difference pattern maximum - Observation of phase between difference lobes measured at constant radius from feed RF axis - TE21 mode type difference pattern will be more or less constant amplitude, and phase varying from 0 to 360 degrees - 4-horn aperture difference pattern will have 4 distinct difference pattern lobes in Az and El planes, and 180 degrees phase difference between opposite pairs. Calculation of expected antenna sum pattern gain Calculation of expected antenna difference pattern gain Calculation of expected antenna difference pattern (tracking) slope



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Polarization discrimination/isolation - linearly polarized feed configurations Cross-polarization features of the feed have contributions from the horn as well as from other feed components possessing some measure of symmetry, such as circular waveguide and OMTs. The final cross-pol value cannot be accurately predicted without measurement.

Swept frequency measurement of cross-pol response of sum channel signal path - on-axis cross-pol - cross-pol level under 1 db beamwidth

Swept frequency measurement of axial ratio on the difference pattern - cross-pol on off-axis difference pattern peak level - cross-pol under 1 db sum pattern beamwidth Axial ratio - circularly polarized feed configurations

Swept frequency measurement of axial ratio of the sum pattern - on-axis axial ratio, to estimate the CP cross-pol response - axial ratio under 1 db beamwidth

Swept frequency measurement of axial ratio on the difference pattern - axial ratio on off-axis difference pattern peak level - axial ratio under 1 db sum pattern beamwidth Return loss Reflection features of the feed have contributions from the horn as well as from all other feed components. The final return loss value cannot be accurately predicted without measurement.

Swept frequency response for all feed terminals - for the case of 180 degree adjustable differential phase shifters - 0, 45, and 90 degree polarization planes, to establish how RL varies with pol angle change Port-to-port isolation Port isolation features of the feed have contributions from the horn as well as from all other feed components. The final measure of signal coupled from one port to another cannot be accurately predicted without measurement.

Swept frequency measurement of isolation between Rx and Tx terminals - Observation of transmit frequency signal level in the receive path - Observation of transmit frequency signal level in the tracking signal path - Observation of receive frequency signal level in the transmit path - Observation of receive frequency sum channel signal level in the tracking signal path

Swept frequency measurement of Rx to Rx isolation - Observation of Rx1 signal in Rx2 signal path

Swept frequency measurement of Tx to Tx isolation - Observation of Tx1 signal in Tx2 signal path Insertion loss Insertion loss features of the feed have contributions from the horn as well as from all other feed components, but in particular from any discontinuities such as flanged joints and points where tuning elements have been implanted into the guide. The final measure of signal lost due to absorption and leakage in the feed assembly cannot be accurately predicted without measurement.

Measurement of signal loss in the path from the horn aperture to the feed terminals - Rx sum signal paths - Tracking difference signal paths - Tx sum signal paths



327

Time or Group delay For some applications, for example involving distance measurement, understanding travel time for the signal from feed flange to target satellite is important. The range between target and antenna aperture is fairly straight-forward; from the aperture to a reference at the feed flange must be measured for the uplink as well as for the downlink.

Measurement of the time for the signal to travel from the horn aperture to the feed terminals - Rx sum signal paths - Tracking difference signal paths - Tx sum signal paths Mode spikes represent the most destructive and therefore most important aspect of terminal measurements. Mode spikes will have a direct impact on signal quality in the transmission through the feed, particularly G/T and Group Delay. Passive intermodulation As described in Section 5.4, this is an interference mechanism that is generated by discontinuities in the current path in feed components and antenna component joints/connections shared by Tx and Rx signals. Feed assemblies are a conglomerate of components joined with connecting flanges. In some cases the components are fabricated using a “split-block” technique. All these bolted joints have the potential to leak RF through incomplete contacts. RF leak To ensure that all components are securely connected. Flanged connections must not leak, typical leak rate of -75db relative to an input signal level of 0db. Mechanical details Any rotating sub-assemblies - polarization adjustment mechanisms - must be secure, since these mechanisms often are not readily accessible once installed in the feed/antenna. For this reason, the mechanisms must be designed to not require maintenance for the lifetime of the feed - 20 years is the design goal for the antenna. Polarization control - remote or manual

LP rotation adjustment over +/- 90 or +/-180 degrees CP/LP switch

Pressurization leak rate To identify

that the feed is inured against humidity feed window is bulging to reduce reflective effects of the window material the pressurization system is operating properly

For more on this, see Section 10.1.2 Dimensional check of feed assembly - To ensure that the feed is placed correctly into the antenna structure, the following features must be identified

Location of the phase center in the horn with respect to the horn aperture Location of the feed mounting interface with respect to the phase center

to be consistent with the reflector geometry



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9.3.2 Feed System – Sample Measurements An example of a feed system is shown in Figure 9.3-1

Figure 9.3-1 X-band 2-port low PIM feed assembly. (Photo used with permission of General Dynamics SATCOM Technologies Inc.) Return loss measurement Signal that is lost due to reflections back out of the terminal being measured:

Figure 9.3-2 Return loss measurement on transmit port of low PIM feed Insertion loss measurement Signal is lost by the mechanism of absorption due to finite conductivity of the components making up the feed network and horn. Figure 9.3-3 shows the results of insertion loss measurements on the electroformed feed network of Figure 9.3-1.



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Figure 9.3-3 Sample feed system insertion loss measurement

Port-to-port isolation measurement Signal is lost because some of it is coupled into other ports. Since the 2-port feed in this example has one transmit and one receive port, the port-to-port isolation will refer to the Transmit↔Receive isolation. Figure 9.3-4 shows Transmit→Receive isolation (rejection) of about 155dB, and Receive→Transmit rejection of 140dB.

Figure 9.3-4 Port-to-Port isolation measurement

Polarization discrimination (cross-pol) measurement Two signal paths at the same frequency can co-exist if they are orthogonally polarized (90 degrees with respect to each other). When the polarization is not exactly orthogonal, some of the signal is lost when it is coupled into the orthogonal port. In this case of circular polarization, polarization discrimination is expressed as axial ratio. The axial ratio displayed in Figure 9.3-5 is <1.5db, which corresponds to 21.3db cross-pol.



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Figure 9.3-5 Axial ratio measurement

Pattern measurements The feed patterns are important. When the reflector/feed configuration is designed, it is based on the feed illuminating the reflector in a particular fashion. If the finally manufactured feed assembly does not demonstrate a close resemblance to the theoretical expectation, then illumination losses will be incurred. One of the reasons for the choice of corrugated horn designs is that they can be quite accurately designed and fabrication per print results in horn patterns which are very nearly equal to expectations. A sample feed system pattern is shown in Figure 9.3-6. Note that both phase and amplitude characteristics are recorded - features of the feed system pattern needed for the calculation of expected antenna gain and sidelobe envelope, based on measured feed performance.

Figure 9.3-6(a) Sample feed system amplitude pattern measurement



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Figure 9.3-6(b) Sample feed system phase pattern measurement Possible difficulties Pattern deformations Mode spikes in polarization responses LP Cross-pol discontinuities CP axial ratio spikes Bandwidth limits Insertion loss non-linearities Return loss limits Port-to-port limits Insertion loss deficiencies PIMs 9.3.3 Reflector System

Figure 9.3-7 Main reflector panels being set and aligned. (Photo used with permission of General Dynamics SATCOM Technologies, Inc.)



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The main reflector surface is generally made up of a set of panels similar to those shown in Figure 9.3-7, which, when mounted correctly, will present a surface that collimates signals from a target satellite to the subreflector (Figure 9.3-8) and into the feed horn.

Figure 9.3-8 9m Cassegrain subreflector and its mount in the apex frame. (Photo used with permission of General Dynamics SATCOM Technologies, Inc.) The reflector surface must be exact. Any panel or any segment of a panel which does not conform to the required shape will cause the signal captured by that segment to be directed elsewhere - which means it will be lost. The accuracy requirement for the fabrication and setting of the panels increases exponentially with an increase in frequency. Panels that may be considered "good enough" for X-band will not be adequate for Ka-band functions.

The term surface accuracy, as applied to the antenna as a system, refers to the statistical summation of the effects of all reflector errors including: Surface errors of the main reflector panels. Typically, this will represent the largest contributor to the

total error.

Errors in alignment of all the panels.

Structural deformations in the reflector support, as occurs when the antenna must operate at widely different angular positions.

Environmental loading from wind, thermal gradients, ice and snow.

Surface and alignment errors of the subreflector.

Alignment errors in the feed mounting. Generally, the exact value of the overall surface accuracy will not be known, but as long as the contribution by the panels alone can be minimized, the results of a professional reflector alignment exercise will allow an accurate statement that says, for all practical purposes, "complies with expectations".

Figure 9.3-9(a) shows the map of a 9m panel for a main reflector to operate at 30 GHz. The distribution of deviations from the required profile is summarized in Figure 9.3-19(b). Peak deviations are recorded. Segments in which profile errors may be concentrated (as may happen if the panel is dented) are recorded as "lumps." Repetitive lumping is a severe error phenomenon. Lumps (or indentations and raised areas) can affect large areas of the reflector, and imply that signal captured by these areas will be scattered away from the required path and therefore lost. In the case of Figure 9.3-9, no lumping is observed. The standard deviation - known as the root mean square (rms) - of all measured points is calculated.



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The apparent shift in the location of the panel with respect to the reference profile (caused by the distribution of the errors) is indicated by the Arithmetic Mean. The rms is the significant quality parameter for the panel.

Figure 9.3-9 (a) The surface map of a 9m reflector panel. The values show the deviations from the nominal profile. (b) The summary sheet for surface measurements on the 9m panel. The errors in the profile (in inches) are sufficiently small to suggest acceptable antenna pattern performance at 30 GHz. The rms value for all panels in the reflector assembly is recorded. The rms for the complete reflector is calculated by taking the square root of the sum of the squares of all panel rms values, as well as the rms of a similar mapping of the subreflector. The example panel has an rms of 0.0050 inches. Interestingly, if all the panels show an rms of 0.0050 inches, then the total for the reflector assembly will also be 0.0050 inches.

Nominally, one tries to achieve an accuracy on the subreflector which is at least 3 or 4 times better than on the main reflector panels, because of the effective magnification brought about by the change in illumination angle from that of the feed to that at the subreflector illuminating the main reflector. However, for large subreflectors, attaining much better than 0.005 inches has its difficulties. This then says the effective subreflector contribution to reflector system accuracy will be .0012 inches. A summation of reflector surface rms errors is shown here:

n

xxxrms n

222

21 ...

(9.3.1)

Example: 48 panels each with 0.005 inch rms 1 subreflector with 0.003 inch rms leads to a 0.006 inch effective overall rms reflector system alignment = 0.005 inch rms Total accuracy = 0.008 inch rms Associated loss in antenna gain at 30 GHz = 0.28db Note: When adding separate inaccuracy components as in this listing, the total system rms is given by

222 ... subrefpanelsrms (9.3.2)



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The loss in antenna gain associated with this feature is given by the expression:

22

24

92.4log10 felosserrorphaserms

(db) (9.3.3)

where rms value measured in inches

wavelength in inches

f frequency measured in GHz

A graphical view of this expression is given in Figure 9.3-10.

Loss in Gain due to reflector errors

0.0

0.5

1.0

1.5

2.0

2.5

3.0

3.5

0 0.005 0.01 0.015 0.02 0.025 0.03

Reflector rms value - inches

Loss

in G

ain

- db

C-band 4 GHz

X-band 8 GHz

Ku band 14 GHz

Ka band 20 GHz

Ka band 30 GHz

Figure 9.3-10 Loss in antenna gain due to reflector rms errors vs. frequency. For 30 GHz, the reflector error loss for an rms of 0.010 inches is 0.4dB.

The antenna is usually aligned at the look-angle to the target satellite, or at an elevation angle very close to this position. The alignment is performed optically with a theodolite, to set the panels on the mechanical support points (see Figure 9.3-12) so that position errors are near zero. This means that any deformations caused by gravity are effectively negligible. See Figure 9.3-11.



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Figure 9.3-11 Dead weight rms surface deflections at various look angles

Figure 9.3-12 Radial with panel alignment supports. (Photo used with permission of General Dynamics SATCOM Technologies, Inc.) If the antenna must work at several different elevation/azimuth positions, the panels will be aligned at an in-between elevation angle. In principle, it will be necessary to measure or calculate the reflector panel alignment at or near these positions, and repeat the arithmetic for the total surface accuracy. Experience suggests that the rms errors in such a case may become as much as twice that determined for the panels alone. This will be frequency dependent - for low frequencies, the errors due to deformations will be negligible. For high frequencies, the errors due to structural deformations will be significant.

As a good rule of thumb, the total reflector rms error must be less than 1/50th of the operating wavelength. This will ensure reasonable sidelobe envelope compliance. 9.3.4 Effects of Reflector Errors Panel errors There are two important parameters (a) the rms determines, via the Ruze equation, the loss in antenna gain (b) the peak-to-peak deviation from the required reflector profile determines the sidelobe response. If the p-p deviations occur randomly, then effect on the pattern will be small. If the p-p occurs in distinct areas (referred to as "lumping"), the effect can be significant. The impact can be seen in Figure 9.3-13.



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Figure 9.3-13 The sidelobe peaks protruding above the envelope are a clear sign of systematic errors in the reflector, the result of high peak deviations in the profile occuring in a regular pattern either in a radial direction, or in a circular pattern around the axis. 9.3.5 Other Subsystems The following is a brief listing of other important subsystems that are essential to a variety of feed configurations. When used, they must be checked, aligned and tested. 1. Polarizer assembly and its control (for linearly polarized feed configurations). LP angle adjustments must be made to optimize the cross-pol performance. If LP must be switched to CP, switch mechanism will be required. 2. The downlink LNAs (Low Noise Amplifiers). The LNA noise temperature will have a direct influence on the antenna system G/T. The lower the noise temperature of the LNA, the higher the system G/T.

3. Low loss interconnection between the transmitter and the feed transmit flange. The smaller the loss value, the larger the transmit power level that can be delivered to the feed.

It is possible to offer verification of antenna performance prior to shipment to site and final installation. In some complex assemblies, a trial assembly of the antenna may be deemed necessary to ensure that the installation goes smoothly. In these instances, the antenna can also be tested for the fundamental performance characteristics listed in Section 9.1. At the Vertex test range, the antenna can be mounted on a full motion positioner to receive a test signal from a distant source representing the satellite. Moving the test antenna in the azimuth and elevation planes and around the polarization axis with the positioner, while observing the response of the test signal, allows the measurement of patterns, cross-pol, gain and G/T with a precision that is difficult, at best, to reach at most field sites.

Four test ranges are available at Vertex, Kilgore. Each is configured for a specific purpose, and together, allow testing at frequencies between 1 and 50 GHz. The most versatile is called the long range, which will permit large antennas to be tested. A short range is dedicated to small antennas. A third range is dedicated to the L-band antennas (around 1 GHz and lower). And the fourth range is project specific for Extremely High Frequency (EHF) antenna testing.



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9.3.6 Outdoor Test Range Length The Vertex "long range" configuration is shown in Figure 9.3-14. The positioner can carry up to a 9m aluminum antenna for test purposes. For accuracy, it is desirable to have a range length greater than

22DR

where D = antenna reflector diameter (meters)

= wavelength of the test signal = f

3.0 meters

= frequency in GHz Practically, a range length of ¼ R is useable, although a small correction for beamwidth and gain may become necessary. A hint at the corrections required can be seen in the graphical display of Figure 9.3-15. This is what will permit a 9m antenna, operating at 30 GHz, to be tested on this range in a satisfactory manner. This near-field response for the 9m working 30 GHz was calculated using the relationships discussed in Section 11.1 in connection with radiation hazard considerations.

2 degrees

Equipment Room

TestSignalCable

Spectrum Analyzer

Antenna Position

Controller

Computer

Bor

esig

ht T

ower

500

ft T

ower

3.5m Compact CassegrainSource Antenna

Signal Generator

Remote Boresight Controller

Test Antenna

Elevation Axis

Azimuth Axis

Polarization Axis

Ground Ground

Flat Reflector

35 f

t P

edes

tal

Reflector Angle Control

2.6 miles (4.2km)

Signal Path

Figure 9.3-14 Antenna test range configuration



338

Power Density vs Distance in front of Aperture

0.0

0.5

1.0

1.5

2.0

2.5

3.0

3.5

4.0

0 100 200 300 400 500 600 700 800 900 1000

Distance in front of Aperture - meters

Pow

er D

ensi

ty -

mW

/cm

^2

1

2

3

4

5

6

7

8

9

100.

000

0.01

0

0.02

0

0.03

0

0.04

0

0.05

0

0.06

0

0.07

0

0.08

0

0.09

0

0.10

0

0.11

0

0.12

0

0.13

0

0.14

0

0.15

0

0.16

0

0.17

0

0.18

0

0.19

0

0.20

0

0.21

0

Fraction of Far-Field Distance

Nea

r Fie

ld 3

db B

eam

wid

th -

deg

rees

D = 11.1 meters

f = 6 GHz

Pi = 500 Watts

Far field distance = 4928 meters

Power Density

Point of Interest in front of Aperture

Beam broadening factor

Figure 9.3-15 The red curve (with right-hand side scale) shows an approximate variation in half-power beamwidth of the antenna pattern with distance along the axis. For this 11m antenna at 6 GHz, a distance of 1000m will permit a reasonable characterization of the antenna pattern. “Reasonable” here to be understood as being able to establish accurate sidelobe levels. Ground Reflections Ideal test conditions exist when the phase and amplitude of the signal received from the source is constant across the aperture of the test antenna. In a satellite link, this condition is achieved by virtue of the 36,000 km distance. On a ground based range of only 4km or shorter, this condition may not be achieved, because of two things: 1. If the source antenna is sized to provide uniform amplitude across the test aperture, it will also illuminate the ground in between. This means that a portion of the signal arriving at the test antenna, along a direct straight line path, will be accompanied by another portion of the signal arriving at the test antenna along a path that has intercepted ground in between. If the ground is uneven, several reflections may occur. The magnitudes of the direct path and ground reflected signals will be different from each other (by virtue of the longer path length travelled by the reflected wave, and the attenuative properties of the ground). This condition results in an uneven/non-uniform illumination of the test aperture, also referred to as an interference pattern. 2. If the source antenna is sized to reduce (if not eliminate) ground reflections, the result is a "tapered" non-uniform illumination across the test aperture. This leads to errors in the measured patterns and gain. One way out of this dilemma is by increasing the look-angle of the test antenna toward the source. The higher the look-angle, the smaller will be the influence of the ground reflections. A second solution is to have a perfectly flat ground and have the source propagate the test signal parallel to the ground, thereby eliminating the ground reflected component. The Vertex L-band range does precisely this. The idea of having a perfectly flat ground range over a 4km distance is, however, impractical. See Figures 9.3-16 and 9.3-17 for a view of these possible range configurations and the interference mechanism.



339

2 degrees

Equipment Room

TestSignalCable

Spectrum Analyzer

Antenna Position

Controller

Computer

Bor

esig

ht

To

wer

500

ft T

ow

er


Signal Generator

Remote Boresight Controller

Test Antenna

Elevation Axis

Azimuth Axis

Polarization Axis

Ground Ground

Flat Reflector

35 f

t P

ede

stal


2.6 miles (4.2km)

Signal Path

(a) Long Test Range Configuration for large antennas at Vertex, Kilgore, TX

100

ft B

ore

sig

ht T

owe

r

Ele

vatio

n A

xis

Azimuth Axis

35 ft

Ped

est

al

Small interference pattern resulting from various ground reflections

(b) Short test range configuration for small antennas

Reflector fence

Equipment Building

Flat ground

Source horn and signal generator mounted on the tower carriage

740 ft

approx. 10o

Figure 9.3-16 Two antenna test range configurations at Vertex, Kilgore, Texas. (a) is a diagrammatic view of the long range, used for “large” antenna qualification testing; (b) the short range utilized for “small” antenna qualification tests



340

2 degrees

500

ft B

ores

ight

Tow

er


Signal Generator

Elevation Axis

Azimuth Axis

Flat Reflector

35 ft

Ped

esta

l


Signal Path

large interference pattern reslting from various ground reflections

Bor

esig

ht T

owe

r


Signal Generator

Flat Reflector


Elevation Axis

Azimuth Axis

35

ft P

edes

tal

Boresight Tower


Signal Generator

Elevation Axis

Azimuth Axis

Test antenna

Signal Path

Small interference pattern resulting from various ground reflections

500

ft B

ores

ight

Tow

er

Elevation Axis

Azimuth Axis

Flat Reflector

35

ft P

edes

tal

Reflector Angle Control Signal Path

[a] Pictorial view of mechanism generating large interference pattern at test antenna at low look angle caused by ground reflections

[b] Pictorial view of mechanism generating small interference pattern at test antenna at high look angle caused by ground reflections

[d] Pictorial view of mechanism generating very small interference pattern at test antenna on a flat ground range

[c] Pictorial view of mechanism generating a tapered illumination pattern at test antenna and reducing effect of ground reflections

Flat ground

Practically uniform illumination of test aperture

Tapered illumination of test aperture by high gain boresight source antenna

Signal Generator

Receiver and pattern recorder

25

ft P

edes

tal

Figure 9.3-17 Examples of the influence of the ground on the quality of antenna pattern testing. (a) shows large influence of the ground for low look-angle measurements. The aperture illumination is greatly disturbed. (b) Higher look angles can alleviate ground interference. (c) Preparing the ground to be smooth (as far as possible) can reduce the level of interference. (d) shows the setup for the test antenna axis to be parallel to the ground, thereby practically eliminating the ground reflections. This method is implemented for very low frequency microwave antennas.



341

Note that when operating with a low elevation angle (1o to 5o) satellite, this ground reflection phenomenon is going to influence the system performance in the same way. For earth stations located in coastal regions and looking out over the water, the interference pattern will be even more severe than over land. The reflective properties of water, plus the effect of waves, increase the magnitude of the reflected component.

A further limitation to the long range is the fact that the patterns can really only be measured in the azimuth plane, and upwards in the elevation plane. To measure the full elevation plane pattern, the test antenna must be rotated 90o in polarization and moved in the azimuth plane; this pattern will only be accurate if the local horizon is clear of reflective obstacles. Only if the test antenna has low gain (for example a horn or dipole) will the main beam pattern recorded on such a range be inaccurate. It is for this reason that low gain devices (such as feed horns for the kind of application being considered here) must be tested in an indoor test chamber, also called an "anechoic chamber," which simulates reflectionless "free space." A test chamber is identical to a test range except that it is cloaked in absorber walls to eliminate all reflections. Because low gain devices imply small apertures, the distance between source and test antenna can be much smaller. Furthermore, feed horn patterns are usually tested at the same distance at which the subreflector is located in a Cassegrain or Gregorian geometry, or the main reflector of a prime focus system. The 6m test chamber is adequate for the antenna/feed designs offered by Vertex.

Advantages of Range Measurements Compared with satellite measurements, the range offers access to tests at any desired frequency

and polarization. Measurements at transmit frequencies are not dependent on the cooperative services of another earth station. Cross-pol tests can be done with the knowledge that the signal source has a known polarization purity. This is not always the case with operating satellites.

For single polarization links, if the e/s (earth station) antenna has an effective cross-pol of 20db (var

= 1.22 or a.r. = 1.75db), this represents a loss in signal of 0.044db. Therefore, the impact on the system of 20db cross-pol is quite small.

For dual polarized links, 20db cross-pol effectively interferes with the orthogonally polarized link,

especially if the antenna on the satellite only has 20db cross-pol. The net result could be 2 x 1.75db a.r.., or a cross-pol = 14db, if the phase of both cross-pol components is equal. If the phase is 180o (opposite), then the resulting cross-pol could be infinitely small, but most likely will be some value in between. Therefore, most dual polarized satellite links demand >30dB cross-pol for the e/s and satellite antennas. System cross-pol now has the chance of reading 27 to 30db.

In order to measure this level of cross-pol in an antenna, the range source and any interfering

ground effects must be known. For LP (linear polarization) systems, open ended w/g (waveguide) represents a perfect LP source. For the long range source antenna, a feed is used that has been designed for >35dB cross-pol feature. For CP (circular polarization) systems, there is no perfect CP source. Therefore, cross-pol is measured in either of two ways:

- Rotating a perfect LP signal in polarization, to measure A.R. (axial ratio)

- Building a good CP source of known A.R. These sources are narrow band devices in comparison with LP sources.

The test range positioner will also permit direct comparison of patterns measured using the range

source with patterns measured on a (visible) satellite at the same frequency, same polarization.

Since most satellite test signals are power limited, dynamic range can be a limiting feature which inhibits measurement of wide angle sidelobe envelopes. The range signal source has sufficient power to achieve a dynamic range allowing verification of -10dBi sidelobe envelope levels at any frequency in the relevant band of interest.



342

Noise temperature measurements The test range is nominally devoid of local horizon effects which contribute to antenna noise temperature. At least the test antenna can be turned into a "clear" direction, and away from the orbital arc. Therefore, it

is an appropriate place to check antT .

Noise temperature is checked over a range of elevation angles between 0o and 90o. For a given LNA,

whose gain and noise temperature is known, the antenna system noise temperature alnants TTT and

therefore all measured values of antenna gain G and system TG / can be established. The established range test plans and procedures for all antennas that can be carried by the range positioner equipment (presently up to 9m) permit accurate measurement of the most essential performance characteristics:

Patterns and sidelobe envelope

Cross-pol

Gain

Noise temperature and G/T

As a final observation, to range test a large antenna will demand time and effort, for what will end up being a double assembly of the reflector components before the antenna is finally operational. Care must be taken to prevent damage to reflector panels. Summary of Range Test Activities

Requires assembly and alignment of the antenna structure

Alignment check by pattern tests focus and sidelobe balance. See Section 9.5 and Figure 9.3-19 for a sample of what might be seen in the process of focusing and balancing a reflector system

Comprehensive tests at any and all frequencies of choice

Actual antenna system RF performance is shown in the following diagrams: Figure 9.3-18 Sample antenna pattern measurement Figure 9.3-19 Sample pattern integration gain measurement

Formal test report, presenting expected on-site performance



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Figure 9.3-18 Sample antenna pattern measurement



344

Figure 9.3-19 Sample gain measurement by pattern integration of Azimuth and Elevation patterns



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9.4 Customer Site Preparations 9.4.1 Pedestal Alignment Check For the RF Test Engineer, everything depends on the results of the mechanical installation. One of the important exchanges of information is a report by the mechanical installation team declaring the alignment condition of the antenna. The RF Test Engineer must take any opportunity to perform a cross-check of the alignment condition. As soon as the antenna drive system is set into a working condition, a simple check of the orthogonality of the azimuth and elevation axes can be done by pointing the antenna to several different geostationary satellites across the orbital arc. The positions recorded are compared with the predicted satellite positions. Differences of less than ±0.05 degrees in Az/El positions across the arc should be considered as suggesting the axes are set to within prescribed limits. The exact position of individual satellites which are not in an inclined orbit is not known more accurately.

9.4.2 Reflector and Feed System Mechanical Alignment Check Before any RF tests are undertaken, it must be unequivocally established that the reflector system is set according to the prescribed geometry. This condition must be cross-checked. It should be conducted by actual dimensional check. The distance between the subreflector vertex and the horn aperture The distance between the feed aperture and the main reflector vertex The antenna geometry information must be available to the RF Test Engineer. A sample antenna geometry is shown in Figure 9.4-1. Appropriate check tools are required to perform this check quickly.

e

bc

d

a

g

Inner edge of reflector panel

Feed system

Main reflector

Subreflector

a, b, c, d, e represent basic antenna geometry

, g, h represent dimensions to check alignment symmetry

h

Figure 9.4-1 Cassegrain antenna geometry showing qualifying dimensional details to be measured before RF tests are undertaken. Apart from dimensions "a", "c", "d", and "e", all other dimensions should be measured symmetrically, in at least 4 quadrants. A suggested set of tools include: Laser distance measuring tool with reference mount Rotating laser tool to identify alignment of the subreflector, and alignment of the feed aperture Figure 9.4-2 shows how these tools can be utilized for the purpose.



346

h

a

r

Vertex of subreflector

Rotating laser mounted on to feed horn axis

Dis

tanc

e la

ser

Edge of main reflector

Laser light trace

Feed

Edge of subreflector

Hub

Figure 9.4-2 Possible approach to checking the alignment of a large reflector system. Use of a measuring tape no longer accurate since the tape will stretch and sag. For high frequency antennas, accurate alignment is mandatory to achieve desired gain and accurate pointing. 9.4.3 Ancillary Equipment Function Check - Control System, LNAs, HPAs Before the antenna system can be calibrated, its drive mechanism must, as a minimum, be operable and the position display functioning.

The feed system polarization control, if available, must be operable from the test position.

The LNA assembly must be installed and operative with a waveguide switch, operable from the test position, to be used to select the satellite signal path in one position, and an ambient temperature termination in the other path.

The output of the LNA downlink must be available for connection to the measuring spectrum

analyzer.

Factory test reports and calibration records for the individual LNAs must be available. The LNA noise temperature information is required in the determination of the antenna noise temperature, gain, and G/T.

The transmit signal path from the transmitter to the feed must be available and operative for the

purposes of transmitting cw signals to a cooperating earth station monitoring the same satellite. The cooperating station will record the uplink transmit patterns, co and cross-pol, and record signal stability over a 12 or 24 hour period.

The HPA performance characteristics record should be available. The calibrated test coupler in the

IFL at the feed Tx terminal will be used to set the uplink power and eirp for the pattern and antenna gain measurements by the cooperating station.

9.4.4 IFL Signal Path Integrity Regardless of whether the connection from the transmitter is installed on the antenna - either

in the hub the pedestal base in a shelter or operational equipment room a long distance from the antenna

an integrated waveguide connection will be necessary.



347

The complexity of this waveguide connection - IFL (Interfacility Link) - may be a single thread run a dual thread run a low loss "Tall Guide" for long distance straight line connections (> 50 meters)

Each connection will require a mechanism to bridge the azimuth, the elevation, and polarization axes. The bridging mechanism will either be flexible waveguide in low power applications (less than 1 kW), or rotary joints when higher power levels are involved. Example configurations - Single signal path over Az-El-Pol axes - Dual signal path over Az-El-Pol axes - Short IFL techniques - Long IFL techniques The receive connections from the feed to the receivers is usually less complicated. The microwave output of the LNA is fitted with down-converters to a lower frequency. Gain and noise power levels are usually sufficiently low to permit the use of relatively lossy coaxial cable. The cable can be fitted with flexible sections to bridge the polarization, elevation, and azimuth axes. The objective of the "integrity examination" is to ascertain that the connections are all correct. This is done both visually as well as by measurement of Return Loss and Attenuation characteristics during the installation. The final integrity check is done with an RF power leak test at all joints, and pressure leak at the dehydrator system. 9.4.5 Pretest Preparations The preparations for the calibration of any antenna system involves some homework to establish measurement boundaries.

List satellite positions for the site with which to measure patterns. Identify geographic coordinates of the site and calculate satellite Az/El positions. Identify that these

positions are actually reachable if the antenna is limited in its motion. Determine radio star positions and applicability for an accurate measurement of G/T and Gain.

Angular range limits for antenna patterns As the elevation angle becomes higher, then, as the antenna is rotated in azimuth, the recorded pattern will not represent the azimuth plane, since only a cone-shaped segment of the true pattern will be measured as shown in Figure 9.4-3. A correction for this can be arithmetically introduced by resizing the azimuth angle scale of the recording that is valid for the range 0o to 180o. The elevation angle to the test satellite will determine angular pattern limits. The correction for the azimuth scale is given by

El

AzAz

mc cos

2sinarcsin2 (9.4.1)

where mAz measured azimuth angle away from the main beam axis El elevation angle of target satellite



348

Ele

vatio

n an

gle

Azimuth rotation

actual conical pattern cut

Tru

e az

imut

h pa

ttern

if

mea

sure

d at

0o e

leva

tion

Azimuthal plane

sidelobe measured in conical trace, instead of this one

Trace of the main beam peak during pattern cut

Note:Antenna axis rotated in azimuth at some elevation angle will trace a conical path. The pattern captured in this manner will not include

all the expected sidelobes in the region 90o to 180o off-axis

Figure 9.4-3 Pattern measurements in azimuth taken at high elevation angle The extreme case is when one attempts to record an azimuth pattern while the antenna is pointing to near zenith. No useful pattern will be measureable. Applicability of radio star observations to measure G/T and Gain

Is the radio star test procedure applicable for the antenna under test ?? As a guide, for antennas equipt with normal commercial LNAs, and using the available radio stars, the following represents practical limits for acceptable accuracy >9m antennas S-band = 1.5 - 2.7 GHz ------ (Cas-A) >11m antennas C-band = 3.4 - 7.0 GHz ------ (Cas-A) >13m antennas X/Ku-band = 7 - 17 GHz ----- (Tau-A) >16m antennas Ka-band = 17 - 22 GHz ------ (Tau-A, the planets) >21m antennas >Ka-band = >22 GHz with cryogenic LNAs --- (the planets) Type of test equipment that will be appropriate for the planned validity and accuracy of particular

test methods. Since the evaluation of Gain and Noise Temperature will require information recorded in various Factory Acceptance Test Reports, it is important that this data be available. Necessary information includes

Feed insertion loss LNA gain and noise temperature HPA output power Expected IFL insertion loss and return loss

These items will identify which tests and associated procedures are applicable. Additional documentation should include

Overall antenna system RF performance specification Reflector geometry, feed and IFL assembly drawings Radio star data, pre-test analysis Test data sheets



349

9.4.6 Test Equipment, Location, Setup, and Function Check The typical complement of test equipment will include

spectrum analyzer signal generator calibrated test couplers (one for each applicable frequency band) to monitor test signal levels,

return loss, and attenuation measurements pattern plot and integration software

Useful, but not absolutely necessary, is a network analyzer for return loss measurements.

waveguide to coax adapters coax cable set with variety of connector types - N, SMA, 7mm, and transitions calibrated test coupler and adapter for Tx IFL signal path return loss tests calibrated test coupler and adapter for Rx IFL signal path return loss tests calibrated variable coaxial attenuator

The idea here is to identify the best location to set up the test equipment to perform most if not all the prescribed tests. Patterns and (if possible) star measurements should be done with the equipment as close to the control system console as possible, since the antenna must be steered from this location. That means the IFL (both Rx and Tx signal paths) must be available and accessible from this location. Any power division networks in the downlink must be by-passed to ensure maximum signal for the tests. Additionally, the LNA switch and polarization control connections must also be available at the chosen place for the test equipment. The test equipment will be used to set up calibrated boundary conditions for the various tests. Pattern measurements in particular rely on the time base of the instrument; it should be checked against a reliable time base - good stop watch, computer clock, external precision time source (NIST, UTC). Note: Spectrum analyzers have been known to possess unstable and inaccurate time base responses. For wide angle pattern measurements, the digital analyzer should be set up to record the patterns with a high density of data points for the purposes of pattern integration, as well as for presenting sufficient detail for the narrow angle pattern segment that will show correct null depths, and sidelobe levels. Choosing a large density of data points permits one wide-angle pattern to be recorded, and the narrow angle segment of this pattern to be extracted in the data-processing without losing accuracy and detail. 9.5 Preliminary RF Checks and Example Difficulties Preliminary RF checks are intended, with the minimum of effort, to show any potential discrepancies in the alignment of the reflector system, before going into the more extensive final system tests. The intention here is to provide a view of difficulties that are frequently encountered, and to indicate the cause of the problem. In some instances, the cause of the problem can be corrected on site; in others only a replacement of components will most judiciously correct the issue.



350

9.5.1 Sum Patterns Antenna patterns as used for anaylsis as discussed in earlier chapters are usually shown in the x-y or

format. Sometimes it is useful to understand what the pattern looks like "head-on" or along the z-

axis. Figure 9.5-1 shows a simplified view.

Ele

vatio

n pl

ane

Azimuth plane

45o plane

First sidelobe

Main beam

Elevation axis

Azimuth axis

Equal amplitude contour lines (db)

0

1020

30

15

25

5

a b

Figure 9.5-1 This view of the sidelobe placement and extent becomes useful when evaluating antenna patterns. It will help identify uncertainties during pattern recording sessions. For example, if the antenna is not pointing exactly at the target satellite, a cut represented by line "a-b" will lead to a distorted pattern with unexpected beam widths and sidelobe levels. (a) First null shallow or completely filled - See Figure 9.5-2 - The axial position of the subreflector is not focussed

Azimuth Pattern Elevation Pattern

Defocussed patterns

0db

Rel

ativ

e P

ower

-

db

Note:Subreflector will need to be moved toward or away from the main relfector by a small amount

15

20

25

30

5

10

0db

Rel

ativ

e P

ower

-

db

15

20

25

30

5

10

Figure 9.5-2 Poorly focused reflector system, but otherwise nicely symmetrical Corrective actions: Adjust subreflector axially outwards by an amount equal to [wavelength/5], and repeat the pattern measurement. If the null has not started to appear, but the sidelobe has transformed into a "shoulder" on the main beam, adjust the subreflector in the opposite direction by [2*wavelength/5]. Repeat adjustment until the null has been reached and started filling in again. Observe both elevation and azimuth patterns, and ensure that nulls in both planes move together. The objective is to reach approximately 25db or more null depth. See Figure 9.5-3.



351


Perfectly focussed, and balanced patterns

0db

15

20

25

30

Rel

ativ

e P

ower

- d

b

5

10

0db

15

20

25

30

5

10

Rel

ativ

e P

ower

- d

b

Figure 9.5-3 Well focused reflector system with beam and sidelobe symmetry (b) Unequal null depths between Az and El plane patterns - See Figure 9.5-4 - The main reflector and/or subreflector is astigmatic (clam-shelled)

Azimuth Pattern

Astigmatic or "clam-shelled" patterns

Rel

ativ

e P

ower

- d

b

Reflector shows one focus for azimuth, and a different focus for elevation

Note:Main reflector or subreflector or both are not symmetrical

0db

Rel

ativ

e P

ower

- d

b

15

20

25

30

5

10

Elevation Pattern

0db

15

20

25

30

5

10

Figure 9.5-4 Evidence for an astigmatic (clam-shelled) reflector system. Either the main reflector, or the subreflector, or both, are astigmatic Corrective actions: Rotate subreflector to next possible position in its mounting, and repeat pattern. If the astigmatic condition persists, the problem lies in the main reflector. The main reflector will need to be realigned. If the astigmatic condition rotates with the subreflector, the subreflector is distorted, and an equalization of the mounting hardware after loosening will most likely alleviate the distortion. If the azimuth null starts to fill while the elevation null is still deepening, the reflector system is astigmatic (clam-shelled). Providing a null of about 22 to 25db can be reached in both planes at the same time, no further action will be required. For simultaneous dual band functions such as 4 GHz Rx and 6 GHz Tx operations. Since the actual phase center in the feed horn for 4GHz and 6GHz are not identical, but may actually be spaced by several wavelengths inside the horn, a slightly defocused condition will exist in the antenna. A small compensatory correction in the focused condition for 4GHz can be made by purposefully moving the subreflector in (toward the main reflector) by a small amount to achieve a balanced optimization



352

between Rx gain and Tx gain. The change in gain will only be in the order of 0.05db or less, and therefore, unless absolutely necessary, this adjustment may be neglected. (c) First sidelobe level is unbalanced - See Figure 9.5-5 - The subreflector is translated off-axis - The subreflector is tilted


Unbalanced patterns

0db

Rel

ativ

e P

ower

- d

b

Rel

ativ

e P

ower

- d

bNote:Subreflector will need to be tilted to equalize the sidelobes(1) Bottom of subreflector needs to be moved away from main reflector(2) Right side of subreflector needs to move away from main relfector

0db

15

20

25

30

5

10

15

20

25

30

5

10

Right hand sidelobe

Upper sidelobe

left hand sidelobe

Lower sidelobe

Figure 9.5-5 An unbalanced main beam and first sidelobe condition due to reflector rotation and/or displacement. Corrective actions: Subreflector translation and rotation have similar effects on the antenna pattern. Rotation is the most likely cause, and easiest to correct. Identification of translation requires a measurement of beam scanning (shift in direction - see Section 9.5.6), or more easily, an optical sighting from the feed aperture center with a laser device. Based on the changes in the aperture illumination as the subreflector is rotated, the first sidelobe levels will adjust accordingly. Note the direction of subreflector rotation for a specific result. See Figure 9.5-6

High 1st sidelobe

Low 1st sidelobe

Higher illumination of the reflector edge

"Normal" illumnination

Correction:In Elevation: - high sidelobe on upper sidelobe side - rotate subreflector downIn Azimuth: - high sidelobe on left (ccw) side - rotate subreflector cw

Rotated subreflector

Feed

Expected sidelobe level

Low illumination of the reflector edge

Figure 9.5-6 The adjustments necessary to correct for unbalanced sidelobes due to reflector rotation or translation.



353

(d) First null levels unbalanced - See Figure 9.5-7 Subreflector translation and feed system droop due to gravitational effects are very difficult to distinguish. The most likely mechanism is subreflector translation in the elevation plane. The feed is generally a very stiff structure, and is aligned in the zenith position.

Elevation Pattern

Focussed, and balanced patterns, but feed is drooping or pointing

downward possibly due to gravitation sag

0db

10

Note:If severe, then feed will need to be shimmed upwards

Azimuth Pattern

20

25

Re

lativ

e P

ower

- d

b5

15

30

0db

10

20

25

Re

lativ

e P

ower

- d

b

5

15

30

Right hand sidelobe

Left hand sidelobe

Upper sidelobe

Lower sidelobe

Figure 9.5-7 Unbalanced first sidelobe nulls indicating feed system may be rotated/drooping due to gravity effects. Corrective action: Adjust subreflector up and observe the trend. The sidelobe balance should change, but ignore this until nulls are balanced. Then repeat sidelobe balance adjustment. If this action is unsuccessful, then the feed system is sagging. If condition is severe, shim the feed base at the mount to the hub in the same directions as indicated in Figure 9.5-7. (e) Narrow angle high sidelobe envelope excursions - See Figure 9.5-8 - Main reflector with periodic surface deviations

0

10

20

30

40

50

60

0-2-4-6-8-10 2 4 6 8 10


Rel

ativ

e Pow

er - d

b

Figure 9.5-8 Main reflector with periodic surface deviations (f) Wideangle high sidelobe envelope - See Figure 9.5-9 - Non-uniform subreflector surface, perhaps even due to defective reflector surface. Low gain with good near-in sidelobe levels an indicator that subreflector has defective reflecting surface. See also Section 9.5.4.



354

Figure 9.5-9 Non-uniform subreflector surface, perhaps even due to defective reflector surface. Low gain with good near-in sidelobe levels an indicator that subreflector has defective reflecting surface. (g) Sidelobe envelope non-compliant at many random angles off-axis - See Figure 9.5-10 - Main reflector panels with large random surface errors

-10 -8 -6 -4 -2 0 2 4 6 8 10

0

20

30

40

50

60

70

10

Anggle Off-axis - degrees

Rel

ativ

e P

ow

er -

db

Figure 9.5-10 Main reflector panels with large surface errors 9.5.2 Difference Patterns Antenna patterns as used for anaylsis as discussed in earlier chapters are usually shown in the x-y or theta-phi format. Sometimes it is useful to understand what the pattern looks like "head-on" or along the z-axis. Figure 9.5-11 shows a simplified view. The antenna equipt with a TE21 mode tracking coupler will show a “donut” pattern with a null in the center. In the case of the array, the null for the Az plane must be coincident with the null for the El plane. If the reflector system displays any misalignment, the null will tend to “fill” or decrease in depth, as shown in Figure 9.5-13(a). Note that the Az and El patterns must be independent. To check independence, measure the Az pattern in the Az plane, then measure the Az pattern in the El plane. Similarly for the El pattern. The degree of “cross-talk” will identify the tracking sensitivity, or quality of the tracking function, sometimes referred as “MOD slope” in military circles.



355

For the case of the antenna equipt with a TE21 tracking coupler, the difference pattern will be the same in both Az and El planes. There is no “cross-talk” pattern, since there is only one error channel.

a b

c

d

Azimuth planeE

leva

tion

pla

neElevation axis

Azimuth axis

10

15

25

40

Figure 9.5-11 This view of the difference pattern lobe placement and extent becomes useful when evaluating measured antenna patterns. It will help identify uncertainties during pattern recording sessions. For example, the pattern cut represented by "a-b" will not show the expected deep difference mode null on axis. The pattern cut represented by "c-d" will show severe asymmetries as well as a filled null. This can be a good indicator of a severely mis-aligned reflector system in which the reflector has effectively been rotated out of the elevation plane. (a) The ideal realizable difference pattern - Figure 9.5-12

Azimuth Pattern

Perfectly focussed, and balanced difference patterns

0db

15

20

25

30

Rel

ativ

e P

ower

- d

b

5

10

Sum pattern

Azimuth difference pattern in Azimuth plane

Elevation difference pattern in Azimuth plane

Figure 9.5-12 The "ideal" realizable difference pattern to be expected from a well aligned reflector system. Azimuth difference peaks between 10 and 15db below the sum reference pattern peak. Elevation difference pattern peaks equal to Azimuth peak levels +/- 1db. The cross-talk from the Elevation difference pattern, measured in the Azimuth plane, should be 10 to 20db lower than the azimuth difference pattern



356

(b) No recognizable tracking pattern - See Figure 9.5-13 - Main reflector is so badly mis-aligned as to upset the sensitive phase relationship between the difference pattern lobes.

Azimuth Pattern

0db

15

20

25

30

Rel

ativ

e P

ower

-

db

5

10

Difference pattern

Sum pattern

Badly distorted reflector with phase errors that destroy

the difference pattern Figure 9.5-13 The reflector path length errors are causing sufficiently large errors to destroy the difference patterns (c) Unequal off-axis error pattern lobes - Figure 9.5-14 - The feed and/or subreflector is tilted.

Azimuth Pattern

Sightly tilted difference mode patterns due to tilted or

astigmatic reflector system

0db

15

20

25

30

Rel

ativ

e P

owe

r -

db

5

10

Sum pattern

Difference patternwith uneven lobes and filled null

Figure 9.5-14 The effect of a slightly rotated subreflector is sufficient to tilt the difference pattern. This is much more sensitive than the first sidelobe unbalance in the sum pattern



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(d) High Az-El cross talk - Figure 9.5-15 - The feed is either tilted, and/or the main reflector surface is tilted and with poor surface accuracy

Azimuth Pattern

High Elevation plane difference cross-talk in Azimuth plane

0db

15

20

25

30

Rel

ativ

e P

ow

er

- d

b

5

10

Sum pattern

Azimuth difference pattern in Azimuth plane

Elevation difference pattern in Azimuth plane

Figure 9.5-15 Difference pattern cross-talk between azimuth and elevation planes (e) Low value tracking slope - Figure 9.5-16 - The LNA used on the error channel must be the same as used on the reference sum channel. - The satellite beacon signal level is lower than expected. - The spectrum analyzer amplitude scale must be calibrated to read uniform amplitude values for both the sum and Az. and El. difference signals. More on this topic in Section 6.

volta

ge

Off-axis angle - degrees

Slope of the difference pattern in the null

Tracking slope(also called "MOD" slope)

= V/θ /(1 volt ref)

V

θ

Difference pattern

Sum pattern

1 volt reference

0 volt

Note: The higher the difference off-axis peak level with respect to the sum pattern peak, the larger the "tracking slope"

Figure 9.5-16 Tracking slope defined. The amplitude pattern scale needs to be converted from "db" to "volts", and replotted as shown here. The region around the central null (or "zero") will be smudged with noise.



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9.5.3 Antenna Gain Unexpected large beamwidth, consequent low gain values - Subreflector badly defocussed so that first sidelobe is buried in the main beam. - Antenna not peaked on the target satellite. Pattern is cut slightly off-axis in both Az and El planes Unexpected small beamwidth, consequent high gain values - check with predicted main beam width value Correct Az and El beamwidth, but star track and/or pattern integration shows low gain values - Main reflector deformed in the 45 deg planes. - Defective subreflector one possibility: a non-metal reflector structure with a metallized (sprayed or painted) reflective surface which has subsequently been damaged near the central axis. The illumination of the main reflector is still sufficient to provide the expected beamwidth, but the leakage through the subreflector is causing the sidelobe envelope to be significantly elevated in wider angle regions. 9.5.4 Antenna Noise Temperature Small y-factor readings - This usually means that the noise power level of the system is very high. If the feed system loss values are high, then the only means for compensation are: - Use of an LNA with considerably lower noise temperature - A radiometer - an instrument that will measure low level voltages while very rapidly switching between the antenna noise and a built-in reference noise source. - A very sensitive spectrum analyzer with high resolution Unexpected noise temperature values - too low - too high

- Low antenna noise temperature is a sure sign of a false reading. It may be caused by a defective LNA, one with a high input return loss. Most of the noise power is being returned to the antenna aperture, and the system seen as "low noise".

- High antenna noise temperature, inconsistent with expectation, is also a sure sign of a false reading, the cause residing in the measurement setup.

- Spectrum analyzer amplitude scale problem. In using analyzer to measure noise levels, the levels must be chosen to show linearity from top to bottom of the scale. Otherwise, introduce a calibrated variable 1 - 10db attenuator into the input line.

- Failure to correct y-factor readings for high analyzer noise floor - Inclement weather - Incorrect analyzer settings - Faulty LNA amplitude response

Deviation from expected elevation noise temperature profile - Cable interconnect between LNA and analyzer defective, causing variable attenuation in the

line as cable moves with changes in elevation angle. 9.5.5 Radio Star Track Check Manual, control system program track

- Record timed star Az, El positions, compare with predicted values, and plot the result. This will offer a record of pointing errors relatable to overall antenna alignment.

Sky y-factor - unexpected low values - Check weather (heavy cloud at higher frequencies can have a serious impact on y-factors). - Check LNA condition. If possible switch in a new/different LNA. - Check amplitude scale of analyzer for linearity



359

9.5.6 IFL Signal Paths Example configurations Single signal path over Az-El axes Dual signal path over Az-El axes Short IFL techniques Long IFL techniques Unexpected high RL (Return Loss) values - Figure 9.5-17 An IFL run will generally consist of many different waveguide components - bends, twists, rotary joints, flex waveguide, filters, and couplers - each with a (voltage) reflection characteristic. If the (nominally acceptably low) voltage reflection components all happen to add in phase, the RL of the full assembly will be high.

5.85 6.856.35START 5.850 000 000 GHz STOP 6.850 000 000 GHz

S21/M log MAG 2 dB/ REF -10 dB14 Mar 2002 15: 36: 44

Smo

T

CH1 >-10db

-20db

-30db

Figure 9.5-17 Return loss measurement on an approximately 50ft long waveguide interconnect, including bends and rotary joints. Corrective action: If possible, assemble complex segments of the IFL one component at a time, all the while monitoring RL. With the addition of each new component, tune for lowest RL. Straight waveguide sections between segments need not be included at this point. Match-mark each component if dis-assembly is required for the installation. Perform the final installation, and record the final RL value. Typical component RL will range from about 25db to 35db. RL of a typical IFL assembly may achieve 14 to 15db, and with a bit of luck 16 to 17db. It is for this reason that IFL designs attempt to reduce the number of "complications" such as bends and joints to a minimum. Mode spikes in RL response - Figure 9.5-18 Generally, large attenuation values can be attributed to inadequately mating flanges. Complex components generally have slightly higher loss than straight waveguide. But when the connecting flanges do not close properly - because inappropriate gaskets have been used, or the flange ridges have been lapped so that there is no longer the space required for the gaskets to fit and allow the flange to close properly - power will leak at the flanges. Because the gasket is in place, the pressurization system will not register a break in the RF continuity of the IFL.



360

5.85 6.856.35START 5.850 000 000 GHz STOP 6.850 000 000 GHz

S21/M log MAG 2 dB/ REF -10 dB14 Mar 2002 15: 24: 44

Smo

T

CH1 >-10db

-20db

-30db

Figure 9.5-18 The effects of mode spikes due to a discontinuity in the waveguide interconnect shows up as a practical short circuit at 5.97 GHz. Corrective action: Check for RF leaking flange joints with a waveguide/coax probe and a spectrum analyzer or sensitive power meter as detector. Once found, remove the gasket. Note: The pressurization system should leak a little, at least to the point where the system will cycle approximately every 30 minutes. See analysis in Section 10.1. 9.6 Formal On-site RF Antenna Tests This section attempts to show a record of acceptable antenna performance characteristics. 9.6.1 Antenna Patterns - Sum, Difference, Cross-pol

Figure 9.6-1 Sample antenna patterns. (a) Narrow angle patterns (b) Wide angle patterns



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9.6.2 Monopulse tracking sensitivity Tracking sensitivity is expressed as the voltage available (for the antenna drive) per unit angle off-axis. The larger the voltage available, the more sensitive the antenna to small angles off target.

Azimuth Tracking Slope and Elev Error Cross-talkFrequency = 7.6 GHz

y = -232.09x3 + 1.7338x2 + 5.0006x - 0.0005

Tracking slope = 4.9 v/v/deg

-0.4

-0.3

-0.2

-0.1

0

0.1

0.2

0.3

0.4

-0.100 -0.050 0.000 0.050 0.100 0.150

Azimuth Angle - deg

Erro

r Vol

tage

- vo

lts

Delta Az in Azim

Delta El in Azim

Linear (Delta El in Azim)

Poly. (Delta Az in Azim)

Elevation Tracking Slope and Azim Error Cross-talkFrequency = 7.6 GHz

y = 204.48x3 + 1.4423x2 - 4.9263x - 0.0058Tracking Slope = 4.9 v/v/deg

-0.40

-0.30

-0.20

-0.10

0.00

0.10

0.20

0.30

0.40

-0.15 -0.10 -0.05 0.00 0.05 0.10


Erro

r vol

tage

- vo

lts

Delta El in Elev

Delta Az in Elev

Linear (Delta Az in Elev)

Poly. (Delta El in Elev)

Figure 9.6-2 Tracking sensitivity as measured on an 18m X-band antenna system for both Azimuth and Elevation. This performance detail is extracted from the difference patterns shown in Figure 9.6-1. 9.6.3 Antenna Noise Temperature Figure 9.6-3 shows a 0 to 90 degree elevation noise temperature profile. Two things may be seen here. 1. The effective temperature of the earth at 0 deg elevation equals approximately 230 Kelvin. 2. The noise profile increases between 60 and 90 deg elevation, indicating that significant wide angle sidelobe structure is beginning to intercept the ground. This was measured on an 18m S-band antenna.

ISRO 18m S/X Antenna SystemAntenna Noise Temperature vs Elevation

Date: 28 Oct 2006Azimuth Bearing = 180 deg

Weather: Light cloud cover, 25 C

80

100

120

140

160

180

200

220

240

0 10 20 30 40 50 60 70 80 90

Elevation - degrees

Noi

se T

empe

ratu

re -

Kel

vin

Frequency = 2.2 GHz

Frequency = 2.25 GHz

Frequency = 2.3 GHz

Figure 9.6-3 Noise temperature profile for various frequencies



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9.6.4 Antenna System G/T, Noise Temperature, and Gain There are two approaches to determine G/T. Measure:

Gain G on satellite by link level Gain by integration of wide angle pattern - if pattern is considered unknown Gain by beamwidth measurement - if pattern is considered known Gain by radio star System Noise Temperature T into a clear sky

Satellite Link method Need to know the following features of the satellite:

downlink eirp and aspect correction of the test signal location of the satellite to calculate downlink path loss measure the received signal level with high resolution - typically 0.1db - with an optimally pointed

main beam An example pattern and associated calculation Beamwidth method Generally, an antenna designed to meet ITU/FCC sidelobe envelope specifications, when properly aligned, can be expected to meet those requirements, and the careful measurement of 3db and 10db beamwidth will result in a very good approximation for the antenna gain. Pattern integration In the case of an antenna being tested which is of unfamiliar design, has been neglected for a long time, has been recently moved to a new location, suffered damage or been modified, or even had a radome installed, the sidelobe envelope characteristics will be unknown. The beamwidth method cannot be used, since the nominal sidelobe envelope is unknown. Therefore, as much of the wide-angle pattern must be measured and then integrated for a best approximation for the antenna gain. The result (called directivity) will automatically include the effects of any defects in the reflector system. The feed system insertion loss must be subtracted from the directivity to determine gain. Radio star method The radio star routine presents a unique means to be able to measure antenna gain, structural stiffness of the reflector assembly, and pointing accuracy. The position of the radio stars is very accurately known, and in a few instances, the noise flux density has been accurately calibrated. In particular, Cas-A is very well documented, and represents the most powerful of the radio stars visible in the microwave segment of the spectrum. Cas-A noise density decreases with time in an accurately known manner. By contrast, other radio sources, in particular Tau-A and Cyg-A, have been calibrated, but the decrease in noise density as a function of time has not been accurately established. Based on several informal observations, in 2007 the flux density correction with time in Tau-A seems to be decreasing more slowly than Cas-A. An example of an antenna calibration sequence for a 32m beam waveguide antenna operating C-band is shown in Figures 9.6-4 to 9.6-9



363

Antenna A-3

G/T vs Elevation Angle at F = 4.0 GHz

41.0

41.2

41.4

41.6

41.8

42.0

42.2

42.4

42.6

42.8

43.0

0 5 10 15 20 25 30 35


Syst

em G

/T -

dbK

Tau-A Star TrackDate: 12 Nov 2002

Frequency = 4000 MHzPolarizaiton = RCP

LNA-1 = L3 Comms FT 40/800 s/n 1279

Figure 9.6-4 Measured G/T vs elevation angle on Taurus for 4 GHz RCP. This measurement is repeated for other relevant frequencies.

Antenna A-3 Noise Temperature vs Elevation Angle

30

35

40

45

50

55

5 10 15 20 25 30 35


Noi

se T

empe

ratu

re -

Kel

vin

Antenna Noise Temperature measured during Tau-A star track

Pol = RCP w/ LNA-1Date: 12 Nov 2002

Weather: Variable cloud, at times heavy rain

Temperature = 11 deg CHigh windsRain

Figure 9.6-5 Measured antenna noise temperature along the path of the radio star Tau-A at 4 GHz RCP. This measurement is repeated for other relevant frequencies.

Antenna A-3 System Gain (F=4.0 GHz) vs Elevation Angle

60.5

60.6

60.7

60.8

60.9

61.0

0 5 10 15 20 25 30 35


Ant

enna

Gai

n -

dbi

Figure 9.6-6 Measured antenna gain vs elevation angle at 4 GHz. Note the very small variation in gain suggesting that the antenna is very stiff, the reflector not changing in shape. This measurement is repeated for other relevant frequencies.



364

Antenna A-3 Gain vs Frequency

58.5

59.0

59.5

60.0

60.5

61.0

61.5

3400 3500 3600 3700 3800 3900 4000 4100 4200

Frequency - MHz

Ant

enna

Gai

n -

dbi

Pol = RCP

Pol = LCP

Gain measured on Tau-A at elevation angles 50 - 60 degrees

12 Nov 2002

Figure 9.6-7 Antenna gain vs frequency at high elevation angles. Star measurements at 6 frequencies occupied the period of time during which the star moved in elevation from approximately 60 to 50 degrees. In this angle range, the star is in a relatively benign portion of the sky, and the results offer a reliable representation of true antenna gain.

Antenna A-3 System G/T vs Frequency (RCP)

for various Elevation Angles

39.31

41.56

40.61

41.56

41.74

40.44

40.81

41.7841.94

39.73

40.60

40.96

41.86

42.06

39.84

40.73

40.99

41.83

42.01

40.43

40.05

41.29

39.40

40.23

39.56

38.0

38.5

39.0

39.5

40.0

40.5

41.0

41.5

42.0

42.5

43.0

3400 3500 3600 3700 3800 3900 4000 4100 4200

Frequency - MHz

Syst

em G

/T -

dbK

Elev = 6 deg

Elev = 7.5 deg

Elev = 10 deg

Elev = 15 deg

Elev = 20 deg

Specification at 5deg Elev

Specification G/T = 40.15 dbKat F = 3.92 GHz and 5 deg Elevation

Figure 9.6-8 Final G/T vs frequency at various elevation angles for RCP, after measuring the sky y-factor into "clear sky" (no obstructions), and subtracting T from G for low elevation angles.

Antenna A-3 Clear Sky Antenna Noise Temperature vs Elevation Angle

Various Frequencies, Pol = RCP

30

35

40

45

50

55

60

0 5 10 15 20 25 30 35


Noi

se T

empe

ratu

re -

Kel

vin

Freq = 3.4 GHz

Freq = 3.6 GHz

Freq = 3.8 GHz

Freq = 4.0 GHz

Freq = 4.2 GHz

Figure 9.6-9 Clear sky noise temperature vs elevation angle for various frequencies. There is no immediate explanation for the unusual behaviour of the noise profiles at 3.6 and 4 GHz, except that the weather was overcast with occasional rainy periods.



365

Important note - only the RCP values have been documented here; the LCP values should also be measured, since the radio star Taurus is slightly elliptically polarized. The values for LCP and RCP conditions of the test antenna must be averaged to find the final value for G/T and gain. This same procedure can be used for Tx frequency band, if an appropriate calibrated LNA and controllable switch with termination assembly is available. 9.6.5 Transmit Uplink Gain and eirp Stability The reader is referred to the EIA-411 (1985) standard document, Chapter 6. 9.7 Measurement Accuracy The reader is referred to the EIA-411 (1985) standard document (Chapter 6) for details of measurement accuracies. A copy of the relevant section is given in Chapter 12 Section E.6.

Chapter 10 – Antenna Protection


366

Chapter 10 Antenna Protection 10.1 Protecting the Feed against the Elements 10.1.1 Feed Horn Window Considerations 10.1.2 Feed Pressurization Principles 10.1.3 Waveguide System Dehydration 10.2 Feed Protection against Rain, Mist, Snow and Ice, and Birds 10.3 Radomes 10.3.1 Sandwich Radomes 10.3.2 Space Frame Radomes 10.3.3 Solid Laminate Radomes 10.3.4 Air Supported Radomes 10.3.5 Selection Criteria 10.3.6 Brief Summary of Radome Features 10.1 Protecting the Feed against the Elements 10.1.1 Feed Horn Window Considerations The feed, mounted in prime focus or Cassegrain reflector configurations, is exposed to the weather. A dielectric window is used as a cover for the horn aperture, to keep rain and dirt out of the feed system. Of necessity, the window must be transparent to RF energy, and therefore the choice of low dielectric constant materials. But these materials all possess reflective properties which will contribute to degrade the VSWR (and for CP systems) the axial ratio. To ameliorate these effects, some curvature is given to the very thin RF window of lowest possible dielectric constant to (a) help scatter any reflected components, and (b) reduce any dielectric refraction effects. Cassegrain feed horns are always pointing into the weather, meaning that rain can accumulate on the RF window surface. Cassegrain and prime focus feeds are, in some places, subject to mist and fog, both of which can impede passage of RF signal. Therefore the idea to have the window material surface tension properties minimize the sheeting action of water, and cause it to bead and run off toward the edge of the horn aperture. The primary way of doing this is to use thin sheet low-dielectric material stretched over the horn aperture, and pressurized to derive the necessary curved shape. Therefore, the material also must possess sufficient strength to not burst under pressure, and not let any of the pressurizing gas out, or even any water in. At the same time, the window should not stretch out from its mounting around the horn aperture. Minimum features for a good RF window would be:

Dielectric constant <= than 2.5 "Thin" means less than 0.005 wavelengths "Curvature" means a divergence from the flat by more than 0.01 aperture diameter Very low surface tension properties Zero porosity High tensile strength Very low expansive stretch



367

Figure 10.1-1 shows a typical installation of a feed horn window. (Photo used with permission of General Dynamics SATCOM Technologies, Inc.) . The feed system for reflector antennas in its waveguide format can represent a large volume of hollow space. Left open, the still ambient air contained by the feed will therefore contribute to internal corrosion by the results of condensation. In order to prevent this, the feed is pressurized with dehydrated air. For most applications, usually an over-pressure of <= 0.5 psig (pounds per square inch gauge indication) or 0.0725 kPascals is applied. However, for large horn aperture diameters (> 1 meter diameter), the tension on the horn window subjected to 0.5 psig pressure may cause failure, and the internal pressure may need to be adjusted lower. Some representative materials useful for this purpose are Teflon™, or PTFE - possesses very good protection against water sheeting Glass-reinforced Teflon™ - has a very low stretch factor and high tensile strength, but may not be sufficiently thin Gor-tex - experience shows a measure of porosity Mylar - has a tendency to age quickly and become brittle, leading to failure Appropriate sheet thickness should be (for microwave frequencies) 0.015 inches for C-band applications 0.010 inches for Ku band applications 0.005 inches for Ka band applications To provide the necessary curvature or bulge in the window across the horn aperture, air is pumped through a dessicant and into one of the feed terminal waveguides. The horn aperture is covered with a window - usually Teflon™ - to keep the air inside.

10.1.2 Feed Pressurization Principles In order to understand what might be a reasonable leak rate for the feed, an examination of the relationship between pressure, temperature, and flow of a gas from a closed space follows. From Boyle's gas law, at a constant temperature and for a given mass of air kPV = constant (10.1.1)



368

This says, that if the pressure on a mass of air is increased by 2, 3, or 4 times, its volume will decrease to ,, 3

121 or 4

1 of its original volume.. Or alternatively, we can say

kvpvp 2211

For a fixed container of volume TV filled with air at ambient pressure ambP , the volume of air will be TV . Consider now TV (feed system( filled with air, and pressurized to 1p . For a change in pressure p due to a leak from the closed system, there will be a corresponding change in volume v . ppp 12

The volume at 1p is 11 / pkv ; the volume at 2p is 22 / pkv and

)/1( 11

2 ppp

kv

(10.1.2)

The incremental change in volume v is

)/1(

1

)/1(1

21111

12ppp

pk

pppp

kvvv

(10.1.3)

For an increase in pressure 0p , 2v becomes smaller than 1v ; for an decrease in pressure 0p ,

2v becomes larger than 1v . A positive 12 vvv represents leakage from the fixed volume TV . For the case iamb pPp 1 and ip starting pressure above ambP ,

iambiamb

Tamb pPppP

pVP

ppp

pkv

/1

1

)/1( 21

21

(10.1.4)

pfVv T

where 2

1 iamb

amb

iamb

pP

P

pP

pp

pf

(10.1.5)

Leak rate is defined as t

pfVt

vT

1

)( (10.1.6)

or the time t during which the pressure change p takes place -

rateLeak

pfVt T )( (10.1.7)

Units: Pressure: 33.899 ft H2O = 14.696 lb/in2 = 406.788 inches H2O 1 lb/in2 = 407.788/14 696 = 27.680 inches H2O 1 lb = 1/(2.2) kg; inch2 = (2.54/100)2 meters2 1 lb/in2 = 1/(2.2)/(2.54/100)2 = 704.5468 kg/m2 0.5 psig = 352.2734 kg/m2 = 13.84 inches H2O 1 inch H2O = 25.3434 kg/m2 Volume: 1 meter3 = 61023.378 inch3 = 35.314 ft3 1 liter = 61.023 inch3 = 0.0353 ft3



369

Example system leak rate calculation A simple pressurization system is shown in Figure 10.1-2.

Dehydration Cell

PumpPessurized Reservoir

Pressure Regulator

Distribution Valves

Transmit Waveguide

Rx Feed Terminal

Feed System

Pressure Relief Valve

Figure 10.1-2 A block diagram of a pressurization system frequently utilized to protect an antenna feed from deterioration by the effects of weather. Pressurized reservoir = 1.5 ft3 (42 liters), pressurizable to 10 psig (high pressure limit), and 1 psig (low pressure limit). Regulator - controls output pressure 0 to 1 psig Contactor activated to initiate pump when output pressure < 0.1 psig. The objective of this system is to provide a continuous constant pressure to the waveguide and feed systems, to replenish whatever air may have leaked out. The principal question of interest here is: Question: How often should the pump recycle to replenish (with dry air) the reservoir ?? Once a day, once per hour, once per ½ hour ?? We can use the above analysis to determine for the case of Figure 10.1-2 what a reasonable cycle time may be. For this system:

TV = 42 liters, ambP = 14.7 psig For the reservoir pressure to drop from 10 psig to 9 psig

2

1 iamb

amb

iamb

pP

P

pP

pp

pf

= 0.02511

t

pfVrateLeak T

)(

= 42 x 0.02511 = 1.055 liters per unit time

If we specify (somewhat arbitrarily at this moment) a leak rate = 0.1 liters/minute or 100 milli-liters/minute, then the time needed for the tank pressure to drop from 10 psig to 9 psig will be

t = 1.054/0.1 = 10.54 minutes Repeating this calculation for each 1 psig drop in tank pressure, the following Table 10.1-1 can be constructed. Times for unit pressure drop in reservoir for various leak rates



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Table 10.1-1 Estimated run times for the example pressurization system Leak Rate (liters/minute) 0.1 0.2 0.3 0.4 0.5 Pressure drop psig 10 - 9 10.5 5.25 3.50 2.62 2.10 9 - 8 11.4 5.70 3.80 2.85 2.28 8 - 7 12.5 6.25 4.16 3.12 2.50 7 - 6 13.7 6.85 4.56 3.42 2.74 6 - 5 15.1 7.55 5.03 3.77 3.02 5 - 4 16.7 8.35 5.56 4.17 3.34 4 - 3 18.6 9.30 6.20 4.65 3.72 3 - 2 20.8 10.4 6.93 5.20 4.16 2 - 1 23.5 11.75 7.83 5.87 4.70 Total times (Minutes) 142.8 71.4 47.5 35.6 28.6

If we specify a minimum cycle time = 28.6 minutes, the maximum leak rate (equal to the sum of the times in the column under leak rate) allowable from the system cannot exceed 0.5 liters/minute. If we limit the differential pressure cycle range from 10 to 3 psig in the tank, the total system leak rate can only be 0.3 liters/minute (the sum of the times for the pressure to drop from 10 to 3 psig = 32.8 minutes or about ½ hour. Providing for a 1.5 safety or contigency factor, then a leak rate of 0.2 liters/minute can be used as a working specification. A practical feed system will possess a leak rate of about 50 to 150 milliliters/minute when pressurized to 0.5 psig (max), depending on size (volume). This then indicates that if additional interconnecting waveguide, Tx and/or Rx links to equipment shelters, are to be added to the feed system, then leakage rates will need to be adjusted according to the capacity of the pressurization system. The waveguide IFL (Interfacility Links), generally with fewer flanges and joints, will have the smaller fraction of total leakage. However, if there are several IFL interconnects, then each w/g will have to be allocated a specified leak rate, depending on the number of flanges, joints, flex sections, transitions to coax, etc. Leakage of air from the feed system The same relationships considered in the previous sections are applicable for the determination of the rate at which air escapes from the feed system. These are generalized in the following expressions:

rateleakPrescribed

pfVtfortimeMeasure T )( (10.1.8)

amb

iamb

P

pP

T pfrateleakdpresecribe

ValdifferentipressuretotalfortimetotalMeasured (10.1.9)

Table 10.1-2 Pressure drop times for various volumes Pamb = 406.788 in.H2O Leak rate = 0.1 liters/minute Manometer Reading )( pf Pressure drop times for various volumes VT Inches H2O 32.77

2,00065.55 4,000

98.32 6,000

131.098,000

163.87 10,000

(liters) (in.^3)

½ psig 14 - 13 2.303 x 10^-3 0.754 1.509 2.264 3.019 3.774 13 - 12 2.314 x 10^-3 0.758 1.517 2.275 3.033 3.792 12 - 11 2.325 x 10^-3 0.762 1.524 2.286 3.048 3.809 11 - 10 2.336 x 10^-3 0.765 1.531 2.296 3.062 3.828 10 - 9 2.347 x 10^-3 0.769 1.538 2.307 3.077 3.846 9 - 8 2.359 x 10^-3 0.773 1.546 2.319 3.092 3.865 ¼ psig 8 - 7 2.370 x 10^-3 0.777 1.553 2.330 3.107 3.884 Total time 5.358 10.718 16.077 21.438 26.798 (minutes)



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Table 10.1-2 above shows the times for each 1 inch H2O drop in pressure to be practically constant. Therefore, a more practical table for leak rates and times can be constructed as shown in Table 10-3. For an initial pressure of 0.5 psig in the feed, the time for the pressure to drop by 1 inch H2O ( p = 1) for a given leak rate is listed. To put the units of measure into perspective, consider the diagram in Figure 10.1-3.

14 inches of water(equivalent to 0.5 psig)

ManometerFeed system

Pump Regulator valve

Pump shut-down contactor

Switch

Relief valve

Leak

Figure 10.1-3 The idea of determining how much pressure and for what leak rate, as discussed in the text, involves the measurement of pressure shown here in terms of the displacement of water in a tube. Modern instruments are available that give indication directly as to pressure and leak rate.

Table 10.1-3 Leak rate for specific volumes of waveguide assemblies, assuming 0.5 psig starting pressure to accommodate a 30 minute dehydrator cycle time.

Volume 310303.2 pf

Leak rate - liters/minute in.^3 liters 0.01 0.02 0.03 0.04 0.05 0.07 0.10 0.20 500 8.2 1.9 0.94 0.63 0.38 Time in minutes 1,000 16.4 3.8 1.9 1.26 0.715 0.54 0.38 2,000 32.8 7.5 3.8 2.5 1.5 1.0 0.75 0.5 3,000 49.2 11.3 5.6 3.8 2.3 1.6 1.1 0.75 4,000 65.5 15.1 7.5 5.0 3.0 2.1 1.5 1.0 0.75 5,000 81.9 18.9 9.4 6.3 3.8 2.7 1.9 1.2 0.95 6,000 98.3 22.6 11.3 7.5 4.5 3.2 2.2 1.5 1.1 7,000 114.7 26.4 13.2 8.8 5.3 3.8 2.6 1.7 1.3 8,000 131.1 30.2 15.1 10.0 6.0 4.3 3.0 2.0 1.5 9,000 147.5 34.0 17.0 11.3 6.8 4.8 3.4 2.2 1.7 0,000 163.8 38.0 19.0 12.6 7.5 5.4 3.8 2.5 1.9

For reference purposes, IFL waveguide interconnect volumes are listed in Table 10-4

Table 10.1-4(a) Volumes of rectangular waveguide Volume per unit length Rectangular waveguide Cubic in./ft liters/ft liters/meter WR-650 253.5 4.15 13.62 WR-510 156.06 2.56 8.38 WR-430 110.94 1.81 5.96 WR-340 69.36 1.14 3.73 WR-284 45.67 0.748 2.45 WR-229 31.46 0.516 1.69 WR-187 19.59 0.310 1.053 WR-159 15.17 0.249 0.815 WR-137 10.9 0.179 0.586 WR-112 6.69 0.1096 0.359 WR-90 4.32 0.0708 0.232 WR-75 3.37 0.0553 0.181 WR-62 2.32 0.0380 0.125 WR-51 1.56 0.0256 0.0838 WR-42 0.86 0.0141 0.0462 WR-34 0.69 0.0113 0.0371 WR-28 0.47 0.0077 0.0253



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Table 10.1-4(b) Volumes of Andrews elliptical waveguide Volume per unit length Elliptical waveguide Cubic in./ft liters/ft liters/meter 18 - 26.5 GHz EW-240 17 - 23.6 GHz EW-220 1.38 0.0026 0.0742 14 - 19.7 GHz EW-180 2.07 0.0339 0.111 11 - 15.35 GHz EW-132 3.111 0.0510 0.167 10 - 13.25 GHz EW-127 4.66 0.0764 0.2505 8.3 - 11.7 GHz EW-90 6.22 0.1019 0.334 7.7 - 9.8 GHz EW-85 7.26 0.119 0.390 6.1 - 8.5 GHz EW-77 10.89 0.178 0.585 5.3 - 7.75 GHz EW-64 13.84 0.221 0.724 5.85 - 7.125 GHz EW-63 15.89 0.260 0.854 4.6 - 6.425 GHz EW-52 19.53 0.320 1.049 4.4 - 5.0 GHz EW-43 31.45 0.515 1.690 3.3 - 4.3 GHz EW-37 36.46 0.597 1.959 3.1 - 4.2 GHz EW-34 43.20 0.708 2.322 2.6 - 3.4 GHz EW-28 62.20 1.019 3.342 1.9 - 2.7 GHz EW-20 104.54 1.713 5.619 1.7 - 2.4 GHz EW-17 122.69 2.011 6.595

Table 10.1-4(c) Volumes of round (circular) waveguide

Round waveguide Volume per unit length (diameter - inches) Cubic inch/ft liters/ft liters/meter 3.425 110.55 1.812 5.943 2.600 63.71 1.044 3.424 2.125 42.55 0.697 2.286 1.370 17.69 0.289 0.948 1.115 11.72 0.192 0.629 1.090 11.19 0.184 0.602 0.990 9.24 0.151 0.496 0.750 5.3 0.087 0.285 0.500 0.400 0.300 0.250 0.200 0.100

10.1.3 Waveguide System Dehydration Unpressurized waveguide systems allow the entry of moist ambient air over time through leaking seals, cracks, etc. The constant change in atmospheric conditions, including pressure and/or temperature changes in the air (particularly below the dew point), will result in the collection of water. Water in waveguide systems causes corrosion, voltage arcing and increased VSWR, all of which reduce system performance.

The solution is to introduce a drying medium under low pressure to both reduce the potential that moisture is going to be created within the confines of the waveguide system and eliminate the possibility of air entering via any small openings.



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The pressurizing source must be able to provide dry gas on demand. The source may be nitrogen tanks with a regulator or an automatic dehydrator.

Nitrogen tanks are used during transport or while in storage. Advantages include a dew point lower than dehydrated air, no power requirements, no moving parts and inexpensive gas. The disadvantages are that one must regularly monitor tank pressure and arrange for replacement, etc. These tanks are typically used when transporting or temporarily storing a feed system.

For long-term permanent applications, desiccant-type dehydrators are used. They are classified as manual, heat or pressure swing regenerative. Manually regenerative dehydrators require frequent inspection and periodic replacement or regeneration of the desiccant. An example system is shown in Figure 10.1-4

Figure 10.1-4 Automatic regeneration dehydrator

Heat regenerative units are only practical for dehydrating low volume, low pressure systems like feed assemblies. A heat regenerative unit operates by using two absorbing desiccant containers. Air is passed through one of these containers in which the moisture is absorbed. When the moisture in the desiccant reaches a specific value, the incoming air is switched to a second container. The moisture in the first container is driven out by heat and the process reverses as required. These units are typically the dehydrator of choice for waveguide system use because they are compact, rack mountable and generate very little noise or vibration.

Pressure swing dehydrators incorporate the principle of moisture separation by desiccant absorption. The units consist of a high pressure compressor and two cylindrical absorption drying chambers switched by a timer control and solenoid-operated valve. These units are more suited for high volume and/or high pressure needs. They tend to be quite noisy.

Feeds are normally composed of several waveguide components, all connected with flanged joints. Some of the components are fitted with tuning screws essential to the proper functioning of the components (for example, differential phase shifters, filters, and complex junctions). All these represent places through which air under pressure can escape. In principle this is good, because now the internal space in the feed will be subject to a more or less continuous flow of dry air. The question that arises now is - how much leakage of air pressure is reasonable ?? An attempt to permanently seal the feed so that no air leaks is practically impossible. A continuously running dehydrator is undesirable - these machines make too much noise, and rapidly wear out. Or is a once-a-day operation of the dehrydrator pump reasonable ??



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10.2 Feed Protection against Rain, Mist, Snow and Ice, and Birds Rainblower An apparatus to blow hot air across the surface of the feed horn cover under high pressure has also proven effective and is typically available as an accessory from antenna manufacturers. It is typically used in conjunction with a moisture probe so that it is only operating when moisture is present.

Rain becomes a problem, even if the window material is Teflon, if the antenna is located in tropical regions with a very high look-angle to the target satellite. In spite of a bulging window, water can still collect around the edges of the fastener ring. The idea now is to provide a means of forcibly moving air across the aperture, with a "rain-blower". See Figure 10.2.1

Figure 10.2-1(a) Rainblower feed nozzles

Figure 10.2-1(b) Rainblower sensor. (Photo used with permission of General Dynamics SATCOM Technologies, Inc.)



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Mist collects on all surfaces, usually during the night in high Mediterranean regions, and during periods of fog. The resulting layer of water on the horn window leads to an attenuation in the signal path, both up and down links. Forced air movement is the only way of quickly eliminating these effects. In the temperate and sub-arctic regions, where temperatures reach below freezing, and in which the propensity for snow and ice to accumulate, the RF signal path becomes impaired. Snow causes small difficulties, water much more so, and ice and hoar frost (because of thickness) is extremely detrimental. The method here is to provide a heating system around the horn which is activated whenever the temperature reaches about +5 deg C. Then, if and when it starts snowing, the forward walls of the horn are sufficiently warm to melt snow and any possible build-up of ice. The heaters are dimensioned to also heat the air inside the forward part of the horn so that any misting that takes place on the window evaporates.

Figure 10.2-2 Feed horn deicing blanket ready to be mounted in place around the horn aperture. (Photo used with permission of General Dynamics SATCOM Technologies, Inc.) Feed Window Material The noise temperature increase caused by water or moisture on certain antenna and microwave feed-system components, in particular the feed window, is often higher than the contribution of rain in the atmosphere. The increase continues to affect the system after the rain has stopped and it can take hours for the water to evaporate. The effect of moisture becomes greater with increase in frequency, thus it becomes interesting to deal with the problem at Ku-band, and a necessity at Ka-band.

There are several effective methods for minimizing the potential noise temperature increase caused by water or moisture forming on the feed horn window. They are:

Crowning or doming of the feed horn cover by internal pressurization

Use of feed horn covers that are made of Teflon®, which provides an inherent hydrophobic surface

Periodic application of a hydrophobic coating after a thorough cleaning

Guiding of pressurized hot air across the feed horn window surface

Often a combination of the above techniques is used to reduce the problem.



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Hydrophobic Coatings Even Teflon® type feed horn covers will attract moisture with age and weathering or in the presence of grime as in a polluted atmosphere. Hydrophobic coatings are known to reduce the adhesion of water on surfaces. There are several proprietary products on the market, but Rain-X, a commercially available product sold to improve visibility through wet automobile glass, has been proven effective for this application. Bird Protection Birds have demonstrated a remarkably destructive temperament for non-edible materials and equipment. The outer edge of feed horns presents a comfortable resting place or even a roost. Of course, the result is that either the claws of large birds penetrate the stretched window material, or the pecking activities of smaller birds shreds the window. Result - water and other material can enter the feed system. Water in any quantity inside the complex component structures will quickly change the RF function of these components, quite apart from any corrosive actions that may result. And simply opening the lowest terminals of the feed will not cause all the water to drain. The grooves of the corrugated horn behave in a similar fashion to that of a tire left out in the rain - once the water is inside, it is difficult to get out. The only way to remove the water is to either disassemble the feed and dry it out, or to attempt to move a large mass of hot air through the internal volume of the feed for some considerable time - for perhaps a day or more. Figure 10.2-3 shows several methods that have been used with varying degrees of success against birds. Since the window represents the weakest element in the antenna system, everything possible must be undertaken to be able to monitor the health of the feed. This is usually done by

monitoring the pressurization system and cycle-times monitoring rate of air flow in the pressure line connected to the feed regular examination of the window regular check on the heater system on the horn and its control regular check on the rain-blower system - heater and blower motor and its control

Feed system

Feed horn

Plastic needles

Feed horn

Razor blade ring about 1 to 1.5 inches high

(a) (b) Figure 10.2-3 Methods of protecting feed windows against birds. (a) provide an alternate roost; (b) provide a roost so uncomfortable to prevent roosting altogether. In the event the feed window is broken, a method of preventing water from penetrating into the feed system network is to incorporate a second window a little behind the outer skin. The second window is punctured with a small slit in the material to let the dehydrated air inside the feed network reach the outer window. The idea here is for rain entering through the broken outer window to not immediately reach the critical part of the feed network. When the low pressure alarm is triggered, there will be some finite time available for the operator to reach the feed window and make repairs before the feed fills with water.



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10.3 Radomes The idea of radomes has a number of redeeming features.

hides the antenna from prying eyes. Preventing observations of antenna type/size and look angle may be part of the mission.

offers a measure of protection from terroristic intentions/activity by obscuring the critical parts of the antenna against destruction.

allows the antenna to be protected from severe weather. offers a measure of comfort for any maintenance activities

And perhaps most importantly,

provides conditions for stable performance; there will be distortions in the reflector system due to wind loads and temperature gradients

Definitions: “Transmission loss” refers to the loss in gain associated with an elevated sidelobe pattern of the antenna under the radome, plus attenuation through the radome material, compared to the gain of the antenna with no radome. The scattered sidelobe energy, as well as reflections intercepted by the ground, contributes to an “effective antenna temperature” which will always be higher than that associated with an antenna with no radome. The drawbacks of radomes are:

Transmission loss and reflections cause degraded gain and increased noise temperature, resulting in lower G/T. When the radome structure and skin move under a variable wind load, the phase of reflected waves can change to shift the monopulse tracking null.

Additional equipment is necessary to sustain the radome-pressurization, dehydration and heating, regardless of whether it is a balloon or space frame radome.

Effects of ice and snow, and to a smaller extent rain, can have a severe effect on operations. Ground based radomes may be between 6 feet (1.8m) and 200 feet (61m) in diameter. They are typically capable of withstanding all environmental conditions such as 150 mph winds, solar loading and ice and snow conditions, and are designed to last 20 years. The initial cost of a radome is primarily dependent on the size of the structure and increases proportionally to the surface area of the radome. Types of radomes There are four major types of ground based radomes: Sandwich Space Frame Solid Laminate Air Supported The sandwich and solid laminate type of radomes are sometimes referred to as dielectric radomes, but space frame radomes can also be considered dielectric if fiberglass frames are used. Radome transmission loss and antenna pattern degradation is a major consideration when considering the use of radomes. Manufacturers of radomes rely heavily on the results of computational modelling to establish the effects of radomes on antenna performance. There is not much in the form of actual comparative measurement - with and without radome. However, one event has been recorded that is representative of the behaviour of a sandwich design radome. Figure 10.3-3 shows the actual pattern measurement of an 11m antenna operating 14 GHz inside a sandwich-style radome.



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Figure 10.3-1 shows the radome cover; Figure 10.3-2 the antenna inside the radome; Figure 10.3-3 shows the antenna pattern taken in the presence of the radome.

Figure 10.3-1 "Igloo" layout of sandwich panels. Compare this with the "radome" pentagon design of Figure 10.3-5. This radome was tested with both "thick" as well as "thin" panels, held in place with 5/16 hardware all along the edges. The RF performance of this radome gave the unexpected high sidelobe envelope at Ku band of 10db above the ITU-580 specification of 29-25log(t) dbi.

Figure 10.3-2 11.1m Ku antenna inside the radome. The regular panel layout is clearly visible in these photographs.



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(a) No radome Ku Tx Az pattern (b) Thick panels Ku Tx az pattern

(c) Thin panels Ku Tx Az pattern Figure 10.3-3 shows the antenna pattern associated with this antenna under the conditions of two values of radome skin thicknesses The influence of the radome in this case is most significant, in that the sidelobe envelope has been lifted by 10db + when compared with the pattern on the same antenna with no radome. The sidelobe performance will prompt this antenna system to be rejected by all regulatory agencies. Additionally, since the scattering from the radome can be considered to be practically isotropic in form, the noise temperature of the system will increase significantly. Although not measured in this case, the sidelobe integration of a simulated case antenna shows that the gain is lowered by approximately 2db, and the noise temperature is raised by some 20Kelvin. The following sections discuss the basic structural design of the four different models of radomes and their relative merits in terms of performance and installation. However it is important to understand that radomes are not completely transparent at microwave frequencies, and therefore have an adverse effect on performance. To make a radome more transparent will mean removing structural elements required to hold it up, and so compromise must be accepted.



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(a) Ku Tx Az at 10deg elevation (b) Ku Tx Az 20deg elevation

(c) Ku Tx Az 30deg elevation (d) Ku Tx Az 40deg elevation Figure 10.3-4 Tx patterns taken on satellites at four different elevation look angles. It may be noticed that the sidelobe envelope, although always about 10db above the ITU level, changes with azimuth and elevation angle to the target satellite. The view through the radome wall is not the same for all viewing angles. This is caused principally by the panel connection geometry and the hardware. Information from various vendors of radome systems all suggest that (a) radomes containing hardware in the aperture, regardless of general design, will cause sidelobe envelope difficulties. (b) radomes which are air-supported and carry no hardware in the region of the aperture will generate the smallest influence in the RF performance, in particular the antenna pattern sidelobe structure.



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10.3.1 Sandwich Radomes Construction Sandwich radomes are rigid, self-supporting structures constructed of a series of panels. Each panel is a molded, one piece unit without bond or seam lines. When assembled with the other panels, the panel array forms a truncated spherical surface. Individual panels may be doubly curved or flat, yielding a faceted or spherically smooth appearance. The domes typically consist of a skin-core-skin sandwich construction. The most common skin and core materials are pre-preg fiberglass and closed cell, polyisocyanurate foam core.

Figure 10.3-5 Sandwich radomes

Individual panels typically are fitted with molded flanges accessible on the inside, thus allowing bolting and even panel removal from the inside. The flanges are electromagnetically tuned to closely match the performance of the antenna system.

Geometry The panel sizes are limited by the criteria for packing, shipping and ease of installation. The individual panels are randomly oriented throughout the radome to reduce boresight error and unwanted sidelobe perturbations (important for radar applications). Electromagnetic Performance The electromagnetic performance of a sandwich radome is made up of two parts: loss or scattering attributable to the panel frames, and loss or scattering attributable to the central part of the panel window area. While loss through the central part of the panel can be made quite low by proper material selection and manufacturing techniques, the loss due to the panel frames can be nine times that of the central part of the panel. For this reason it is necessary to tune the frames or impedance match them to the window area.



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10.3.2 Space Frame Radomes Construction Space frame radomes are rigid and self-supporting and are composed of triangular panels assembled into a geodesic dome. In general, a quasi-random geometry is used to optimize electromagnetic performance. They are typically constructed using aluminum for the panel frames, but steel frames are also used for certain applications. Dielectric space frame radomes are constructed using fiberglass frames.

Figure 10.3-6 Space frame radome A thin electromagnetically transmissive membrane material is attached to the frame to create a finished panel. Membrane materials can be optimized for enhanced performance at specific frequencies. Electromagnetic performance The electromagnetic performance of a space frame radome is made up of two parts: loss or scattering attributable to the panel frames, and loss or scattering attributable to the membrane material. These two components add up to an overall transmission loss. Space frame radomes are usable over relatively broad bandwidths. The characteristic framing represents a small blockage for the antenna aperture. Figure 10.3.7 shows a cutaway view of an antenna in a space frame radome, as well as the view of the radome seen by the aperture of the antenna. The radome support structure represents a quasi-random array of conductive elements, all located in the near field of the antenna, and as a consequence each illuminated by the aperture field of the antenna. The array will have its own characteristic pattern. The antenna has its characteristic pattern. The two patterns will add into a far field pattern, characterized by higher sidelobes, and as a consequence possess lower gain. This loss in gain may represent about 98% of the transmission loss. The remaining 2% can be accorded to reflections from the frame, and the absorptive and reflective loss of the membrane or skin stretched over the triangular frames. The principal contributors to transmission loss are the mounting nodes and the associated hardware for the radome panels.



383

Radome foundation wall

Ante

nna

pede

stal

Rad

ome

axis

Elevation axisElevation jack screw

Illum

inat

ed s

egm

ent o

f rad

ome

Illuminated segment of radome.Note:This array of elements represents a new antenna, which has its own characteristic pattern. The superposition of antenna pattern and radome pattern results in the antenna+radome pattern.

Radome frame elements Frame node points

Center line of antenna is placed on the center line of the radome

Feed

Figure 10.3.7 Cutaway view of the antenna inside a space frame radome, and the view which the antenna aperture sees for the antenna at 0o elevation angle. It can be further visualized that for other azimuth and elevation positions, the view by the antenna aperture will be different, because of the random arrangement of radome elements. Therefore, one will expect to see variations in the antenna pattern of the antenna+radome system, as well as gain variations. Why the randomness of the array elements ?? If a symmetrical layout of elements is chosen, then the contributions from each symmetrical element pair will tend to add, increasing the gain of the radome pattern. The general idea is to minimize the radome gain. Why the need to set up the antenna on the coordinate system of the radome ?? If the aperture plane is not parallel to the local plane of interception through the radome, then a beam tilt will occur. For most applications, a small misplacement of the antenna axis from the radome axis can be tolerated - small meaning < 2% of the radome diameter. . Predicted performance features of a metal space frame radome are listed in Table 10.3.1.



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Table 10.3.1 Predicted space frame radome performance features Radome Noise temperature and Insertion Loss Data for a Dry Radome

Frequency (GHz)antenna 4 7.75 11.2elevation transmission noise temp transmission noise temp transmission noise temp

angle loss (db) K loss (db) K loss (db) K0 0.63 11.2 0.67 12.9 0.71 14.35 0.63 10.9 0.67 12.2 0.71 13.8

30 0.63 9.2 0.67 10.1 0.71 10.860 0.63 5.8 0.67 6.7 0.71 7.490 0.63 4.1 0.67 5 0.71 5.7

Radome Noise Temperature and Insertion Loss Data for a Wet radomeRain Rate (mm/Hr)

Frequency 11 18 28GHz Transmission Noise temp Transmission Noise temp Transmission Noise temp

Loss (db) K Loss (db) K Loss (db) K4 1.87 60.21 2.04 65.16 2.23 69.85

7.75 3.93 114.9 4.38 117.06 4.76 121.5211.2 5.39 141.57 5.84 145.52 6.27 148.61

Recent measurements on an 18m antenna, both without and with a space frame radome, gives clear indication of smooth gain response without radome Figure 10.3-8(a), and rippled gain while pointing through different segments of the radome Figure 10.3-8(b). Both measurements were conducted on a moving radio star, allowing the gain to be measured through a sequence of azimuth and elevation positions for the antenna.

Antenna Gain vs ElevationMeasured on Tau-A; Tlna = 40K

Date: 15 July 2008Weather: Clear, scattered cloud; temp = 20C, humidity 65%

59.0

59.2

59.4

59.6

59.8

60.0

60.2

5 10 15 20 25 30 35 40

Elevation - deg

Ant

enna

Gai

n - d

bi

Frequency = 7550 MHzLinear (Frequency = 7550 MHz)

Figure 10.3-8(a) Gain measurements on an 18m antenna with no radome. Notice the smooth response versus elevation angle. Notice also the small increase in gain with increasing elevation angle, generally a sign of a stiff antenna whose reflector does not change its shape as it sweeps through a large elevation angle range.



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Antenna with Radome - Gain vs ElevationMeasured on Tau-A; Tlna = 40K

Date: 24 May 2009Weather: Clear, calm; temp = 17C; humidity = 45%

59

59.2

59.4

59.6

59.8

60

60.2

5 10 15 20 25 30 35 40 45 50

Elevation - deg

Ant

enna

Gai

n - d

biFrequency = 7550Linear (Frequency = 7550)

Figure 10.3-8(b) After emplacement of a 28m radome over the 18m antenna, the gain was again measured using the same radio star with identical test equipment and operators. Notice the loss in gain by approximately 0.8db and additional +/- 0.20db ripple. But notice also the general downward slope in the gain response with increasing elevation angle, suggesting an overall gain degradation of 1.0db. Design aspects of metal space frame radomes 1. Structural dimensions are determined on a test range by statistical observation of peak gain variations as seen as the radome is moved around the fixed antenna. Best gain with smallest variations will determine the frame geometry. 2. Consider a radome of fixed size. As the panels decrease in size, the performance improves - meaning gain increases, but the gain disturbances increase. As the frequency reaches the optical range, the beam will be disturbed by the shadows of the frame elements. As the frequency is decreased, the frame array will appear as a cage with holes approaching cutoff for the wave. 3. The principal trick is to generate a random arrangement of frame elements in front of the aperture. The frame must possess structural strength for given wind conditions. The larger the frame size, the fewer the members, the lower the cost, the greater the wind load. The smaller the frame size, the larger the number of members, the greater the cost, and possible limit for low frequency operations. 4. The frame members for the MSF consist of aluminum elements approximately 6 x 0.5 inches. The 0.5 inch side is directed toward the enclosed antenna. In order to not let the enclosed antenna "see" the broad dimension of the frame element, the antenna is placed at the center of the radome. A small misplacement of the antenna is permissible, the size of which decreases as the radome becomes smaller. For large antenna/radome (>12 to 18m / 50 to 75 feet) combinations, 1 or 2 feet is permissible. The size of the frame members will permit the operation at frequencies > 30 GHz. There is no impact on cross-pol. There can be an impact on pointing when target tracking is based on monopulse functions. The difference pattern being asymmetrical can find a situation in which one half of the pattern "sees" a frame geometry which is different from that which the other half "sees". This will cause a small beam shift as well as possible null filling. 5. The MSF configuration only has a lower frequency limit. There is no real upper limit except as the skin starts to offer increasing resistive loss. The MSF offers a uniformly random distribution of small blocking elements in the aperture of the antenna.



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Results of measurements on antennas under metal and dielectric space frame radomes Expected gain response: (a) a variation of +/- 0.1db. Measurements showed +/- 0.25 to 0.3db. (b) gain loss ("transmission loss") = 0.69 to 0.73db. Measured values range from 0.7 to 1.3db. (c) G/T degradation is 0.9 to 1.1db Measured values 0.6 to 1.9db (d) Sidelobe envelope is governed by the radome acting as a complex array, which will never reach the ITU 580 envelope, being about 5 to 7db above the prescribed envelope. The antenna+radome pattern will therefore never reach the ITU 580 pattern. If the antenna pattern sidelobe is reduced to be about 6db below the SLE, then its contribution to the overall SLE will be minimal. (e) There appear to be no significant performance differences between metal space frame and dielectric space frame radomes. However, metal space frame radomes offer wideband performance. But because of resonance effects induced by the dielectric frame members, particularly at higher frequencies, some segments of the spectrum will display unacceptable high losses. For this reason, dielectric radome frame members are “tuned” for best performance in required frequency bands; “tuning” referring to specific dimensional design of the frame members. Passive intermodulation issues in metal Space frame radomes Following up on the previous discussion on PIMs in Section 5.4, one needs to be aware that space frame radomes can also be a contributor to PIM problems. For large radomes, issues that typically affect PIM generation with respect to transmit power density levels used and receive signal levels of concern, are as follows:

Metal to metal contact between radome components. This can generate PIM problems as a result of a poor contact between the metal components, contributing to the phenomenon of microarcing. In order to reliably prevent this type of PIM generation from a metal space frame radome, the metal components must be insulated from each other.

Improper installation of metal space frame radomes. Proper procedures must be followed during installation of a PIM-reduced radome to ensure that all insulated components are in place. If isolation bushings are not installed or if the strips that are used to isolate back-to-back beams are dislodged, problems with PIM generation may occur.

PIMs are assessed based on the test results taken on a sample node structure. PIM contribution from nodes are assessed statistically and totalled, depending on the number of nodes exposed to illumination from the antenna aperture. PIM level of -140dbm predicted for the radome. Short comparison of metal space frame and air-inflated radomes In contrast, the Air Inflatable radome has a uniform distribution of non-random seams between panels which converge with increasing elevation angle as seen from the enclosed antenna. Additionally, the panel thickness for the AI is significantly greater than for the MSF. So with increasing frequency, AI radomes will present increasing difficulties. Redeeming feature - can meet standard sidelobe envelope specifications, and little to no problem for low PIM applications. Dielectric Space Frame and Sandwich type radomes have significant frequency band limitations. DSF, same as MSF in construction, have glass frame elements that possess reflections from both front and back surfaces of the members, which can mix constructively and destructively, causing possible large variations in gain, depending on frequency. Similarly for the panel joints. Tuning elements can be installed into the joints to match these reflection mechanisms, but will be frequency sensitive. Sandwich radomes ("A" type = two skins enclosing a dielectric foam; "C" type = three skins with dielectric foam between them) can be designed for optimum frequency behaviour, but will require tuned panel joints.



387

10.3.3 Solid Laminate Radomes Construction Solid laminate radomes are rigid, self-supporting shell type structures which use doubly curved panels to form a truncated spherical dome. The panels are typically constructed of pre-preg fiberglass. Panels are generally arranged in an orange peel pattern or regular geometry to minimize costs.

Figure 10.3-9 Solid laminate radome

Solid laminate radomes use vertical and horizontal rows of panels making them extremely easy to assemble. This technique, along with the utilization of a minimum number of panels, makes this type of radome cost-effective for smaller radomes. Electromagnetic performance These radomes provide reasonable electromagnetic performance at frequencies below 3 GHz, thus they are an effective choice for satellite communications and weather radar antennas operating below 3 GHz.

Figure 10.3-10 Solid laminate radome on a shipboard installation



388

10.3.4 Air Supported Radomes Construction An air supported radome consists of a thin fabric envelope, with reliable power supply and air pressurization systems essential to its operation. The air supported radome is an active system. It must be inflated at all times. Its reliable operation depends on non-interruptible power supplies and redundant blower systems.

Figure 10.3-11 Air supported radome The air supported radome envelope is constructed of shaped fabric sections which are fused together during the manufacturing process. In general, the seams are run in a vertical direction. The radome envelope can be constructed from a variety of fabrics; Teflon fiberglass is the most commonly used, but Hypalon®/Dacron® and vinyl have also been used.

Figure 10.3-12 Inside view of zenith: air supported radome Electromagnetic performance These radomes provide good broadband performance, particularly below 10 GHz, and they are virtually PIM free.



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10.3.5 Selection Criteria

The principal purpose of a radome is to shield the antenna from the environment. This improves system availability since the antenna is not affected by winds, rain or ice. It can also improve performance since high winds can distort the shape and pointing direction of the reflector. Radomes can also provide a benign environment for any electronics and personnel that must be in the vicinity of the antenna.

Radomes have proven to be very effective when considering life cycle costs. Since the antenna is in a protected environment, maintenance costs are held to a minimum. The structural requirements of the antenna are less stringent, resulting in reduced fabrication and installation costs and the use of smaller positioning motor assemblies.

The final advantages of a radome are that the dome structure is aesthetically pleasing (colored radomes are available to blend with the environment) and radomes are very effective in concealing the type of equipment inside the dome.

The following environmental factors must be considered when specifying a radome:

Snow and wind loads: The severity of the snow and wind loads will be drivers in selecting the size and structure of a radome. They will also determine the need for and size of a pressurization system within the radome.

Solar radiation: In hot, dry conditions found in the northern deserts of Africa and Asia, the intensity of solar radiation can reach 1120 watts/meter squared. This can produce thermal differences that have a profound effect on the antenna performance. While radomes block this solar radiation by varying amounts, it is critical to circulate the air within the radome. The hard ultraviolet component of solar radiation is also responsible for deteriorating typical radome surfaces and is a major factor in the degradation of hydrophobic coatings.

Base or foundation construction: The determination of the type of base required can be influenced by antenna siting requirements, type of antenna, need for access to the radome area and interest in using the base of the radome for auxiliary support equipment such as air handlers, storage, etc.

Radome access: One must consider what type of access is likely to be needed within the radome. Personnel doors allow limited access and airlocks are awkward for maneuvering large items. A raised foundation readily allows garage door size access.

Air circulation: Air handlers are required to pressurize the air supported radomes. However, some sort of light internal pressurization scheme is useful to reduce flutter on certain space frame radomes as well. Additionally, air tends to stratify in larger radomes, with the temperature rising as one gets higher in the radome. This temperature gradient can distort the antenna shape, thus making it important to consider air handlers to circulate the air within the radome.

Area heating: If the interior area of the radome is used to house delicate equipment or there is a need for personnel to work in comfort, then one should consider adding heating elements to the air handlers. Heating the ambient inside air also works well at keeping ice and snow from forming on the radome.

The ideal radome would appear totally transparent to any electromagnetic signal. Since this is not possible, radomes must be designed to minimize the impact of the radome on the enclosed antenna. Application requirements determine the importance of signal distortions such as insertion loss, boresight error and scattering into the antenna sidelobes. The following electromagnetic performance concerns will also influence radome selection:



390

Electromagnetic Performance Radome transmission losses: Radome transmission loss is the sum of the ordinary insertion loss

of the antenna signal passing through the radome panel plus the scattering loss off the radome panel framework blocking (shadowing) the antenna aperture. While radome insertion loss is typically less than 0.1 dB, surprisingly, the scattering loss off the framework of a rigid radome is typically 4 to 100 times larger than the panel insertion loss. Therefore, one must take into account the radome panel framework scattering loss in order to understand radome performance for protected antennas.

Antenna pattern degradation: How the framework shadow members disturb the antenna pattern

is a complex function of panel shape (framework orientation), length and electromagnetic properties. Stringent sidelobe level envelope requirements apply in satcom applications that employ satellites in geosynchronous orbital slots. The paramount operational requirement is that the antenna neither illuminates other satellites, nor receives signals from such satellites. All regulatory agencies have mandated sidelobe envelope requirements that assure that such crosstalk is at an acceptable level.

Maintenance and Support

Periodic maintenance: All radomes will require some level of maintenance support over its lifespan. All radomes will require periodic inspections and, as a general rule, a close check on bolt torques should be made about six months after installation. Air inflated radomes do need regular evaluation and maintenance of the air handling systems. Rigid radomes may require some joint recaulking and even recoating of the outside surface during its lifespan. Depending on the resilience of the outer surfaces, some form of hydrophobic coating may also need to be applied. As a general rule, the cost to maintain the radome over its life span should be less than that for maintaining the exposed antenna over the same period.

Life span: In the distant past, air supported radomes were considered to have a much shorter life expectancy than rigid radomes, but advances in fabrics have brought the two in line. One can easily expect a radome to have a life of about 15 to 20 years without much maintenance, and there are certainly radomes in use that have far exceeded this expectancy. Life is dependent on the environment the radome is exposed to and the amount of routine maintenance it has seen.

10.3.6 Brief Summary of Radome Features Reasons for use

protection against effects of adverse weather provide cover against prying eyes

In adverse weather, without radome protection: In high wind areas

o more expensive "hi-wind" antenna structures required o the antenna drive system is operationally more active, contributing to performance/link

degradations o more maintenance on the drive system

In coastal areas:

o antenna subject to the combined effects of variable water, salt and sun, leading to severe corrosion

o subjecting the antenna to limited lifetime o demanding greater maintenance effort and costs

In more benign weather/wind conditions:

o radome not really necessary, unless to protect against unwanted observers



391

Impact on antenna performance by the radome - Gain, G/T, sidelobe envelope The following predictive information has been provided by the named manufacturers.

Air inflated (balloon) type - manufacturer St Gobain (a) 100 mph < wind conditions < 200 mph [Glass/Teflon 0.050 inch membrane with Teflon gel coating] (b) wind conditions > 200 mph [Kevlar membrane with Teflon protective coating] a. Predicted Gain and G/T X-band Approximate gain loss = 0.15db Estimated degradation in G/T = 0.25db Ka-band Approximate gain loss = 1.1db in gain Estimated degradation in G/T = 1.3db b. Predicted Gain and G/T X-band Approximate gain loss = 0.3db Estimated degradation in G/T = 0.5db Ka-band Approximate gain loss = 0.8db Estimated degradation in G/T = 1.0db [Note: Kevlar offers greater strength and lower loss, at greater cost] Note: Sidelobe envelope performance will be degraded with respect to a no-radome condition, but not sufficient predictive or measured information of details is available at this time.

Space-frame type - manufacturer L3-Essco

(1) 100 mph < wind conditions <200 mph [2-ply membrane each 0.025 inch thick] (2) wind conditions >200 mph [3-ply membrane] a. Predicted Gain and G/T X-band Approximate gain loss = 0.5db Estimated degradation in G/T = 0.6db Ka-band Approximate gain loss = 1.5db Estimated degradation in G/T = 1.7db b. Predicted Gain and G/T X-band Approximate gain loss = 0.6db Estimated degradation in G/T = 0.75db Ka-band Approximate gain loss = 1.8db Estimated degradation in G/T = 2.1db Note: Measured performance suggests significantly higher losses can be expected, depending on radome design and configuration. See summary of results of measurements performed on 68ft space frame radomes at X-band on page 386. Comparative radome attributes Air inflatable:

Design parameters - Diameter and wind speed Offers smallest degradation in performance over wide bandwidth - no structural obstructions

- X and Ka bands easily accommodated with no extra design effort Water on the radome - in the form of rain, fog or misting effects, will reduce antenna performance. Does not contribute to PIM conditions Requires double doorway entry construction



392

Requires reliable power source to maintain inflation of the radome Additional blowers required to circulate air inside radome, to prevent humidity and air stratification

(hot in the upper part of the antenna, cold at the ground level) Small damage to radome skin easily repaired Large damage to radome may be catastrophic to antenna Requires large crane, large number of hands to install Lifetime of radome claimed to be >20 years

Space frame:

Design parameters - Diameter, wind speed, and space frame geometry Performance will be degraded slightly - Due to the presence of the space frame (whether metal or dielectric), Water on the radome - in the form of rain, fog or misting effects, will reduce antenna performance May contribute to PIM issues, since frame elements are held in place with hardware. Special

plastic hardware can be applied to reduce PIM effects, with some installation/lifetime reliability issues

Inflation of radome required to provide small over-pressure inside radome to prevent skins from buffeting from wind action

Additional blowers required to circulate air inside radome, to prevent humidity and air stratification (hot in the antenna, cold at the ground level)

Small damage to radome skin easily repaired Large damage to radome not catastrophic to antenna Lifetime of radome claimed to be >20 years

Self supporting dielectric (sandwich structure elements):

Design parameters - Diameter, wind speed, operational signal frequency, sandwich geometry Assembly consists of building-block elements which must be held together with hardware - narrow

frequency band performance. System may be designed and tuned to accommodate X and Ka frequencies simultaneously, but proof of design still to be demonstrated

Water on the radome - in the form of rain, fog or misting effects, will reduce antenna performance May contribute to PIM issues, since frame elements are held in place with hardware. Special

plastic hardware can be applied to reduce PIM effects, with some installation/lifetime reliability issues

Inflation of radome not required Blowers required to circulate air inside radome, to prevent humidity and air stratification (hot in the

antenna, cold at the ground level) Small damage to radome skin easily repaired Large damage to radome not catastrophic to antenna Lifetime of radome claimed to be >20 years

References: [1] Doucette, C., “Introduction to Satellite Earth Station Antenna Systems – Module 9” An informal course prepared for the US Army at General Dynamics-Satcom Technologies, March 2005. [2] Kay, A. F., "Electrical Design of Metal Space Frame Radomes", IEEE AP-Trans, March 1965, pp 188-202. [3] Rudge, A.W., Milne, K., Olver, A.D., Knight, R., "The Handbook of Antenna Design", vol1 and vol 2. Peter Peregrinnus - IEE, 1986

Chapter 11 – Site Considerations


393

Chapter 11 Site Considerations 11.1 Radiation Hazard 11.2 Earth Station Site Planning 11.2.1 Obstructions and Safety 11.3 Antenna Site Interference Issues 11.1 Radiation Hazard Every antenna has a radiation pattern. The pattern in the far field is that which is normally measured and used to characterize the antenna quality. The far-field (Fraunhofer zone) is recognized as occuring at a distance of

22DR fieldfar . (11.1.1)

where D diameter of the antenna aperture, and wavelength of the signal. In the near field (Fresnel zone), at distances from within a meter or so of the aperture out to about

222.0

DR fieldnear , (11.1.2)

the radiation is to be seen as a cylindrical beam with diameter equal to that of the antenna aperture. As the distance from the antenna increases toward the far-field, the beam will begin to narrow down with an effective beamwidth, initially very wide, but quickly becoming smaller, until at the far field distance, the beam will be characterizable with the expected 3db beamwidth. Pictorially, this may be seen as in Figure 11.1-1.

Pattern shape changes with distance in front of reflector

0 0.1 far field 0.5 far field0.25 far field Far field

3db beamwidth θ

3db beamwidth θ

3db beamwidth θ

3db beamwidth θ

3db beamwidth θ

Fraunhofer zoneFresnel zone

Antennaaperture

5 degreesafety zone

Very small low level power beyond 5 deg boundary

Figure 11.1-1 Pattern changes with distance from antenna aperture The space around any antenna transmitting RF power is illuminated. Levels of RF power are extremely variable in the immediate vicinity of the aperture, and are to a large extent determined by the following factors: a. The transmit power levels b. The antenna size c. The look angle to the satellite d. The field distribution in the main aperture e. The nature of the antenna structural elements f. The nature of the surrounding terrain



394

The power density immediately in front of and along the axis of the radiating aperture can be determined with some degree of accuracy. The power density at the edge of and behind the main reflector can only be determined accurately by direct measurement. However, with the use of wide angle radiation patterns (showing relative levels behind and to the side of the antenna) and the following discussion, some reasonable bounds as to the expected power density levels around the antenna can be calculated. Two factors of interest: a. Maximum power density envelope b. Gain reduction, which is also approximately the beamwidth broadening factor For the present practical purposes, these factors are considered for the circular aperture with a tapered illumination. Relative to the power density that may be measured at the far-field distance R axially in front of the antenna, the on axis power density is given by

8cos1

128

8sin

1611.26

2

2

P (11.1.3)

where

/2 2D

R (11.1.4)

and represents the fraction of the Fraunhofer distance R . The black curve Figure 11.1-2(a) shows the behaviour of P as a function of R . It may be noted that the

peak power density occurs at about

22

1.0D

, nearly 42 times the value at /2 2D . The asymptotic

value at the aperture is 26.1. Coupled with this relationship is a beam-broadening factor given by

2

1

8cos1

128

8sin

16116

2

2

(11.1.5)

shown graphically with the red curve in Figure 11.1-2(b) Here the asymptotic value is

R

Da

22

16 (11.1.6)

The asymptotic value of is useful in determining a Fresnel-Fraunhofer transition point which is defined as

the value of R at which a goes to unity. Of particular interest for a tapered circular aperture, the Fresnel range is

8

2DR (11.1.7)

The power density on axis at distance

22DR for an input power oW Watts is found from

222 64

3

24

D

W

D

GWP oo

a

(11.1.8)



395

The power density at distance d along the antenna axis is given by PPP ad (11.1.9) The distance along the axis at which the maximum power density occurs is given by

2

max 190.0D

d (11.1.10)

The secondary power density pattern approximation for the distance r offset from the antenna axis at axial distance d is

d

rDPP ddr arctan692.0cos2

, (11.1.11)

Typically, without any extensive calculations, within the immediate vicinity of the aperture, the radiation hazard zone occurs approximately within the cone of the aperture generated by 10 times the half-power beamwidth measured in the far field, and the edge of the main reflector, extending out to about

/22.0 2D . Note: this assumes non-saturating operational power levels. Also see [1], [2]. As an example: An 11m antenna operating at 6 GHz pointing along the ground at 0o elevation. If the total uplink power radiated is 1000 Watts: a. The distance along the axis at which maximum power density occurs = metersd 460max

The power density on-axis at /2 2D meters in front of the antenna = 2/12.0 cmmWPa

The power density at maxd along the antenna axis = 2max /0.5)( cmmWdP

At a distance metersd 10 , the power density = 2/2.3 cmmWPd b. At a distance metersr 5 off-axis, 2

, /7.1 cmmWP dr

The far-field half-power beamwidth for the 11m antenna at 6 GHz = reesdegdb 3.03

At 10 meters in front of the antenna, the effective half-power beamwidth is 6.283.0 degrees The beam-broadening factor 3.95 The off-axis distance at 10 meters in front of the aperture and reesdeg3.142/ is metersr 55.2 .

The power density at this point is 2/67.2 cmmWPr . c. At distance maxd , the radius at which 2/1 cmmW power density is encountered is given by

dP

P

Ddr arccos

692.0tanmax

(11.1.12)

where P is set equal to 2/1 cmmW . Now 2/5.5 cmmWr This means that at 10 meters axial distance from the aperture at 5.5 meters off-axis, a power density of

2/1 cmmW is encountered. With the antenna pointed toward the orbital arc, the power levels at the ground will decrease rapidly. A graphical view of this example is shown in Figure 11.1-2(c)



396

Power Density vs Distance in front of Aperture

0.0

0.5

1.0

1.5

2.0

2.5

3.0

3.5

4.0

4.5

5.0

5.5

6.0

0 100 200 300 400 500 600 700 800 900 1000


Pow

er D

ensi

ty -

mW

/cm

^2

1

2

3

4

5

6

7

8

9

100.

000

0.01

0

0.02

0

0.03

0

0.04

0

0.05

0

0.06

0

0.07

0

0.08

0

0.09

0

0.10

0

0.11

0

0.12

0

0.13

0

0.14

0

0.15

0

0.16

0

0.17

0

0.18

0

0.19

0

0.20

0

0.21

0

Fraction of Far-Field Distance

Nea

r Fie

ld 3

db B

eam

wid

th -

deg

rees

D = 11.1 meters

f = 6 GHz

Pi = 1000 Watts

Far field distance = 4928 meters

Power Density

Point of Interest in front of Aperture

Beam broadening factor

(a)

Power Density on Axis in front of Aperture

0.00

0.50

1.00

1.50

2.00

2.50

3.00

3.50

4.00

4.50

5.00

0

2000

4000

6000

8000

1000

0


Flux

Den

sity

- m

W/c

m^2

Flux Variation from Center of Aperture

to the Reflector Edge

0.0

0.5

1.0

1.5

2.0

2.5

3.0

3.5

4.0

4.5

5.0

0 5 10

Distance Off-Axis - meters

Flux

Den

sity

- m

W/c

m^2

(b) (c) Figure 11.1-2 Characteristics of the main beam calculated for an 11m Cassegrain antenna radiating 1000 Watts power at 6 GHz. (a) represents the sideview along the antenna axis in the Fresnel zone. (a) also shows that the effective beamwidth of the main beam rapidly reduces to that in the far field within 1000 meters, or about 0.2 times far field distance. The radiated flux density very close to the antenna fluctuates markedly. (b) the distance in front of the aperture to the "far field" in this case equals nearly 5000 meters. (c) represents the sectional view of the flux density across the main beam, showing the nearly cylindrical nature of the near-field beam.



397

This information is typically provided to satisfy compliance with radiation hazard safety regulations, particularly for station staff who may be working in the vicinity of an operating antenna system. A somewhat arbitrary safety zone represented by a 5 degree cone around the aperture is usually considered for protection of people, as shown in Figure 11.1-3

Earth station antenna

Pedestal

Reflector assembly

Basic cylinder of radiation associated with the main beam

5o cone around the "main beam"

Nominal clearance around the aperture of the antenna.It is in this 5o cone that the high flux density will rapidly decrease toto levels that will not cause serious interference. Obstacles, suchas buildings, towers or other antennas should be kept out of this zone in the vicinity of the antenna.

Figure 11.1-3 Persons working around an operational antenna should ensure that they are out of any high flux density regions as calculated in the routine shown in Figure 11.1-2 11.2 Earth Station Site Planning When planning an earth station site, there will be several issues that need to be examined.

1. Permission/license by local/state/federal authorities 2. Authorization to access satellite(s) from system owner(s) 3. Clearance from interference by spectrum survey around the site

11.2.1 Obstructions and Safety Satellite Link Obscuration Sources Site selection issues are in principle mission dependent. For an operator with a single antenna, a site survey identifies a clear view toward the target satellite from a place which is not subject to the influences of other ground based (terrestrial) communications links that may be operating in or near the same frequency band(s). Since satellite systems and operational requirements may (quickly) change with time, such a site should have a clear view of the orbital arc. For an established site, with one or more antennas operating in the different bands or even the same band on different satellites, such as a teleport, the problems of situating a new antenna for a new satellite link becomes more difficult. The new antenna must be located so that it does not cause interference or be interfered with by other existing antennas and/or the necessary buildings on the site. In city centers, the local horizon may present partial obstruction of the orbital arc. Under these circumstances, an additional issue becomes critical - radiation hazard in the path of the off-axis transmit power, as it applies to personnel who work on the site.



398

Given the right to proceed with site planning for multiple antennas, it will be necessary to understand which viewable satellites are to be accessed, how to place the antennas in relation to each other, and will there be other objects in or near the line-of-sight. As an initial guide, antennas on a north-south line offer the least obstruction problems for the case of maximum flexibility in changing from one satellite to another anywhere in the viewable orbital arc. An east-west orientation inevitably has satellite viewing limits when the antennas are closely spaced. See Figure 11.2-1(a) and (b). In the event that the antennas involved are sensitive to passive intermodulation products (as discussed in Chapter 5), then special attention will need to be given that adequate clearance between antennas is provided.

5o

5o

Figure 11.2-1(a) Side view North-South of antennas, one in front of the other, so that they do not interfere with each other

Figure 11.2-1(b) Plan view East-West of antennas, so that they do not interfere with each other The impact of this situation is that on-site testing of patterns and G/T becomes particularly difficult, if not impossible. Figure 11.2-2(a) shows a site with multiple antennas with sufficient room between each antenna. Other sites exist in which antennas cannot move except to measure the main beam and a couple of sidelobes. See Figure 11.2-2(b) showing some of the difficulties discussed here.



399

Figure 11.2-2 (a) Site with several widely spaced large antennas (b) Site with several closely spaced small antennas Within the boundaries of the near-field radiation pattern described in Section 11.1, with the antenna transmitting toward a target satellite, the line-of-site must remain clear of obstacles, such as

other antennas on the site buildings that may be occupied by people local horizon blockage issues as presented by mountains, civil structures, trees.

Planning for an appropriate layout of antennas on the site will take these factors into account. Some arithmetic is available to aid in deciding an optimal configuration of antennas so that they do not interfere with each other, or with other structures. In general terms, an earth station antenna has a far field main beam and sidelobe envelope as we have seen in Figure 9.44. In the near field main beam, represented by the distance nearfieldR

2

5

1 DR fieldnear

the shape of the pattern changes considerably. The power flux density (power/unit area) fluctuates significantly, and the beam dimensions increase markedly as one approaches the antenna aperture from the front. Figure 11.1-3 suggests that a 5o cone around the cylinder containing the antenna aperture needs to be clear for an operationally satisfactory satellite link. Therefore, if the new antenna is to fit into a line of existing antennas, then neighboring antennas need to afford this 5o cone on either side - see Figure 11.2-1(b). If the new antenna must sit behind one or more existing antennas, then this 5o cone must clear the existing antennas in elevation angle - see Figure 11.2-1(a). This may even mean the new antenna must be elevated to higher ground, or be fitted with an extra-high pedestal. When there is a radiation hazard issue for the man who has to cut the grass in front of the antenna with a low look angle, then Figure 11.2-3 displays the scene.



400

5o

Figure 11.2-3 Potential for radiation hazard for maintenance staff For the protection of people in the vicinity of the antenna, the station owner will be obliged to submit some sort of report indicating that the antenna is operating safely. A sample report might look something like that shown in Figure 11.2-4 and Figure 11.2-5.

Dimensional Analysis - 11.1m Antenna at 6 GHz Page 1View of Clearance between edge of reflector and groundReference:

12-Oct-09

h

H1

re

g

D

p

q

theta

phi

Elev

axi

s

Azim

axi

s

MSL = (Mean Sea Level)

Foundation Level

H2

MSL = (Mean Sea Level)

Reflector Axis

Ped

esta

l hei

ght

d

f

s

P

L3

L1

L2

c2

b1

a2

E2 E3E1

m

na3

a1

b2

Local ground level

E

t

Q

c1

P = Safe distance in front of reflector aperture

L1 = Safe distance from bottom edge of reflector

RR = Far Field Distance

Figure 11.2-4(a) The dimensional configuration of the antenna and its immediate frontal area in which high density radiation may be expected.



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Far field distance R = 4928 meters Approximate near-field distance P = 967.69 metersPerson 2.0 meters high can approach edge of reflector to within clear in front of reflector

L1 = 966.95 meters E1 = 53.18 metersF/D = 0.315 L2 = 4916.35 meters E2 = 259.81 meters

L3 = 4931.40 meters E3 = 260.66 metersAntenna dimensions Antenna Configuration Critical points in front of the aperture

D = 11.1 meters aperture diamter = D = 437.01 inches E = 2.50 meters 98.59145h = 278 inches Reflector depth = d = 86.71 inches n = 967.69 meterse = 38 inches r = 254.87 inches Q = 4921.65 metersg = 24 inches c1 = 172.6557 metersf = 78 inches phi = 49.74 degrees c2 = 257.9325 meters

phi - theta = delta = 44.74 degrees b1 = 15.0479 meterstheta = 5 degrees b2 = 15.057107 meters

t = 2 degrees p = 179.41 inches a1 = 171.99868 metersq = 181.03 inches a2 = 0.5254855 meters

H1 = 355 meters Pedestal to reflector edge m = 219.03 inches a3 = 33.792447 metersH2 = 355 meters s = 208.2205 inches

H1 - H2 = 0 meters Figure 11.2-4(b) For the given antenna and transmitted power, calculation of the approach a person 2 meters in height may take to remain in the safe zone.

12-Oct-09 Analysis of Power Flux Density in Front of the Antenna Aperture

For a Specified Power Input11.10 m Antenna transmit frequency = 6 GHz

eirp = 84.7 dbWFar Field Distance = 4928 meters

Near Field Distance = 968 meters

freq Diameter Power Distance Power Distance PowerInput in front Density off-axis density

of aperture at "R" at r,ROn-axis

f D Pi R Pd rMHz meters Watts meters mW/cm^2 meters mW/cm^2

6000 11.1 1000 1 3.12 0 3.122 3.12 0.2 3.125 3.13 0.5 3.11

10 3.15 1 3.0720 3.08 1.5 2.9150 2.99 2 2.71100 2.97 2.5 2.54200 3.41 3 2.63500 4.92 3.5 2.891000 2.37 4 1.712000 0.69 5 0.604000 0.18 6 0.176000 0.08 7 0.088000 0.05 8 0.0410000 0.03 10 0.0315000 0.01 20 0.0125000 0.00 100 0.00

From "Dimensional Analysis": Condition at the "Safe Distance" 0 #DIV/0! 0 #DIV/0! from bottom edge of reflector = clear 0.00 0.50 0.05

11.1 m Antenna Radiation Hazard Analysis for Near Field Locations

The Table above considers a VertexRSI 11.10 m antenna. At points along the axis (R)in front of the the aperture, the expected peak flux density in the near field is

4.92 mW when 1000 Watts total power is transmitted.At points with coordinates (r,R) near the edge of the reflector, the power density will varyfrom about 3.1 mW/cm^2 to less than 0.1 mW/cm^2 as shown in the last column of the table. Flux values at other points can be ascertained from the graphical presentations given here.Note:As a rough safety guide-line for radiation exposure: See ANSI or IEEE C95.1-1991

5mW/cm^2 for 6 minutes, or 1mW/cm^2 for 30 minutes

Flux Variation from Center of Aperture

to the Reflector Edge

0.0

0.5

1.0

1.5

2.0

2.5

3.0

3.5

4.0

4.5

5.0

0 5 10

Distance Off-Axis - meters

Flux

Den

sity

- m

W/c

m^2

Power Density on Axis in front of Aperture

0.00

0.50

1.00

1.50

2.00

2.50

3.00

3.50

4.00

4.50

5.00

0

2000

4000

6000

8000

1000

0


Flux

Den

sity

- m

W/c

m^2

Figure 11.2-5 Radiation Hazard Calculation around the Aperture of an Antenna. The top diagram shows the formal radiation hazard notice. The bottom left graph indicates the changing flux density and effective half-power beamwidth vs axial distance from the antenna aperture. The bottom right view gives an idea of the variation in flux density moving off to the side of the beam. 11.3 Antenna Site Interference Issues Terrestrial Interference Terrestrial interference is controlled by the FCC and similar authorities elsewhere. Professional organizations exist (such as Comsearch) who maintain a database for all earth station and terrestrial communications links, and can identify if mutual interference will occur or not. Another source that can interfere with an earth station is that caused by aircraft radio altimeters in the approach paths to airport runways - at least the large airports handling airline traffic. Radio altimeters operate at about 4.25 GHz and possibly other frequencies.



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Antenna test range facilities operate with an FCC license to ensure that they are known. Depending on frequency, wireless telephone sites can cause unwelcome interference, particularly during attempts to measure antenna noise temperature in a nearby satcom band. Interfacility Links After assuring that the antenna has a clear view of the required satellite orbital arc and is clear of interference, the planner must decide where the earth station electronics will be located and the means of interconnecting the two parts. An important element is limiting the losses between the transmit high power amplifier (HPA) and the feed flange. At C-band, elliptical waveguide can be used at large distances without excessive losses (1.2 dB/100 ft). At Ku-band the loss in WR75 is about 4 dB/100 ft, significantly limiting the EIRP available from the terminal. Though expensive, the use of oversized waveguide such as Tallguide can greatly reduce these losses, generally by a factor of 6 compared to rigid waveguide. Special transitions must be used at each end of the run and a mode suppressor is required since energy is easily converted into the higher order waveguide modes and lost. Special waveguide bends and twists must be used for the same reason. The loss in the receive RF link is also of importance. Most terminals have the electronics in a building or shelter near the antenna, but some have interfacility links (IFLs) over many hundreds of feet long. In these cases, the e/s downlink performance (G/T) can be degraded by the losses. The use of suitably low loss coax cabling (typically 7/8" diameter for C-band with loss of about 3 dB/100 ft) minimizes the degradation. As a rule of thumb, the IFL losses (between the LNA output and down converter input, including power dividers) should be kept to under 25 dB or extra amplification will be required. Many modern earth stations are being designed using L-band IFLs to reduce the losses. In this case, the HPA with a block up converter from L-band to RF is mounted at the antenna base or in the hub. Low Noise Block Converters are used on the downlink to convert the signal to L-band. Another approach is to use RF fiber optic runs. Fiber optic equipment is available from several manufacturers that interfaces at frequencies from L-band to Ku-band. Once in fiber, separations of several kilometers is possible between the antenna and electronics. The extra expense of fiber optics is partially offset by the protection given by isolating the two sites from problems with grounds and lightning. RF Leakage Typically, high power RF equipment and connecting waveguide are equipt with flanges, most predominantly grooved choke flanges. The choke construction is intended to reduce RF flange leakage. The groove carrying an "O"-ring is intended to prevent leakage of a pressuring agent - either dry air or nitrogen gas as examples. The pressurizing agent is intended to prevent the ingress of humidity and/or harmful solids into the waveguide system. However, "O"-rings, choked groove constructions, or flat flanges do not always provide a positive connection, allowing RF to leak. When the preparation of the flanges entails lapping to ensure a flat contact surface, groove depths are reduced. Now the gasket has insufficient space, the net result being that the flange does not close. Often this is not noticed, since the pressurization system does not register a leak. In these instances, it is best to exclude the gasket, to ensure that RF does not leak. If the pressurizing air leaks a little, it will only help the dehydration of the system. In order to detect sources of RF leakage, a power flux density meter and probe is used to detect "hot spots". The probe is a wideband detector, the meter displays approximate flux in Watts/cm2. Additionally, a spectrum analyzer and test probe may be used to detect RF leakage. Typically, flanges possess -70db to -80db isolation. See [3] for further details about instrumentation and interpretation of measurement data.



403

Figure 11.3-1(a) Upper segment of the waveguide interconnect between the feed and the fixed waveguide tray. The 4 parallel beige-colored waveguides are flexible guides over the azimuth axis. The elevation flex guides are to the left, but partially hidden.

Figure 11.3-1(b) Segment of the waveguide interconnect to the elevated azimuth axis between the transmitter and the base of the antenna. (Photos used with permission of General Dynamics SATCOM Technologies, Inc.) Weather Although weather as a variable is a temporal issue, it can have a dramatic effect on reliability for a link that is required to be available all the time. There are some sites in which the effects of severe rain/thunderstorms will periodically disrupt a link, forcing some operators to install a backup (diversity) earth station in another (not distant) region that statistically is not weatherbound, when the primary station is caught by severe weather.



404

Severe weather does not have to be immediately over the primary earth station to influence it. The line of sight from the earth station to the target satellite may pass through a storm cell and completely disrupt the link. In many instances, increasing power by 3dB or even 6dB will not be adequate to bridge a >20dB storm fade, and the cross-pol effects of rain will not be easily handled. References: [1] Bickmore, R.W., Hansen, R.C., Antenna Power Densities in the Fresnel Region, Proc. IRE, Dec. 1959, pp. 2119-2120. [2] Mumford, W.W., Some Technical Aspects of Microwave Radiation Hazards, Proc. IRE, Feb 1961, pp. 422-447 [3] ANSI C95.3-1973, Techniques and Instrumentation for the Measurement of Potentially Hazardous Electromagnetic Radiation at Microwave Frequencies.

Chapter 12 - Appendices


405

Chapter 12 - Appendices A. Critical Antenna Measurements A.1 Feed insertion loss determination A.2 Determination of Antenna Gain and G/T using Calibrated Radio Stars B. Satellites and Radio Stars B.1 Pointing Angles to Geosynchronous Satellites B.1.1 The case for the Elevation–over–Azimuth antenna B.1.2 The case for the Declination–over–Hour Angle antenna B.1.3 Polarization twist B.1.4 Elevation-over-Azimuth pattern angle correction B.2 Sun Outage B.3 Pointing Angles to Radio Star Positions B.3.1 Introduction B.3.2 The coordinate system and time B.3.3 Positional geometry of the sun over the earth B.4 Radio Star Information B.4.1 Star flux densities B.4.2 Star flux change with frequency - spectral index

B.4.3 Angular extent B.4.4 Correction for atmospheric attenuation B.4.5 Correction for star polarization C. Waveguide C.1 Characteristics of Waveguide C.1.1 Signal velocity in waveguide C.1.2 Attenuation in waveguide C.1.3 Rectangular waveguide attenuation C.1.4 Circular waveguide attenuation C.1.5 Power handling of waveguides C.1.6 Standard waveguide features and characteristics C.1.7 Ridged waveguide C.2 Aperture Patterns C.2.1 Rectangular or square aperture C.2.2 Rectangular waveguide aperture with higher order modes C.2.3 Circular waveguide aperture C.2.4 Diagonal horn aperture with square aperture D. General Information D.1 Exponentials, logarithms, and db D.2 Bessel Function Polynomial Approximations E. Reference Performance Documents E.1 Regulatory Specifications for Antenna Pattern Performance E.2 Recommendation ITU-R S.580-6

E.3 Recommendation ITU-R S.465-5 E.4 FCC Document 47 CFR Ch. (10-1-97 Edition) Containing Para 25.209 and 25.134 E.5 Recommendation MIL Std 188-164



406

A.1 Feed System Insertion Loss Determination A.1.1 Test equipment necessary for the measurement Test equipment for calibration of the Low Noise Amplifier (LNA, LNB, or LNC) • Standard Gain Horn (SGH), orientable towards the sky • Waveguide switch and termination or sheet absorber • Thermocouple or thermometer • LNA • Spectrum Analyzer

Test equipment for measuring the insertion loss of the feed under test • Waveguide switch and termination or sheet absorber • Thermocouple or thermometer • LNA, calibrated as described in the procedure outlined in Section B.1.2 • Spectrum Analyzer Test procedures A.1.2 Calibration of low noise amplifier against clear zenith sky temperature as seen by a standard gain horn Note that all temperatures T carry the unit Kelvin. Step 1. Determine/Measure the return loss of the SGH and input terminal of the LNA and have recorded data available. Step 2. Set up the equipment as shown in Figure A.1-1, using the equipment listed in Section B.1.1.

Temination

Switch LNARlna

T*lna

Standard Gain Horn

Taper = Tsky

Th

Spectrum Analyzer

R

Tlna

Figure A.1-1: Measurement setup for the calibration of the LNA.

Step 3. Measure ambient temperature ambT

Measure LNA body temperature LNAT

Measure termination body temperature hT

Step 4. Configure Spectrum Analyzer to the following condition: (a) Set the span to zero at the first frequency of interest. (b) Set the resolution bandwidth to 1 MHz. (c) Set the video bandwidth for the best possible amplitude resolution. (d) Set the (single) sweep time to ensure adequate time between waveguide switch settings for y-factor measurements.



407

(e) Set the amplitude scale as required for the expected y-factor values (f) Set the attenuation to 0 db. Step 5. Measure the y-factors:

(a) Place the absorber over the horn or select the terminated port. The y-factor obtained is represented by the expression

LNA

LNALNA

TTT

TRTy h

21

1 (A.1.1)

where 1T is the noise temperature collected by the pattern of the SGH from the zenith sky and, as

presented to the input of the LNA, given by

LNASGH

SGH

SGH

RTT

T ambaper

1

11

(A.1.2)

where 3.3 skyaper TT

and 10/10dbSGH

SGHofLoss

aperT is dependent on the horn pattern, elevation angle of the SGH, and the frequency at which the horn

operates. aperT may be determined for most apertures by referring to Figure A.1-2, which shows the sky

noise temperature skyT versus frequency and elevation angle [1].



408

Figure A.1-2 Sky temperature as seen by an idealized pencil beam antenna. See also Table 5.2-1. Based on the result of pattern integrations of corrugated horns used here as SGH references, it was found

that 3.3 skyaper TT Kelvin. This result has been verified by independent calibration of LNA’s using

cryogenic loads at both 4 GHz and 11 GHz.

In most instances, the input terminal of the LNA is fitted with an isolator which will radiate noise LNAT , which

equals the body temperature of the LNA, back into the SGH. This power will be intercepted by the SGH

terminal, a portion of which will be intercepted by the return loss fR of the SGH and reflected back into the

LNA.

LNALNA RRTT f 12 (A.1.3)

where LNAT is the body temperature of the LNA.

LNAR is the return loss characteristic of the LNA input terminal as measured or offered by the LNA vendor,

i.e.

10/

10dbLNA

LNA

ofLossReturnR

and fR is the return loss characteristic of the SGH as measured or offered by the SGH vendor, i.e.



409

10/10dbSGHofLossReturn

fR ,

Substituting equations (A.1.2) and (A.1.3) into (A.1.1), and re-arranging to solve for LNAT ,

1

)1( 21

y

TTyRTT h

ALNA

LN (A.1.4)

Step 7. Calculate the LNA noise temperature LNAT (in Kelvin) from (A.1.5) for all frequencies of interest

Step 8. For selected frequencies, calculate/plot LNAT versus frequency and best fit the values. These best

fit points will represent the LNA temperatures to be used in the following measurements of Section A.1.3. A.1.3 Determination of the feed system insertion loss Step 1. Determine/measure the return loss and port-to-port isolation of the feed system terminals and have recorded data available .

Step 2. Measure the ambient temperature ambT

Measure the LNA body temperature LNAT .

Measure the termination body temperature hT .

Step 3. Configure the spectrum analyzer as in the previous section. Step 4. Measure the y-factor as a ratio of the noise power from the feed terminal and the “hot load” termination. Step 5. Convert the return loss and port-to-port isolation values to represent the power unavailable at the feed terminal being measured. This additional loss must be added to the "insertion loss" being measured here. The measurement setup is displayed in Figure A.1-3.

Temination

Switch LNARlna

T*lna

Feed Systemunder test

Taper = Tsky

Th

Spectrum Analyzer

R

TeminatedCoupled

portPortIsolation

Feed horn

Tlna

Figure A.1-3: Setup to measure the insertion loss of a feed system via the noise temperature method.



410

The noise temperature of most LNAs will vary slightly with ambient temperature. If the body temperature is different from the measurement during the calibration of the LNA, then a correction must be applied as

5.1*

ref

c

T

TTT LNA

LNALNA (A.1.6)

where refT is the ambient temperature during the calibration of the LNA and LNAT is the body temperature

of the LNA as measured during the feed insertion loss measurement. The components of the noise power at the input of the LNA can be considered as follows:

(a) Noise due to the sky as collected by the feed horn pattern and modified by LNAR :

LNARTT

T ambf

f

f

aper

1

11

(A.1.7)

where f includes all the ohmic loss of the feed system in the path from the aperture to the test terminal

10/10dbLossInsertionFeed

f (A.1.8)

(b) Noise reflected by the test terminal fR back into the LNA input terminal

LNALNA RRTT fc 12 (A.1.9)

(c) Noise reflected by other reflective components, particularly the orthogonally polarized terminal is

LNARIsolTT term 13 (A.1.10)

where

10/101dbIsolationporttoPortIsol (A.1.11)

and termT denotes the body temperature of the termination on the unused port. This may be a termination

or a second LNA. The y-factor for this configuration is given by

c

ch

TTTT

TRTy

LNA

LNALNA

321

1 (A.1.12)

Substituting equations (A.1.7) to (A.1.10) into (A.1.12), and solving for f

c

hc

amb

aperambf TRTTTTRTy

TTRy

LNALNALNALNA

LNA

11

1

32

(A.1.13)

Remaining loss components are )10/101log10 RLdbRL

and 10/101log10 IsoldbIsol

Now, the total feed insertion loss in decibels follows from the expression

IsolRLfdbFeed 10log10 (A.1.14)

For selected frequencies, calculate Feed versus frequency. The best fit points will represent the

most likely values for the feed insertion loss. References

[1] L.V. Blake. "Antennas". Artech House Inc., 1984. [2] General Dynamics test procedure # 925-1092 - 2009



411

A.2 Determination of Antenna Gain and G/T using Calibrated Radio Stars The intent here is to provide the details of a measurement procedure to determine the Gain and G/T characteristics of an antenna using the reference datum of known celestial radio sources. The antenna system must be equipt with a high gain low noise receiver, and a precision antenna control and positioning system. Limited motion antennas in the northern hemisphere, which can only access the southern skies, may be limited in their view of radio stars such as Cas-A and Cyg-A. Antennas located in the southern hemisphere can access all the known most powerful radio stars, with limited view of Cas-A. Orion-A, whose sky track lies close to the geosynchronous arc, may present an interference problem from operational satellites. This method is generally only useable for antennas with G/T greater than 30dbK. The noise flux density characteristics of a number of these celestial sources have been documented and calibrated by the NIST and Radio Astronomical Laboratories around the world, and most recently by COMSAT Labs/Intelsat (1999). As a first step in this exercise, it is recommended that a prediction of measured values for the expected test conditions be undertaken. A.2.1 Test equipment. The following test equipment or equivalent substitutes for appropriate frequency band are required: Equipment Listing

Spectrum analyzer Waveguide termination (hot-load) with temperature readout - thermometer or

thermocouple. LNA with fixed IFL to the receiver (may include d/c and line amplifier) - part of station equipment or

special test unit. Unit to be defined for the test procedure. A.2.2 Configuring and checking the test setup prior to the measurement Note: Perform this test only under clear weather conditions. Clear weather means:

clear skies relative humidity less than 90% for C-band or lower frequencies, less than 75% for Ku-band, and

lower for higher frequencies. preference is night-time measurement, to reduce the effects of thermal gradients induced by the

sun. Step 1. Connect the circuit shown in the block diagram of Figure A.2-1. The spectrum analyzer must be set up to display the lowest noise power level. Depending a little on the type of analyzer used, the following settings are suggested as an initial guideline. For ease in reading the display, the settings may have to be adjusted slightly. The objective is to see a steady non-noisy trace moving slowly across the screen. Table A.2-1 For frequencies f < 6 GHz

thin overcast skies and Relative Humidity (RH) < 90% For test frequencies 6 < f < 17 GHz

partly cloudy skies and RH < 75% For test frequencies f > 17 GHz

clear skies (no clouds) and RH < 50%



412

If G/T and Ts are to be measured at low elevation angles – e.g., o5 - the local horizon in the direction

of the target star must be less than 1o. If the local horizon is >1o, or if the localized weather conditions are not consistent with Table A.2-1, turn the antenna toward clear weather conditions and local horizon and plan on recording a separate antenna noise temperature profile in elevation angle for all frequencies of interest. This will permit extrapolating G/T at low elevation angles using measured values for gain G.

Antenna Position Control and Display

Radio Star Position Coordinates

or Program Track

Spectrum Analyzer

LNASw

Terminationwith

thermocoupler

Interconnect cableor low loss

IFL connection

Clock set to UTC (GMT)

Feed System

Figure A.2-1 Block diagram for the radio star measurement Note: The recommendation is to perform this measurement at microwave frequencies and as close to the feed terminals as possible. Doubtful linearity of any additional equipment such as down-converters and/or long lengths of interconnecting cable between the LNA and the analyzer (receiver) may impair the accuracy of the measurement. The following analyzer settings are suggested:

▪ Select a measurement frequency f in the band of interest.

▪ Resolution Bandwidth - RBW = 1 MHz ▪ Video Bandwidth - VBW = 1 Hz ▪ Scan = 0 Hz ▪ Sweep Rate = 100 seconds ▪ Amplitude scale = 1db/div ▪ Attenuation = 0db

Step 2. View the analyzer trace, and operate the LNA/"hot-load" switch. The trace amplitude should change by several db. If not, check if the LNA is operative. The lower level will correspond to the noise

power level associated with the sky noise collected by the antenna - sT .

Step 3. Operate the LNA/"hot-load" switch to observe the noise power level - hP - from the "hot load". Set

the analyzer display so that power levels corresponding to hP and skyP are viewable on the screen.

Note: The ratio skysky

h yP

P must show a value close to the expected value. If skyy is less than expected,

and/or the value is not stable, then before proceeding, record the profile of the local sky noise profile in a swept frequency check across the band of interest. External signal/noise sources may be interfering. If



413

skyP is not seen as a steady-state value in an azimuthal scan of the local horizon (or even at higher

elevation angles), then the TG / measurement will be impaired.

If the sky noise profile shows no sources of interference, and the skyy value is significantly larger/smaller

than expectation, the analyzer may not be showing a linear response. Calibrate with a step attenuator, or use another instrument.

If skyy is still not showing expected values, perform a swept frequency measurement for skyy . Any large

variation will indicate that the feed system may have a problem. Possible issues are leaking flanges in front of the LNA assembly. Step 4. View the antenna position screen of the ACU. Set the position offsets to zero. View the star-track screen and select the radio star position program. Position the antenna to the az/el coordinates for the chosen star. Step 5. Point the antenna into the expected position of the radio star. Set the star-track program, and identify that the star has been "captured". This is done by observing the spectrum analyzer trace increasing

in amplitude. Adjust the az/el controls of the ACU to find the maximum star noise power level - starP .

Step 6. Set the offsets on the ACU screen so that the displayed star position coordinates are equal to the predicted values for the time of the measurement. Record the offset values. Step 7. Continue the program track of the star. Manually maximize the screen trace. Record the elevation angle for the observation. Record the time for the observation. Note: The radio stars are not point noise sources. The nominal angular dimension of the radio stars is approximately 4 x 4 arc minutes. 4 arc minutes ~ 0.067 deg. The star Cas-A in particular does not present a patch with uniform noise distribution, but shows to have an asymmetrical “ring” of noise. Small beamwidth antennas can readily see the noise variation across the star, and so the trick is to attempt to capture the noise “peak”. This can practically only be achieved by moving the antenna to an elevation slightly ahead of the present position, and carefully oscillating the antenna in azimuth to ensure capturing the maximum star noise level. Step 8. Move the antenna in azimuth about 5 beamwidths. This represents a position relative to the star

at which a "sky noise" power level - skyP - measurement can be made with negligible influence from the

star.

Step 9. Operate the LNA/"hot-load" switch to observe the noise power level - hP – from the "hot load".

Set the analyzer display so that power levels corresponding to hP and starP and skyP are all viewable on

the screen.

Step 10. Repeat these measurements of starP and skyP and hP to get used to the sequence of events

and the nature of the display. Optionally, set "delta marker" to observe difference in power level observations directly.

skystarmstar PPy (db)

[The superscript m refers to a measured value]

skyhmsky PPy (db)



414

Disconnect the input cable from the analyzer. Adjust the amplitude setting to view the trace for this

analyzer condition. This will correspond to the noise floor contribution - instrP - of the analyzer to the noise

measurements at the chosen frequency. Calculate

instrskyminstr PPy (db)

[The superscript m refers to a measured value] On the test data sheet, record the following information:

▪ Date and time, identify the site, test antenna, geographic coordinates ▪ Weather conditions, including cloud cover, ambient temperature, relative humidity ▪ Test configuration: Antenna size, point of measurement ▪ LNA identification and its configuration ▪ LNA characteristics (Noise Temperature and Gain vs Frequency as calibrated

by LNA vendor, as described in Section A.1.2) ▪ Feed polarization ▪ IFL configuration (if included in the test) ▪ Nature of local horizon (e.g., buildings, mountains, sea,) and estimated elevation angle

Step 11. Record the following temperature values:

▪ "hot load" temperature - hT - in degrees C. Also read the ambient temperature outside (e.s.

weather observation instrumentation). Step 12. Record onto the data sheet, or into the designated spaces of the data sheet/spreadsheet, the following information:

▪ elevation angle of the star observation - theta - in degrees ▪ time of observation

▪ instry and stary and skyy - in db

▪ test frequency - - in MHz ▪ azimuth angle of the star observation - - in degrees

▪ hot load temperature - hT in deg C

▪ ambient temperature - ambT deg C

▪ LNA operating body temperature - LNAT in deg C

Evaluate gain and TG / and check if this is consistent with expectation - specification, and/or previous experience. If the result is same/similar with expectation, proceed with the formal measurements of Section A.2.3 below. Note: If the result does not meet expectation, check all network connections, and re-evaluate step 3 above. A.2.3 Formal measurement procedure It is assumed that steps in Section B.2.2 above have been completed successfully. Step 1. Pre-set expected elevation angle, test frequency, LNA switch assembly configuration to display

skyP on the analyzer screen.

Step 2. Disconnect the analyzer input test cable, and measure instrP .

Calculate instrskyminstr PPy (db)



415

Note: Perform this only once for each test frequency. Step 3. Adjust azimuth position to intercept the star. Program-track (if available) the star for a short

time. Manually maximize the analyzer trace for starP by adjusting antenna position in both az and el in

small angular increments. Step 4. Move the antenna in azimuth about 5 beamwidths away from the star. Observe the analyzer trace

to show skyP for a short time. Record an average value for skyP .

skystarmstar PPy (db)

Note: At high elevation angles, (larger than 35 degrees elevation), the azimuthal travel for "5 beamwidths" can be quite extensive. Under these conditions, it is acceptable to move the antenna "5 beamwidths" in elevation without affecting the results of the measurement.

Step 5. Switch the LNA to "hot-load" and observe an average value for hP .

skyhmsky PPy (db)

Note: Reset the LNA switch to view skyP at this time.

Step 6. Record starP and skyP and ambT , frequency, time. An example data sheet is shown at the end of

this section on page 422. Continue through the required list of frequencies in this manner. Then return to the first frequency, and repeat the sequence. Note: Attempt to start the star-track sequence at a high elevation angle, and proceed to follow this test procedure for star positions moving down in elevation angle towards the horizon. Attempt to acquire as many readings as possible. (Experience shows that 1 star reading per minute is possible). Step 7. Record the following information: • Site location and geographic coordinates • Date, time and weather condition local airport ATIS information can also be used • Frequency and polarization

• Analyzer noise floor marker level reading instrP (dbm)

• Azimuth and elevation position at which the star flux maximum was observed

• Analyzer marker level readings hskystar PPP ,, (dbm)

• Ambient temperature of hot load, hT Kelvin

• LNA Noise temperature, pT Kelvin, corrected for measured operating temperature – see

(A.2.6) Step 8. Repeat, so that for all frequencies (and polarizations as required), at least two readings for neighboring elevation angles can be averaged. Step 9. Repeat for as many elevation angles as possible.

Step 10. Calculate G/T, sT and sG for each measured point and plot G as a function of elevation angle.

Step 11. In the event the star track measurements end up in a high local horizon and/or an unacceptable

localized weather condition, measure sT for the antenna turned into a “clear sky” and low local horizon for

all frequencies of interest.



416

For a set of convenient elevation angles, establish the most likely antenna gain G .

From the “clear sky” noise temperature profile, select values for sT at the same elevation angles, and

generate the “most likely” values of G/T for the various frequencies and polarizations of interest. A.2.4 Data analysis Basis for the measurement method The measurement of G/T relies on comparing a noise power received from a known star with the noise from

the background sky. The ratio of star noise power to sky noise power stary is given by

sky

skystardbstarskystar N

NNyPP

log10

from which the power ratio stary is,

1

sky

star

sky

skystarstar N

N

N

NNy (A.2.1)

where: starP Analyzer marker reading for noise power from star and sky together (dbW)

skyP Analyzer marker reading for noise power of the sky alone (dbW)

starN Noise power of the star collected by the antenna (W)

skyN Noise power from the sky collected by the antenna (W)

Further, effostar ASN 21 and ssky kTN

and from the above relationships,

121

s

effostar kT

ASy (A.2.2)

Therefore,

4

12

21

21 G

kT

S

kT

ASYy

s

o

s

effostar (A.2.3)

and YS

k

T

G

os

2

8

(A.2.4)

where effA Effective area of the antenna aperture

k 1.380658 · 10-23 (Joules/K) (Boltzmann constant)

oS Star flux density (Watts/m2)

1 staryY

Wavelength (m)

sT Antenna system noise temperature in Kelvin

G Antenna Gain

The factor ½ refers to the fact that most star noise flux is randomly polarized, and therefore only half of the flux is received in either RCP or LCP (HP or VP).



417

Radio star flux densities The discrete radio sources listed in the following table appear to be the most appropriate for measurements of G/T by appropriate earth station antennas. Table A.2-1(a) – Radio star flux densities - (1999)

Radio Star Identification

Cassiopeia –A 3c461

Cygnus-A 3c405 NGC 6913

Taurus-A 3c144 NGC 1952

Virgo-A 3c274

Orion-A 3c145

Omega M17

Right Ascension Declination

350.2833 23h 21m 7.99s 58.540 58o 32’ 24.00”

299.4359 19h 57m 44.62s 40.5961 40o 35’ 45.96”

82.8810 5h 31m 31.44s 21.9818 21o 58’ 54.84”

187.0734 12h 28m 17.62s 12.6672 12o 40’ 1.92”

83.2083 5h 32m 49.99s -5.4225 -5o 25’ 21.00”

274.3875 18h 17m 33.00s -16.2000 -16o 12’ 0.00”

So (4) Flux density at 4 GHz Watts/m2/Hz (Jansky)

936.29 x 10-26

See notes 1 and 2

445.62 x 10-26

620.34 x 10-26

79.058 x 10-26

382.102 x 10-26

494.79 x 10-26

So () Flux density at ƒ GHz Watts/m2/Hz (Jansky)

770.0

4)4(

fSo

279.1

4)4(

fSo

278.0

4)4(

fSo

289.1

4)4(

fSo

204.0

4)4(

fSo

378.0

4)4(

fSo

Table A.2-1(b) – Alternative expression for radio star flux densities as used in ITU-732 Radio Star Identification

Cassiopeia – A 3c461

Cygnus-A 3c405

Taurus-A 3c144

Virgo-A 3c274

Orion-A 3c145

Omega M17

Star Flux Parameter - So

5.745

7.256

3.794

6.541

3.317

4.0560

Star Flux Parameter - S1

0.77

1.279

0.278

1.289

0.204

0.378

Star flux density at frequency ƒ is given by

fSfS 1000logS26 1o10x10 Watts/m2/Hz or Jansky (A.2.5)

where f frequency in GHz.

Notes: (1) Cassiopeia-A is subject to a frequency-dependent reduction in flux with time.

(2) Values for oS (4) valid for 1980 for f between 1 and 30 GHz

The values shown in the tables here have been taken from a recent update of radio star flux densities performed by E. Ekelman - Comsat/Intelsat [4], [5].



418

A.2.5 Correction factors In order to compensate for a number of measurement disturbance mechanisms, the expression for G/T equation (A.2.4) must be modified by a number of factors. Time dependence of the star flux density Star flux density is decreasing with passage of time. The variation for Cas-A has been established [3].

ndb f

s

100

log3.097.01log10 (A.2.6)

where n is the number of years after 0.00 hrs UTC 1 January 1980, and f is frequency in GHz.

Taurus-A and Cygnus-A appear to be stable time-independent sources, but in fact recent measurements suggest a (smaller) time dependence, as yet not formally calibrated. Recent work [7] on Tau A (in the Crab nebula) shows s -0.17 +/- 0.02 %/year

or approximately

ndb f

s

100

log3.045.01log10 (A.2.7)

Flux density variations as a function of time in the other radio stars have not been documented. However, measurements taken on a variety of antennas over the last 30 years indicate that flux densities of all the radio stars vary significantly. Precision measurements will demand a comparisonal average of y-factor measurements taken on several stars, or even with the planets. Frequency Dependence of the Star Flux Density Frequency dependence is expressed in the Table A.2-1a and A.2-1b in the form of the negative exponent, showing decreasing flux with increasing frequency. This is usually referred to as "spectral index". The

frequency dependence has been included in the final flux density value fS as determined in (B.2.5).

Atmospheric Absorption Atmospheric absorption or attenuation has been established as given by the following expression.

sin

0044.00196.0 GHzdb f (A.2.8)

where: = frequency GHz = elevation angle above true horizon in degrees

This expression is valid for oo 905 .

Angular extension of radio stars If the angular extension of the radio star in the sky is significant compared with the antenna beamwidth, a correction must be applied. The correction is given by the following expression:

2

2

1log10

x

eabs x

(A.2.9)

The variable x is shown in the following table for each of the radio stars:



419

Table A.2-2 Beamwidth correction factors – (1999) Radio Source Identification

Cassiopeia-A 3c461

Taurus-A 3c144

Cygnus-A 3c405

Virgo-A 3c274

Orion-A 3c145

Omega M17

x db3

06382.0

db3

06382.0

db3

03468.0

db3

03468.0

db3

06382.0

db3

06382.0

where Ddb

703 = half power beamwidth in degrees, or a measured value.

and where is the wavelength, D is the antenna aperture diameter. The factor 70 implies an antenna aperture efficiency of about 85%, achieved by those antennas compliant with the ITU 580 sidelobe envelope = 29 – 25log(t) dbi. Other designs with higher aperture efficiencies will

have half-power beamwidths approaching Ddb

653 , but may not be compliant with the ITU 580

requirements. Polarization correction Taurus-A is elliptically polarized and it is therefore necessary to use the mean of two readings taken in orthogonal polarizations. If only one polarization is available for measurement, then a mean polarization correction for the flux density p = 0.04 db is applicable.

Correction to stary due to receiver noise.

Since the measurement of starN and skyN cannot be made without the influence of the test receiver, a

correction must be made. This is seen in the interpretation of the noise power measurements starN and

skyN and instrN as the analyzer presents them on the screen.

The measured stary is given as a power ratio by

instrsky

instrstarmstar NN

NNy

Dividing the fraction both top and bottom by skyN , we get

sky

instr

sky

instr

sky

star

mstar

N

N

N

N

N

N

y

1

(A.2.10)

Here, sky

star

N

Nthe required stary ; instr

sky

instr yN

N

From which we have the required corrected value for stary equal to

instrinstrmstar

correctedstar yyyy 1 (A.2.11)

or, as a corrected value in "db"

10/^1010/^10110/^10log10 dbinstr

dbinstr

mstar

dbcstar yyyy

db



420

Instrument noiseN instr

sky noiseN sky + N instr

star noiseN star + N instr

hot load or reference noise

N h + N instr

instrsky

instrhmsky NN

NNy

instrsky

instrstarmstar NN

NNy

Time

Power - dbm

Figure A.2-2 Simulation of spectrum analyzer screen and its interpretation- see (A3-6) A.2.6 The final expression for G/T and gain The final form of the expression for G/T with all correction factors included is:

dbdbdbdbdbdbo

db

db

s

sYST

G

)(597.214 2 (A.2.12)

In those instances when the antenna size and frequency of measurement dictate the use of either the sun or the planets, the increased complexity of the analysis and method of measurement goes beyond what can conveniently be discussed here. For these extended measurements, the reader is referred to two papers by Koury [1] and Guidice [2] for full details: Cas-A has, over the years, been documented very carefully by a number of agencies. The most detailed documentation of Cas-A may be found in [3] and references contained therein. Antenna system noise temperature

The measurement of sT relies on the comparison of noise power received by the antenna from the cold sky

skyP with that of a known reference noise source refP most commonly represented by an ambient

temperature termination. The ratio skyy is given by

sky

refdbskyskyref N

NyPP log10

from which the power ratio skyy is

sky

refsky N

Ny

where:

refN Noise flux of the reference noise source seen at the LNA input

skyN Noise flux from the sky collected by the antenna and seen at the LNA input.



421

skyN is made up of noise contributions from the sky as collected by the antenna pattern, noise generated

by antenna (feed system) losses, and generated by the LNA as seen at the input to the LNA.

Therefore, we may rewrite the expression of skyy as

LNA

LNA

NN

NNy

ant

hsky

(A.2.13)

where:

hN ambient temperature of reference termination in Kelvin and

amtN antenna noise temperature expressed in Kelvin

LNAN noise temperature of the LNA, including the noise contribution form the receiver

Since kTN , where T is the equivalent noise temperature (K)

system

h

ant

hsky T

TT

TT

TTy LNA

LNA

LNA

sky

hantsystem y

TTTTT LNA

LNA

(A.2.14)

where ssystem TT represents the sum of noise components operating in the antenna.

Note: All noise temperature components are expressed in Kelvin

From (A.2.13), the antenna noise temperature characteristic antT is found as

LNATTT sant . (A.2.15)

sT and antT can be plotted as a function of elevation angle.

Antenna system gain Antenna system G/T was established by direct measurement and using a known reference celestial noise source.

sYST

Go

s

597.214 expressed in dbK (A.2.16)

and antenna system noise temperature sT is a power ratio

sky

hs y

TTT LNA

(A.2.17)

In practice, skyy is measured in db, and sT is then rewritten as

10/10

273skyy

oh

s

TCTT LNA

and expressed in dbK as

10/10

273log10

skyy

ohdbK

s

TCTT LNA (A.2.18)

By adding sT

G (dbK) and sT (dbK), the value for the antenna gain can be established.



422

dbK

s

dbK

s

dbi TT

GG (A.2.19)

Upon viewing the behavior of G vs elevation angle, a “most likely” value for antenna gain can be established for each of the various test frequencies. If any elevation angle dependence is detected, then the gain values for specific elevation angles can be chosen as final reportable values.

Correction to skyy due to receiver noise

Since the measurement of hN , starN , and skyN cannot be made without the influence of the test receiver, a

correction must be made. This is seen in the interpretation of the noise power measurements skyN , hN

and instrN as the analyzer presents on the screen.

The measured skyy is given by a power ratio.

instrsky

instrhmsky NN

NNy

Dividing the fraction top and bottom by skyN :

sky

instr

sky

instr

sky

h

msky

N

N

N

N

N

N

y

1

(A.2.20)

Here, sky

h

N

Nthe required skyy equal to

correctedskyy

and sky

instr

sky

instrmsky

csky N

N

N

Nyy

1 (A.2.21)

and 10/^1010/^10110/^10log10 dbinstr

dbinstr

dbmsky

dbcsky yyyy

References [1] A. Koury, K.G. Johannsen, “The Moon as Source for G/T Measurements”, IEEE Trans AES, September 1974, PP. 718 through 727. [2] D.A. Guidice, J.P. Castelli, “The Use of Extra-Terrestrial Radio Sources in the Measurement of Antenna Parameters”, IEEE Trans AES, March 1971, PP. 226 through 234 [3] David F. Wait, “Precision measurement of Antenna System Noise Using Radio Stars”, IEEE Trans IM-32, No. 1, March 1983, pg 110-116 [4] E.P. Ekelman, C.B. Abler, “Antenna Gain Measurements using Improved Radio Star Flux Density Expressions”, IEEE AP-S Symposium Digest 1996, pg. 172-175. [5] E. P. Ekelman, “Radio Star Flux Density Expressions for Accurate Antenna Gain Measurements”, IEEE AP-S Symposium Digest 1999, pg. 1048-1051 [6] Recommendation ITU-R 733-2 Radio star antenna performance measurements [7] E.N. Vinyaikin, Radio-Physical Institute, ul. Bolshaya Pecherskaya 25, Nizhnil Novgorod, 603950, Russia. September 2006. Astronomicheskii Zhurnal, 2007, vol 84, No.7, pp 634-641



423

SYSTEM G/T - CELESTIAL RADIO SOURCE METHOD DATA SHEET ______ Station: Date: _______________________ Latitude: Longitude: Local Horizon: ________________ Polarization: LNA Ident: ___________________ Radio Source: ________________ Weather conditions: ___________________________________________________________________ Remarks: ___________________________________________________________________________ Freq MHz

Time GMT

Elev deg

Azim deg

Pstar db

Psky db

Ph

db T

h C

TLNA Kelvin

T*LNA

C Tamb C



424

B. Satellites and Radio Stars B.1 Pointing Angles to Geosynchronous Satellites For a given earth station location, it is important to be able to accurately predict a. The location of the operating satellite relative to the position of the earth station on the ground b. the rotation of the polarization ellipse as seen by the antenna relative to the local vertical The following brief analysis explains the mathematical relationships involved in these predictions. Since the satellite antenna axis will not necessarily be pointing toward the the center of the earth , and the polarization ellipse orientation at some angle away from a N-S line, polarization adjustments on the earth station antenna will need to be optimized. The analysis demands information about satellite longitude latitude and longitude of the earth station antenna boresight coordinates to which the satellite axis is pointed relative polarization of the satellite antenna. B.1.1 The case for the Elevation–over–Azimuth antenna The position of the satellite from the earth station, given by Azimuth and Elevation angles, can be found using Figure B.1-1

E

BA

C

r

a

c

R h

b

Loe

Los

Equator

Station Meridian

Satellite Merdian Greenwich Meridian

Vy

Hx

Z

N

S

Satellite

Earth Station

Dimensional aspects of the earth

A B (A-B)/A E=sqrt(1-B^2/A^2)Equatorial radius Polar radius Flattening eccentricity of earth's

6378.137 6356.75231 1/298.257223563 cross-sectionaverage= 6367.444657 6367.43568 0.003353 0.0818192

Ref: NAD83 / WGS84North American Datum 1983

The mean radius of the earth at MSL is r = 3956.546137 statute miles r = 6367.444657km Figure B.1-1 Earth station – satellite relationship



425

Typical altitude of a geostationary satellite h = 19327 nautical miles h = 22255.04 statute miles = 35816.02 km In the spherical triangle EBA

so

eo LLa ; aLb ; o90

where eoL longitude west of Greenwich for the earth station

soL longitude west of Greenwich for the satellite meridian

aL latitude of the earth station

From Figure B.1-1,

aso

eo LLLc coscos(arccos (B.1.1)

The azimuth angle relative to the local meridian

c

a

sin

sinarcsin (B.1.2)

azimuth bearing of the satellite

if so

eo LL then add 180o to

if so

eo LL then subtract 180o from

The elevation angle is found from Figure B.1-2.

S

Re

c

E

90-c

C

r(1-cos c)

90o

rsin

cr

A Satellite

c

North Pole

M

R "

t

e"

m

z"

z

r

(r+m)cos c (r-(r+m)cos c

w y

h

Antennaabove ground

Earth

Figure B.1-2 View across the satellite-earth station plane For m = 0, meaning the antenna is at MSL (mean sea level);

cr

crhec

sin

)cos1()tan(

from which

ccr

crhe

sin

)cos1(arctan (B.1.3)

Note: Given e (elevation), )cos1()tan(sin creccrh

The range of the satellite from the earth station is found from



426

cz

crcos

sin and 222 cos1sintan crwcrcr

Re-arranging this expression

c

crw

cos

cos1

Also why

The range R from the station to the satellite

21

sin222 cyzyzR or 21

222 )cos1(sin crhcrR (B.1.4)

For the antenna located at m>0, meaning above MSL (mean sea level); From the geometry of Figure B.1-2

222 sincos" cmrcmrrwz (B.1.5)

22

2 sincoscos

cos1" cmrcmrr

c

crz

(B.1.6)

and for the range to the satellite from the elevated location of the antenna, we have

2

122 cossin" cmrrhcmrR (B.1.7)

The new elevation angle as a result of its height above MSL is given by the angle t , and therefore, from (B.1.3) tee " (B.1.8)

Sv

u

ve

ue

h

E

a

c

C

Np

La

Lo

rEquator

Satelliteve

S

Meridian of Satellite

r

Merid

ian

of E

arth

Sta

tion

Local Zenith

Local Zenith

Vy

Hx

Earth Statione

R

Local Horizon

zb

aM

N

PT

R

Figure B.1-3 Satellite-Earth coordinate system



427

Notes: Satellite polarization components occur due to

the satellite coordinate system rotations su and sv

intentional polarization twist p

earth station generated polarization twist ep

Earth station polarization components occur due to the type of antenna mount or pedestal inherent earth station depolarization characteristic

Polarization twist due to vu, is given by

)sin()sin(arcsin sss vvuup (B.1.9)

e.s. polarization twist due to Az-over-El antenna is ep

The Hour Angle-over-declination type of antenna produces no polarization twist B.1.2 The case for the Declination–over–Hour Angle antenna From Figure B.1-4, we have

"

sincossin

R

abrve

Therefore

"

cossinarcsin

R

barve (B.1.10)

The Hour Angle is given by evaHA

"

cossinarcsin

R

baraHA (B.1.11)

Note: The maximum for ev occurs forhr

rve

sin , and the angle a corresponding to this situation is

va 90 , and reesdega 626.81687.890max

The angle subtended by the earth at the satellite = reesdegv 374.172

The point on the equator closest to the satellite lies at a distance kmh 35816

The range from the point "R (Figure B.1-4) for maxa lies a distance kmh 41704max



428

C

N

P

h

HA

ve

ve

West

East

r

b=90o r

Lat = b

EM,N

b=0oR

SatelliteS

Equator

a

v

R

Figure B.1-4 Determination of the Hour-Angle of the satellite from the earth station Declination is the tilt angle of the HA axis from the local horizontal plane. For a satellite infinitely far away, this angle is equal to the latitude of the point P. From Figure B.1-3,

"

sinarcsin

R

brue

Declination is defined as eu

and

"

sinarcsin

R

br (B.1.12)

B.1.3 Polarization twist Polarization twist is generated by the satellite when viewed from the earth while looking at the satellite from any point other than the boresight. If the satellite boresight axis is considered rotated in the equatorial plane by v and tilted by u away from the direction of the observer on the earth, then the polarization vector

or the propagating downlink signal will appear twisted by the amount sP , and given by

vup

upvpupPs coscoscos

sincotarctancossinsincosarctan

21

222

(B.1.13)

The definitions for vu, and p are given in Figure B.1-5



429

0

r

Equatorial plane

z'

z"

zSatelliteboresight on earth

Observer position on earth

x"x, x'

Satellite

y', y"Pe

Ps

u p

v

ub

y

vb

ue

ve

Figure B.1-5 Definition of the polarization rotation coordinates p is the nominal polarization of the satellite antenna relative to the vertical axis of the spacecraft. The

"vertical" refers to the orthogonal to the equatorial plane.

sP is defined as the projection of the polarization vector back into the yx, plane after rotations

vu, have taken place. Note: u and v refer to the angular displacements between observer and

boresight. Therefore

be uuu and be vvv (B.1.14)

Further contribution to polarization twist as seen at the earth station depends on the type of antenna used. Hour angle / declination type antennas do not contribute to the system polarization twist. For Elevation/Azimuth antennas, however, the polarization twist contribution is equal to the Azimuth angle away from the reference direction of the satellite. If the earth station is in northern latitudes, reference direction = 180o. If the e.s. is in southern latitudes, reference direction = 0o. Polarization twist contribution due to the e.s. is

Azpe 180 for e.s. north latitude

Azpe for e.s. south latitude

Positive ep means cw rotation, negative ep means ccw.

B.1.4 Elevation-over-Azimuth pattern angle correction As a follow-on from equation (B.1.10), for the earth station located at point R,

"

sinarcsin

R

arv

since 0b , and 1cos b .



430

For the earth station located at point P along the same meridian as R, but at a latitude b from the equator

"

cossinarcsin

R

barve

Therefore bba

a

v

v

e cos

1

cossin

sin

sin

sin

Now )cosarcsin(sin bvve When measuring the azimuth pattern around point P, the angular range v will stretch from 0 to 90 for the first leg of the sin function, and then from 90 to 180 for the second leg of the sin function. This means that

2

measuredAzv

where v is understood to be the true azimuth angle when the earth station antenna is moved off-axis in

azimuth in one direction while pointing into an elevation angle b . The correction to the measured azimuth angle scale is now

El

AzAz

measuredcorrected cos

2sinarcsin2 (B.1.15)

B.2 Sun Outage As defined in Section 4.5, the intersections of the sun's ecliptic and the equatorial plane represent the vernal and autumnal equinoxes. The sun passes through these points during 22 March and 22 September each year. This occurrence places the sun directly behind the geosynchronous orbit, presenting to the observer on the earth a large noise disturbance. The time during which the sun is seen by the e.s. antenna is called "sun outage", and the communications link to the satellite is broken. The duration for "sun outage" can be determined given the following information:

6015

15..'""

beamwidthdbantennasediskssuntheofdiametertimeoutageMaximum

The sun moves 15 deg/hour. The sun outage will begin when one edge of the sun is tangent to the projection of the circle of the antenna main beam. It is suggested here that the effective main beam is represented by the 15db beamwidth. The maximum "outage" is expressed here in minutes for the day when the sun moves directly through the middle of the antenna pattern. Example: For a 2.4m antenna operating C-band (4 GHz downlink)

db15 3.75 deg

The diameter of the sun's disk = 0.534 deg Maximum "outage" time = 17.2 minutes The degree of interference by the sun will be about 11 to 12 db compared to the no-sun condition. The sun's shift with each day after the time for maximum outage is approximately 0.4 deg/day. The time to move out of the main beam of the antenna will be 3.75/2/0.4 = 4.7 days. The outage will be experienced for about 5 days before and after the day of maximum outage. The daily outages during this time will become shorter each successive day. For larger antennas with narrower beamwidths, the duration for this event will be correspondingly shorter.



431

B.3 Pointing Angles to Radio Star Positions B.3.1 Introduction The intersection of the celestial sphere with the plane of the orbit in which the earth moves around the sun is called the ecliptic. The plane of the ecliptic is inclined at about 23o27' to the plane of the equator. The ecliptic crosses the equator in two points - the vernal equinox, through which the sun passes on or about 22 March each year; and the autumnal equinox through which the sun passes on or about September 22. The Right Ascension of a star is the distance measured along the equator eastward from the vernal equinox to the hour circle of the star. It varies from 0o to 360o. The right ascension is like the hour angle in that it is measured along the equator. But it differs from it not only in being measured eastward instead of westward, but more importantly in that its origin is the vernal equinox, a fixed point on the celestial sphere, instead of the point where the equator crosses the observer's celestial meridian, which depends on the position of the observer. The declination and right ascension therefore furnish a system of coordinates wholly independent of time and the observer's position. Definitions: Solar minute = 1.002737812 sidereal minute

1560

minutehourT so

G solar hours in degrees

04106718.1560

minutehourT Si

G sidereal hours in degrees

Midnight

Noon

Meridian of Vernal Equinox

Meridian of StarSun's Meridian

Meridian of Earth Station

Greenwich Meridian

Rotation of Earth

RA star

RAsun

LHAstar

LHAsun

Low

TG

Earth

Figure B.3-1 Nomenclature in the celestial sphere B.3.2 The coordinate system and time

Local hour angle of star starLHA Local hour angle of sun = sunLHA

Right ascension of star starRA Right ascension of sun = sunRA

Greenwich Mean Time (GMT) or

Coordinated Universal Time (UTC) = GT Station longitude (east) = eoL

Station Latitude = aL Station Longitude (west) = woL



432

sunsunstarstar RALHARALHA

osun

woG LHALT 180 or o

suneoG LHALT 180)360(

from which owoGsun LTLHA 180 and ow

oGsun LTLHA 540

C

a

c

b

Equatorial plane

N

S

Earth StationE

S

P

La

Lo

LHAstar

c

Local zenith

Star's sighting lineby the station

Substar point on earth

Rotation of earth

Gre

enw

ich

mer

idia

n

Noon

Earth

Figure B.3-2 Celestial coordinates From Figure B.3-2 cossinsincoscoscos babac

or staraa LHALLc coscoscossinsinarccos

= great circle distance between E and S Elevation = c90

Therefore Elevation staraa LHALL coscoscossinsinarcsin (B.3.1)

cossinsin

coscoscos

cb

cba

Azimuth =

cb

cba

sinsin

coscoscosarccos

Azimuth

ElL

ElL

a

a

coscos

sinsinsinarccos

arccos

(B.3.2)

From the geometry of Figure B.3-1 and Figure B.3-2

starstarsunsun RALHARALHA

starsunsunstar RARALHALHA

But 180 woGsun LTLHA or 540 e

oGsun LTLHA

Therefore starsunwoGstar RARALTLHA 180 degrees



433

or starsuneoGstar RARALTLHA 540 degrees

1560

minutehourT so

G solar hours in degrees

starRA Right Ascension of star East of Vernal Equinox

The Newcombe time equation

sunRA Right Ascension of sun East of Vernal Equinox

reesdegTT 24108722222.376892.360006909833.279 (B.3.3)

Where 36525

1TT

and

24605.24979

minutehour

dayKT (B.3.4)

T the number of mean solar days between 1900 Jan 1 0h 0m and the particular Epoch at which sunRA

is sought. Epoch refers to a precise moment in time for which celestial coordinates or orbital elements are specified by international agreement, usually periodically reset to centennial and half-century dates. The epoch date for the expression in (B.3.4) is 1968 June 23 0h 0m. Then from the spherical trigonometry relations on Figure B.3-2

staraa LHALLElevationEl coscoscossinsinarcsin

ElL

ElLAzimuthAz

a

a

coscos

sinsinsinarccos

(B.3.5)

where declination of the star, +ve North, -ve South

Table B.3-1 Star positions for the year 1973

Star Positions

Cas-A 3c461

Cyg-A 3c405

Virgo 3c274

Orion 3c145

Tau-A 3c144

Omega M17

Right Ascension

350.49083 deg 23h 21m 57.80s

299.5933 deg 19h 58m 22.39s

187.31083 deg 12h 29m 14.60s

83.44042 deg 5h 33m 45.70s

83.165 deg 5h 32m 39.60s

274.353 deg 18h 21m 12s

Declination

58.65417 deg 58o 39' 15.01"

40.64972 deg 40o 38’ 58.99”

12.56 deg 12o 33’ 36.00”

-5.40472 deg -5o 24’ 16.99”

21.99944 deg 21o 59’ 57.98”

-16.15 deg -16o 09’ 00”

Center of RF emission for Cas-A is placed at 23h 21m 11s and 58o 39' 40" [1]. Comparison of star positions for the years 1973 (Table B.3.1), and 1999 (see Section B.4) show variation that may be considered due to relative movement of the earth within the celestial coordinate system. Since the earth is not a perfect sphere, the gravitational pull exerted upon it by the sun causes a gradual precession of the earth's axis around the pole of the ecliptic, one cycle being completed in approximately 26,000 years. This gradual motion shifts both the celestial equator and the celestial poles with respect to the star pattern, causing an apparent shift in the position of the stars.



434

The difference in the RA and referred to 1950.0 are given by reesdegRAnmRA tansin per year (B.3.5)

reesdegRAn cos per year (B.3.6)

deg012805.0099050.46sec07327.3 " m

deg005567.00426.20sec33617.1 " n

B.3.3 Positional geometry of the sun over the earth

C

Equatorial plane

N

S

S

P

Rotation of earth

Sighting line of the sun

First point of Ariesor

The Vernal Equinox

Position of the Sun on 21 March

Position of the Sun on 21 June

Earth

RAsun

Plane of the Ecliptic

Figure B.3-3 Position of the sun relative to the earth in the celestial sphere Path length between the first point of Aries and the position of the sun is given by

cos

tanarctan sun

sun

RA (B.3.7)

The sun's declination sun is then given by

sunsunsunsunsun RARA coscossinsincosarccos (B.3.8)

Sample relative star position calculation: Radio Star Position Calculation

Earth Station: Antenna - 53

Station Latitude - deg 0 +ve = north -ve = southStation Longitude - deg 0 +ve = east, -ve = west

year month dayDate 2008 4 21

Hour Minute SecondsTime - GMT 12 1 35.94K - days since 1968 Jan 1, 0 hr, 0 min 14557

Cass-A Cygnus Taurus Virgo Orion Omega SunAzimuth - deg 339.03 310.74 63.18 60.22 96.64 252.24 68.30Elevation - deg 23.56 -0.17 33.49 -64.73 35.99 -24.04 56.06 References: [1] Wait, D.F. et al., "A Study of the measurement of G/T using Cassiopeia-A" (pg 19), Technical Report ACC-ACO-2-74, Advanced Concepts Office, US Army Comms.Command, Fort Huachuca, AR 85613.



435

B.4 Radio Star Information B.4.1 Star flux densities Six stars are known to date with sufficient noise flux to be observed with some of the larger antennas used in satellite communications. The flux densities of these stars have been calibrated over the last 50 years or so, and periodically revised. It is to be noted that the flux from each of the stars is gradually decreasing with time as well as with increasing frequency. For frequencies above Ku band (10 to 15 GHz), the radio stars are so week that only the very large antennas can "see" them. And even then, the beamwidths of these antennas becomes so small that, because of the relatively large angular extent of the stars, some of the flux is not received. The only option at this point, for the high frequency calibration of very large antennas, is to choose one or several of the planets, which have also been calibrated. However, the problem is made more difficult by the fact that the distance between the earth and the planets is always changing, and therefore the noise flux density is variable. The distance to the planet, and its occultation, must be known at the time of the measurement for accuracy. Table B.4-1 Flux density at 4 GHz for 1965 in Jansky 1 Jansky = 10-26 W/m2/Hz Source Date Cas-A Cyg-A Tau-A Orion Virgo Omega Szirtes 1965 1061 489 685 NBS Ref: [2]

1968 1047

Satoh, et al. Ref: [3]

1982 1067 483 679

Wetzell 1995 Ekelman Ref: [4]

1996 936 445.62 622.3

Rudge, A. Ref [6]

450 70

Ekelman Ref: [5]

1999 936.3 445.62 620.34 382.102 79.058 494.79

See also Figure B.4-1 showing a graphical plot of observations for various frequencies and times. The NBS and RAS have documentation to show the decay in the present epoch to be 1.1% per year for Cas-A [1].

fn log0126.0042.01 (B.4.1)

where n number of years elapsed since 1965.0

f frequency in GHz

D. Wait [2] has suggested that Cas-A flux decreases at 1.1% per year, and offered the following expression

n25.365

2 25.365100

1.11

(B.4.2)

where n number of years since 1965.0

Baars et. al. and Dent et. al. suggest

GHzflog003.09903.03 referenced to 1980.0 (B.4.3)



436

Flux density for Cas-A suggested by D.F. Wait [2].

12260097.0 103154 HzmWattsfeS ancas (B.4.4)

where n number of years since 1965.0

na 0012.0792.0

f frequency in GHz

Flux Density for Cass-A1 Jansky = 10-26 Watts/m2/Hz

0

500

1000

1500

2000

2500

3000

3500

0 5 10 15 20 25 30 35

Frequency - GHz

Flux

Den

sity

- Ja

nsky

1981 D.F. Wait Trans IM-32Mar 1983 Star FluxEkelman 1996

Wetzel, Germany 1995

Wetzell 1996

1996

Guidice 1964

Flux Density - Cyg-A

0

500

1000

1500

2000

2500

0 2 4 6 8 10 12

Frequency - GHz

Flux

Den

sity

- Ja

nsky

(a) (b)

Flux Density - Tau-A

0

200

400

600

800

1000

1200

0 2 4 6 8 10 12

Frequency - GHz

Flux

Den

sity

- Ja

nsky

Flux Density - SunDate: 17 August 2008

Sag Hill, Local NoonRef: sec.noaa.gov/alerts/solar_indices.html

0

50

100

150

200

250

300

350

400

450

500

0 2 4 6 8 10 12 14 16 18

Frequency - GHz

Flux

Den

sity

- (W

/m2 /H

z x

10-2

2 )

(c) (d) Figure B.4-1 Star flux density variations as a function of frequency as published by various sources. Although all the above mentioned radio stars except Cas-A have flux densities classified as having no significant time dependence, an examination of Table B.4-1 suggests that Tau-A does have a decay rate of approximately 0.26% per year, and Cygnus may have a decay rate of approximately 0.15% per year. For very high accuracy purposes, there is good reason to consider a calibration comparison measurement conducted on Cas-A when using other stars as a check. Cas-A is the most well-documented star, and therefore considered a reasonable reference.



437

B.4.2 Star flux change with frequency - spectral index Observations over time have elicited improvements in the accuracy of the spectral index for the various stars. These are listed in the following table. Table B.4-2 Spectral indices observed and measured over time Star Cas-A Cyg-A Tau-A Orion Virgo Omega Spectral Index at 4 GHz Ref: ICSC 1970

-0.792 -1.205 -.263

Spectral Index at 4 GHz Ref: [3] 1986

-0.792 -1.198 -0.287

Spectral Index at 4 GHz Ref [4] 1996

-0.770 -1.279 -0.278 -1.279 -1.279 -0.378

B.4.3 Angular extent The radio stars of interest are not point sources. Sample flux density maps for Cas A, Cyg A, and Tau A are shown in Figure B.4-2. Notice the angular extent for each of the stars of about 4 arc minutes. The flux map does not show a uniform distribution, particularly for Cyg A. Cas A is the most well behaved. Cyg A is made up of two related flux sources. Tau A is more regular in its makeup, but is, in contrast to Cas A, significantly polarized.

(a) Cas A (b) Tau A

(c) Cyg A Figure B.4-2 Three-dimensional representation of brightness temperature for (a) Cas A; (b) Tau A; and (c) Cyg A



438

(a) (b) Figure B.4-3 Another form of radio star flux mapping is shown here. The noise contour maps of (a) Cas A and (b) Cyg A. The flux density is directly proportional to the flux noise temperature. When the test antenna beam is directed toward one of these sources, the main beam encompasses the source. If the star were a point source, all of the available flux would be accepted. For the star which is not a point source, but has an angular extent smaller than the main beam, a small amount of the star flux is lost. If the angular extent of the star is larger than the main beam of the antenna, the out-of-phase sidelobes will capture some of the star flux and subtract it from the total available. This is expressed as Total sum of the product {Energy available within the angular extent of the star} x {Antenna pattern in the same angular extent} divided by the {total sum of energy the antenna pattern is able to pick up}.

)}({

)}({

patternAntenna

patternAntennamaplevelnoiseStar

receivedfluxStar

When compared to the star flux that is available as given by

)}({ maplevelnoiseStaravailablefluxStar

the correction to cover for that portion that is missed can be expressed by the ratio of availablefluxstar

and receivedfluxstar . Based upon the good assumption that all the power received by the observing

antenna is contained within the half-power beamwidth, and can be represented by the half-power

beamwidths db3 and db3 .

Comparing the available flux with the total star flux offers a correction factor . Then plotting as a

function of main beam width - expressed as the db3 width - one can get an idea of the limits of the

measurement with a particular antenna. Fig B.4-4 compares the results offered by a number of authors.



439

For the stars Cas A, Tau A, Orion, and Omega, correction appears nearly the same. For Cyg A and

Virgo, with an uneven distribution of flux, the correction is significantly different. Polynomial

approximations to the correction curves have been used, which take into account the small differences in

beta. For db3 > 0.1 deg, the form or shape of the correction curve is very nearly the same.

The more recent and generally accepted correction is expressed with the "exponential"

2

2

1log10

x

eabs x

(B.4.5)

where x is related to the half-power beamwidth db3 of the observing antenna as indicated for the

various stars in Table B.4.3.

db

x3

(B.4.6)

where a constant

Ddb

703 degrees

D aperture of the antenna

operating wavelength

Table B.4-3 Angular extent of the radio stars

Radio Star

Cas-A 3c461

Cyg-A 3c405

Tau-A 3c144

Virgo 3c274

Orion 3c145

Omega M17

x

db3

06382.0

db3

03468.0

db3

06382.0

db3

03468.0

db3

06382.0

db3

06382.0

As can be seen in Figure B.4-4 for wide beamwidth (low gain antennas), the correction is small. However,

for larger antennas, when db3 becomes less than 0.1 deg, the correction becomes very large, and thereby

creates additional uncertainty. Small beamwidth antennas demand use of targets with appropriately small angular extent such as is seen among the planets Jupiter or Venus. In these cases, the difficulty resides in the fact that the planets have a variable flux density due to the diurnal change in distance from the earth and by its phase with respect to the sun. Illumination from the sun is the principal source for noise temperature seen from the planets.



440

Beamwidth Correction Factors for Cas-A

0.00

0.50

1.00

1.50

2.00

2.50

3.00

3.50

4.00

4.50

5.00

0 0.1 0.2 0.3 0.4 0.5 0.6

Half-power Beamwidth - degrees

Cor

rect

ion

- db

Exponential 1 - Wait at NBS(1983)

Exponential 2 - Kanda (1982)

Polynomial = Satoh(1982/Kanda(1976)

Polynomial

Exp1

Exp2

Beamwidth Correction Factor for Cyg-A

0.00

0.20

0.40

0.60

0.80

1.00

1.20

0 0.1 0.2 0.3 0.4 0.5 0.6

Halfpower Beamwidth - degrees

Corr

ectio

n - d

b

Polynomial - satoh(1982)/Kanda(1976)

Exponential - Kanda 1982)

(a) (b)

Star Beamwidth Correction Factor for Tau-A

0.00

0.50

1.00

1.50

2.00

2.50

3.00

3.50

4.00

4.50

0 0.1 0.2 0.3 0.4 0.5 0.6


Cor

rect

ion

- db

Polynomial - satoh(1982)/Kanda(1976)

Exponential -Kanda(1982)

Star Beamwidth Correction Factor for Vir-A

0.00

0.50

1.00

1.50

2.00

2.50

3.00

3.50

4.00

4.50

0 0.1 0.2 0.3 0.4 0.5 0.6


Corr

ectio

n - d

b

Polynomial -Satoh(1982)/Kanda(1976)

Exponential - Kanda(1982)

(c) (d) Figure B.4-4 Angular extent of the radio stars showing the improvements in analysis with time. B.4.4 Correction for atmospheric attenuation Atmospheric attenuation has been established as

sin

0044.00196.0 GHzdb f (B.4.7)

where f frequency in GHz

elevation angle of observation

This expression is valid down to about 5 degrees elevation in the presence of a water vapour content of 7.5g/m3. This corresponds to 40% relative humidity at 20oC and 1 atm pressure. Table B.4-3 Atmospheric attenuation values across the C-band expressed as a function of elevation angle Ref: RS-411 / ICSC data Frequency - GHz Atmospheric Absorption (at zenith)3.7 0.036 4.2 0.040 5.9 0.045 6.4 0.048



441

B.4.5 Correction for star polarization All radio stars seem to be slightly elliptically polarized. However, Tau-A possesses singularly high elliptical

polarization. The degree of polarization of the radio star starp will affect the flux density received by the

observing antenna. The degree of polarization of the observing antenna, expressed by its axial ratio var will also influence the flux density received by the observing antenna.

varpstar arctan2cos1 (B.4.8)

where starp radio star degree of polarization or axial ratio

and var antenna voltage axial ratio

Nominal polarization =

1

1log20

PD db

and the loss in gain due to depolarization is given by

10101log10PD

p db (B.4.9)

For Taurus, starp = 1.6 percent or var = 1.016. For Cygnus, starp = 1.5 percent. For Cassiopeia, there

appears to be an even distribution of polarizations across the noise disk. For most practical applications, except for very large antennas, the error in the determination of G/T and Gain is significantly larger than the value of p .

References: [1] Wait, D.F. et al., "A Study of the measurement of G/T using Cassiopeia-A" (pg 19), Technical Report ACC-ACO-2-74, Advanced Concepts Office, US Army Comms.Command, Fort Huachuca, AR 85613. [2] Wait, D.F., “Precision Measurement of Antenna System Noise Using Radio Stars”, IEEE Trans IM-32 No.1, March 1983 p110-116. [3] Satoh, T., Ogawa, A., IEEE Trans AP-30 No.1, Jan 1987 pg 157. [4] Ekelman, E.P, Abler, C.B., “Antenna gain measurements using improved radio star flux density expressions”, IEEE AP-Symposium Digest, July, 1996, vol. 1, pg 172-175, Baltimore, MD. [5] Ekelman, E.P., Radio star flux density expressions for accurate antenna gain measurements, IEEE AP-Symposium Digest, July 1999 vol. 3, pg 1048-1051, Orlando, FL [6] Rudge, A.W., Milne, K., Olver, A.D., Knight, P., "Handbook of Antenna Design", IEE Publication - Peter Peregrinus Ltd. [7] Kanda, Motohiso., "An error analysis of absolute flux density measurements of Cassiopeia A", IEEE Transactions IM-25 No.9, Sep 1976, pg 173-182. [8] Schwerdtfeger, R, Classified test report on 18.3m X-band antenna, 13 August 2008. General Dynamics-Satcom Technologies, Kilgore, Texas.



442

C. Waveguide C.1 Characteristics of Waveguide The concept of waveguide as transmission line and propagation modes in standard waveguide was introduced in Section 1.4.2. and 1.5.1 Complex waveguide components were presented in Section 1.4.3 and 1.5.2. The following will discuss additional features of signal transmission in rectangular and circular waveguide, in particular propagation velocity, attenuation and phase relationships of waveguide modes, power handling characteristics, and associated thermal properties. C.1.1 Signal velocity in waveguide The general relationship for wavelength is given by

f

c (C.1.1)

where c = 2.997925 x 108 meter/sec = velocity of unimpeded propagation of the wave in free space. and f = frequency in Hertz

This also means that an observation of a specific point on the wave shows that its velocity will be "c" and can be referred to as "phase velocity". The propagation characteristics in waveguide is given by

222

111

cg (C.1.2)

or rearranged

2

1

c

g

(C.1.3)

where g = "guide wavelength"

wavelength in free space

c "cut-off wavelength"

Guide wavelength vs Frequency

0

2

4

6

8

10

8500 9500 10500 11500 12500 13500 14500

Frequency - MHz

Gui

de W

vale

ngth

- cm

Diameter = 0.75 inches

Series2

Figure C.1-1 Guide wavelength response vs frequency for circular waveguide of diameter 0.75 inches over the band 8.5 to 14.5 GHz.



443

Phase velocity Another form of the above expression is

2

1

f

f

cvf

c

pg (C.1.4)

where pv = phase velocity of the wave in the guide. The connection between g and c is the velocity

pv . At high frequencies, the phase velocity will approach the value c . As frequency is reduced toward cf ,

the propagation through the waveguides reduced to zero. The pictorial view of this situation is shown Figure C.1-2

0

g

v p

Operational condition at c < ~ c/

v p

Operational condition at = c/g

v p

Operational condition at = c/c

c

2

a'

a

b' b

(a) (b) (c)

Figure C.1-2 A diagrammatic interpretation of the cut-off condition in waveguide. (a) describes the

unimpeded flow of energy with phase velocity pv . (b) As the frequency is decreased toward cf , the guide

wavelength increases, and the phase velocity in the forward direction decreases. At cut-off (c), there is no forward transport of energy.

Seen in (b), sin

cv p , indicating that the phase velocity pv increases to infinity at cutoff. However, the

transport of energy at cutoff is zero in the direction of the waveguide axis. What does it mean " pv increases

to infinity at cff " ?? One conceptual interpretation: In the direction of the waveguide axis, the points

a-a' along the phase front will intercept the wall of the guide as sin

cv p . In (c), for

cc

cf

, the points

along the phase front b-b' will intercept the waveguide simultaneously - the point of interception travelling from b-b' in zero time, with infinite velocity.

Plottingc

p

f

fvs

c

v, (Figure C.1-3) the following picture emerges: pv approaches for cff . For this

condition, there is no transport of energy along the axis of the waveguide. Group velocity Instead of considering single frequency signals, let's consider a modulated signal with bandwidth B. Signal power is now spread over the frequency band B. This signal is injected into the waveguide system of the

earth station antenna. If phase velocity pv were constant for all frequencies, then each frequency

component of the signal would be propagated with equal velocity. However, the non-linear shape of the

fvsg characteristic will cause the higher frequency to travel more quickly down the guide than the low

frequency, causing a distortion in the signal at the output when compared with the signal spectral shape at the input.



444

Analogue signals will suffer distortion, and data rates are limited because of the spreading of pulses in digital signals. The degree of distortion is measured by the slope of the propagation curve. For f much

greater than cf , the group of frequencies will travel along the line with some dispersion equal to

c

v

c

v gp 1~ . For cff , the group of frequencies will have an effective velocity given by 0gv .

The slope of the curve will be c

v p at cf .

Therefore

g

g

d

dfv

1

. (C.1.5)

Performing the differentiation, the group velocity is then

2

1

f

fcv c

g (C.1.6)

and shown in Figure C.1-3

Wave Velocities for Closed Waveguide

0.00

0.50

1.00

1.50

2.00

2.50

3.00

3.50

4.00

1 1.1 1.2 1.3 1.4 1.5 1.6 1.7 1.8 1.9

Frequency relative to cutoff

Relative Phase Velocity

Relative Group Velocity

WR-159; Cutoff = 3.712 GHz

3.85 4.15 4.45 5.05 5.35 5.95 6.856.25 6.555.65

4.75

Frequency - GHz

Rel

ativ

e gr

oup

velo

city

Rel

ativ

e ph

ase

velo

city

2

1

f

fcv c

g

2

1

ff

cvf

c

pg

Figure C.1.3 Phase and group velocities for rectangular waveguide

Derivation of gv from the expression for pv .

2

1

f

f

cfv

c

gp (C.1.7)



445

g

g

d

dfv

1

or df

d

v

g

g

1

1

f

c

f

fc

g

2

11

2

1

21

21

2

2

2

2

2

2

2

4

22

1

12

12

11

f

f

f

c

f

c

f

c

f

c

f

f

f

ff

f

f

f

c

df

d

c

ccc

g

Now the group velocity

f

fcv c

g 1 . (C.1.8)

Points of interest: 1. Phase velocity is the velocity of the propagating wave 2. Group velocity is the velocity of the transport of energy C.1.2 Attenuation in waveguide A current in a conductor can be seen as the transport of free electrons in the conductor. For low frequencies, the influence of the field supporting the current has time to penetrate the conductor to influence more free electrons. For higher frequencies, the inherent insertion of the free electrons will cause only so-called "surface currents" to be generated with small penetration, meaning that the current density in the conducting material will increase near the surface. This is equivalent to forcing larger amplitude currents through smaller conductors. This will automatically increase the resistance to flow, causing more attenuation, and therefore more heat energy. The surface resistivity of a conductor is found as

f

Rs ohms (C.1.9)

The associated depth of surface current penetration is given by the "skin depth"

f

1 meters (C.1.10)

showing here the phenomenon of decreasing "skin depth" with increasing frequency f .

Now

1

sR



446

where material conductivity (mho/m or Siemens/meter)

7104 x (H/m or Henry/meter)

f frequency (Hertz)

C.1.3 Rectangular waveguide attenuation

a

b

TEmn modes

Cut-off wavelength

b

an

a

bm

bac

22

2

(C.1.11)

Cutoff frequency sec/10997925.2; 8 mxcc

fc

Attenuation (TEmn) for frequencies cff (above cutoff).

686.8

1

11

2

2

2

22

22

/

f

f

f

f

a

b

f

f

b

an

a

bm

na

bm

b

R

c

cmn

cmn

smdb

(C.1.12)

where 1, nm if 0, nm

2, nm if 0, nm

The case for 0 nm is excluded

o

osR and

fo 1

where conductivity mho/meter

f = frequency Hertz

7104 xo Henry/meter

121085.8 xo Farad/meter



447

fc

fR

o

mr

o

o

o

o

os

1

o

mrs

c

fR

where o

o

= intrinsic impedance of free space

This can be rewritten as

mrs f

c

R

7102

1 /meter (C.1.13)

The ratio r is known as dielectric constant; and m is called magnetic permeability.

Typically, 1m for practically all materials of interest in microwave work.

Equation (C.1.15) has been plotted for several standard rectangular waveguide sizes as encountered in feed systems and waveguide interconnects for use in C, Ku, and Ka bands are shown in Figure C.1-4.

Rectangular waveguide WR-159 Attenuation vs Frequency

0.00

0.05

0.10

0.15

0.20

0.25

0.30

0.35

0.40

0.45

3500 4000 4500 5000 5500 6000 6500 7000

Frequency - MHz

Atte

nuat

ion

- db/

m

TE10 1/4 heigh WR-159 guidet

TE10 1/2 height WR-159 guide

TE10 Std WR-159 guide

TE10 double height w aveguide

Rectangular waveguide WR-75Attenuation vs Frequency

0.00

0.10

0.20

0.30

0.40

0.50

0.60

0.70

0.80

9000 10000 11000 12000 13000 14000 15000

Frequency - MHz

Atte

nuat

ion

- db/

met

er


TE10 1/2 height WR_75 guide

TE10 std WR-75 guide

TE10 WR-75 double height guide

(a) (b)



448


0.00

0.10

0.20

0.30

0.40

0.50

0.60

0.70

0.80

0.90

1.00

17000 18000 19000 20000 21000 22000

Frequency - MHz

Atte

nuat

ion

- db/

met

er




TE10 double height WR-51 guide


0.00

0.20

0.40

0.60

0.80

1.00

1.20

1.40

1.60

1.80

2.00

27000 28000 29000 30000 31000 32000

Frequency - MHz

Atte

nuat

ion

- db/

met

er




TE10 double height WR-34 guide

(c) (d)

Figure C.1-4 Insertion loss for copper waveguide as commonly used in feed assemblies for (a) C-band Tx signal paths,(b) Ku-band Rx and Tx signal paths, (c) Ka-band Rx signal paths, and (d) Ka-band Tx signal paths. In some instances, feed networks use ½ and even ¼ height waveguide, with the attendant significant increase in loss. As seen in lower curves, use of square waveguide (double height) components reduces slightly insertion loss in dual polarized feeds.

Attenuation (TMmn) for frequencies cff (above cut-off).

Cut-off wavelength

b

an

a

bm

bac

22

2

(C.1.14)

Cut-off frequency sec/10997925.2; 8 mxcc

fc

2

1

c

g

or 2

1

f

f

f

c

c

g

686.8

1

112222

3

322

/

f

fb

anm

b

anm

a

R

c

smdb

(C.1.15)

Attenuation of TEmn and TMmn modes for frequencies cff (below cut-off)

686.812

2

/

cc

mdb

f

f

(C.1.16)

a



449

As f is decreased below cf , increases from 0 to the constant value c2

. This leads to the idea that

waveguide operating below cut-off can be used as a calibrated attenuator. C.1.4 Circular waveguide attenuation

a

TEmn modes

Cut-off wavelength '

2

mnc

a

(C.1.17)

'mn is the thn vanishing root of the thm order Bessel function )(' mJ .

Guide wavelength 2

1

f

f

f

c

c

g

Attenuation 686.8

1

112

2

22'

2/

f

ff

f

m

m

a

R

c

csmdb

(C.1.18)

TEmn modes nm, 0,1 1,1 2,1 3,1 0,2 1,2 2,2 3,2 0,3 1,3 2,3 3,3

'mn 3.832 1.841 3.054 4.201 7.016 5.331 6.706 8.015 10.713 8.536 9.969 11.346

TMmn - modes


c

a

2

(C.1.19)

mn is the thn vanishing root of the thm order Bessel function )(mJ .

Guide wavelength 2

1

f

f

f

c

c

g

Attenuation 686.8

1

1122

/

f

fa

R

c

smdb

(C.1.20)



450

TMmn modes

nm, 0,1 1,1 2,1 3,1 0,2 1,2 2,2 3,2 0,3 1,3 2,3 3,3

mn 2.405 3.832 5.136 6.380 5.250 7.016 8.417 9.761 8.654 10.173 11.620 13.015

Waveguide items: Question: Can one connect square and circular w/g without a transformer ?? A smooth transition will take place if the guide wavelength in both guides is equalized. Example: For a circular w/g of diameter 2.125 in dia.

mmg 129 at f 4000 MHz; 3255cf MHz and mmc 1.92

For square waveguide with mmg 129 is found as having sides equal to 1.810 inches. The ratio of

dimensions is 852.0125.2

810.1k .

Interesting notes: 1. The relative attenuation characteristics at 4000 MHz are:

WR-181 square mdb /044.0 for copper w/g mmhox /101.4 7

R - 2.125 circular mdb /031.0 showing that the round w/g is less lossy for the same

propagation velocity. By comparison, the loss of WR-229 waveguide is mdb /032.0 .

2. Waveguide bends are inherently asymmetrical waveguide structures. If the w/g structure is symmetrical square or round, then the possibility for orthogonal (cross-pol) modes can occur. Therefore, w/g bends are normally only made in rectangular waveguide. 3. From the fvs curves, it is clear that as the w/g size increases, the attenuation decreases.

However, at frequencies cff , attenuation starts to increase for all modes except TE01, for which mode

attenuation continues to decrease. 4. Providing the radius of curvature of the TE01 bend can be made sufficiently large the following configuration will assure suppression of cross-pol, due to circular waveguide distortions in the bend, of more than 30db. diameterwaveguidexRadiusBend 10

Therefore, for the purposes of building a low loss waveguide interconnection (e.g., between a transmitter and the antenna), two options can be considered. (a) oversized rectangular waveguide in TE10 mode (b) oversized circular waveguide in TE01 mode. Example: (a) Consider operating 14 GHz in WR-75 waveguide

Attenuation mdb /157.0 with mmhox /101.4 7 for copper.

For a 20m w/g IFL (Interfacility Link), the total loss = 3.135 db. There are instances in which this may represent an insurmountable excess, and some means is required to reduce this loss. The above attenuation represents ½ of the available RF power lost as heat.



451

Consider transforming WR-75 to WR-229. See Figure C.1-5

0.75

0.375

1.145

2.290

Mode suppression plates

Approximately > 24.0

WR-75

WR-229

Figure C.1-5 Outline of a transformer from WR-75 to “Tall Guide” WR-229 to suppress unwanted modes WR-229 w/g operating at 14 GHz in the configuration shown presents an attenuation of 0.031 db/m, or a total loss over 20m of only 0.622 db. In order to prevent orthogonal modes, the oversized w/g system must incorporate the mode suppressor blades as shown. (b) Alternatively the round w/g system with diameter = 2.125 inches operating at 14 GHz can be considered. Again a mechanism for launching the rectangular TE01 mode without generating any other orthogonal modes is a problem. The resulting attenuation will be 0.008 db/m. By contrast, the attenuation for the TE11 mode will be 0.015 db/m. 5. The principal difficulty with oversized / over-moded w/g is the requirement to inject and extract the power with no loss of power to other / orthogonal modes. The situation is shown here for a standard w/g train:

Figure C.1-6 Waveguide train from rectangular to circular back to rectangular (disregard the transformation to the oversized format for the moment) Rectangular to square is clear enough, and can easily be made by maintaining symmetry. The field distribution in each of the guides is as shown. If the circular w/g is perfectly symmetrical, then the integrity of the transfer of fields is complete. If however, the circular w/g suffers some asymmetry, or includes the elements of a pin loaded differential phase shifter, then an orthogonal mode will be generated.



452

resultant orthogonal field this mode in cut-off here

Figure C.1-7 Waveguide train from rectangular to circular, with obstacles such as encountered in pin loaded differential phase shifter, back to rectangular. The consequent orthogonal modes will not be supported The orthogonal modes cannot get out of the system. It therefore resonates between rectangular w/g terminals, and shows itself as a "spike" in the frequency response, representing a "trapped" mode. The result of this situation is large loss at the "spike" frequency, and large distortion in the frequency spectrum (represented by the group velocity dispersion or group delay) around the operational frequency.

0db Ref

12

Input-to-output response

Figure C.1-8 Possible response from the waveguide configuration shown in Figure C.1-7. In the oversized/over-moded w/g assembly, the same phenomenon will occur, but with several more orthogonal modes available to become trapped, and correspondingly more spikes. C.1.5 Power handling of waveguides Voltage breakdown A very important design point - how much power can be injected into rectangular waveguide ?? If waveguide components utilize tuning elements, irises, steps, posts, then the resulting concentrated electric fields can cause voltage breakdown by ionization of the contained air. Air at normal atmospheric pressure and temperature will break down at a voltage of about 30,000 volt/cm. When the distance between electrodes is much smaller than the oscillation path of the free electrons, break-down will occur. To reduce these effects, corners in the construction of tuning elements are rounded. For the purposes of high power transmission, air pressure is either increased, or the air is replaced with another gas with much smaller ionization properties. In standard waveguide, without the complications of tuning elements, voltage breakdown is independent of the attenuative properties of the waveguide material, and only dependent on the waveguide dimensions and signal frequency. Maximum cw or average power is given by [2].

cccc

o

go

o aa

a

bEP

2

sin4

1

2/sin

1

2 2

2

max (C.1.21)

where a waveguide width

b waveguide height

= free space wavelength

c = cutoff wavelength

g = guide wavelength

oE = voltage breakdown in air at standard temperature and pressure



453

Figure C.1-9 shows maximum power handling for specific waveguide sizes typically used in transmit functions. For practical purposes, power levels are also shown when a safety factor = 2 is applied.

CW Power handling in Rectangular Waveguide

1

10

100

1000

0 5 10 15 20 25 30 35 40 45 50

Typical Transmit Frequency Bands - GHz

CW

Pow

er -

kWat

ts WR

-159

WR

-75

WR

-62

WR-28WR-22

WR

-284

WR

-430

WR

-137

Maximum

Safety factor = 2

Standard rectangular waveguide commonly utilized for high powerearth station transmit functions.

Maximum power determined by voltage breakdown in the w/g.

Safety factor = 2 chosen in casesof waveguide systems with practicalheat dissipation cooling mechanisms.

Figure C.1.9 Break-down power handling capacities of rectangular waveguide as calculated with (C.1.21) Thermal limits The resistivity of the waveguide material indicates attenuation. The ohmic loss involved will induce heating of the waveguide as power is transported from input to output. As the conductor becomes hot, the surface temperature will increase until an equilibrium is reached in the convective heat transfer to the surrounding atmosphere. As the surface temperature of the conductor increases, the current flow will encounter an increased number of free electrons which will tend to impede the current flow. This suggests that the effective conductivity will decrease with increasing temperature. As a result, there will be a peak power handling capability of the waveguide dictated by a surface temperature limit. Additionally, if the waveguide components involved demonstrate high VSWR characteristics, then localized high current and therefore local "hot-spots" will occur. Let us examine the case of a waveguide transmission line WR-159 operating at 6 GHz in an environment at 20C. What is the body surface temperature likely to become when a power of 10kW is applied at one end ?? Using the attenuation relationship of (C.1.14)

mdb /048.0 ; MHzfc 6000 ; mmg 6.63 ; metermhox /109.3 7 for copper.

The power lost due to resistive effects from the 10kW input is 115 W per meter of w/g at the input end. Consider the waveguide in a still-air environment. Feed systems are generally contained in protective enclosures in still-air conditions. Figure C.1-10 shows the surface temperature rise resulting from the dissipation of 115 W. The surface temperature will be about 60oC over 1 meter length. Conductivity due to the new surface temperature decreases to 3.4x107 mho/m, causing an effective attenuation of 0.053 db/m and a new surface temperature of 65oC. This would represent the beginnings of thermal runaway, if not controlled.



454

Waveguide Surface Temperature vs Dissipated Power

0

50

100

150

200

250

300

0 200 400 600 800 1000 1200 1400

Dissipated Power - Watts/meter

Wav

egui

de S

urfa

ce T

empe

ratu

re -

deg

CWaveguide Size WR-159

Material = Copper

Frequency MHz 6138

Input power watts 10000

Power dissipated watts/m 110

Surface temp

Conductivity of Copper as a Function of Temperature

0

20

40

60

80

100

120

140

160

2.50

E+

07

2.70

E+

07

2.90

E+

07

3.10

E+

07

3.30

E+

07

3.50

E+

07

3.70

E+

07

3.90

E+

07

4.10

E+

07

4.30

E+

07

Conductivity - mho/meter

Tem

pera

ture

of C

oppe

r - d

eg C

Figure C.1-10 Thermal behaviour of WR-159 waveguide subjected to an input power of 10kW at 6.138 GHz while operating at 20oC ambient conditions. The surface temperature of the waveguide can be determined through a thermal balance. This is done by equating the power lost to the sum of the convective and radiant losses, to the power of the heat source in the waveguide. The convective loss is equal to the free convection from the heated surface to the surrounding still air. Calculation of this value is iterative because the values used to calculate the surface temperature are dependent upon the temperature. Similarly the radiant loss is also dependent upon the surface temperature. The analysis below does not take into account the presence of large flanges, or the orientation of the waveguide run, both of which will enhance heat dissipation. Power lost is given by

)()( 44ambsambs TTeSTThAq (C.1.22)

where h convective heat transfer coefficient for air

A surface area of the waveguide m2

sT surface temperature Kelvin

ambT ambient air temperature Kelvin

e emissivity of the waveguide material = 0.3

S Stefan-Boltzmann constant = 5.67 x 10-8 Watts/m2K4

Further, the convective heat transfer coefficient is determined as

kl

Nh u (C.1.23)

where

)(43

44

rr

u PgG

N

(C.1.24)

21)( rPg

and k thermal conductivity of air

;36

;32

;26

k

k

k

CT

CT

CT

oamb

oamb

oamb

200

100

20



455

2

3

v

lTT

T

gG ambs

sr (C.1.25)

where l waveguide length per meter

v viscosity of the air at sT = 20 kg/m sec

g acceleration due to gravity = 9.8 m/sec2

The total power handling capacity of the waveguide system will therefore be dictated by waveguide size and the nature of the internal structure, and the thermal conditions in which it is being applied. Generally, in high power conditions, a blower system will be utilized to achieve a thermal balance between power dissipated and heat removed from the waveguide system. C.1.6 Standard waveguide features and characteristics Table C.1-1 Reference table of rigid rectangular waveguide data – Microwave Specialty Corporation, San Diego, CA 92111.



456

Table C.1-2 Modal transverse field distributions in rectangular waveguide (After C. S. Lee, S.W. Lee, and S.L. Chuang 1985 IEEE



457

Table C.1-2 continued. Modal transverse field distributions in rectangular waveguide (After C. S. Lee, S.W. Lee, and S.L. Chuang 1985 IEEE



458

Table C.1-3 Modal transverse field distributions in circular waveguide (After C. S. Lee, S.W. Lee, and S.L. Chuang 1985 IEEE



459

Table C.1-3 continued. Modal transverse field distributions in circular waveguide (After C. S. Lee, S.W. Lee, and S.L. Chuang 1985 IEEE



460

C.1.7 Ridged waveguide Rectangular waveguide with aspect ratio b/a has a useful operational TE10 bandwidth of 1.25<f<1.9fc. At 2

times cf , the next mode TE20 is able to exist. In waveguide work, if a mode is able to exist, it will exist.

The cutoff wavelength

.c

c f

ca 2

For those instances in which a bandwidth greater than 2:1 is required, ridged rectangular or even circular waveguide will do the trick. See Figure C.1-11 .

a

bl l

s

dd

a

l ld

Figure C.1-11 Ridged waveguide configurations The behaviour of ridged w/g characteristics described in the following paragraphs is given in comparison with those of standard rectangular waveguide. Ridged waveguide can be viewed in the following way. The effective “a” dimension of ridged waveguide is

)(2 dbslaeff

which is larger than the “a” dimension of the rectangular waveguide, causing the effective cf to be

lowered. At the same time, the cut-off frequency for the TE20 mode is moved up, thereby providing an increased useful bandwidth. The increase can be as much as 6 times (see Figure C.1.12). The effect of the ridge is to concentrate the electric field onto the ridge.



461

Double Ridge - TE10 mode Cut-off wavelength for b/a = 0.5

2.0

2.5

3.0

3.5

4.0

4.5

5.0

5.5

6.0

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

Ridge width S/a

Cut

-off

wav

elen

gth

/ a =

c/a

c/a

d/b = 0.2

d/b = 0.1

d/b = 0.15

d/b = 0.25

d/b = 0.3

d/b = 0.35

d/b = 0.4

d/b = 0.5

Figure C.1-12 Cut-off wavelength values have been calculated by Hopfer [2] for double ridged guide, as a function of the normalized ridge width s/a, for various ridge heights d/b.

Double Ridge - Bandwidth Curves for b/a = 0.5

2.0

2.5

3.0

3.5

4.0

4.5

5.0

5.5

6.0

6.5

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

S/a

Ban

dwid

th - c

1/ c2

d/b = 0.2

d/b = 0.1

d/b = 0.15

d/b = 0.3

d/b = 0.35

d/b = 0.4

d/b = 0.5

Figure C.1-13 Bandwidth extension as a function of normalized ridge width s/a, for various ridge height values expressed as d/b for double ridge waveguide. Bandwidth features of single ridge waveguide are slightly smaller, but similar in nature. The higher the ridge, the smaller the gap between top and bottom of the two ridges. The smaller the gap between the ridges, the greater the propensity, under high power, for voltage breakdown to occur. Under standard atmospheric pressure and temperature, voltage breakdown occurs at 30,000 volts across a gap of 1 cm. Since the “skin depth” is dependent on frequency and finite conductivity of the ridge material, the relatively large current supporting the concentrated field on the ridge will cause heat to be generated on the ridge – more so than for the waveguide with no ridges. This can be seen as an increase in the effective attenuation, compared with standard rectangular waveguide. See Figure C.1-13. In order to present ridged



462

guide attenuation in a general fashion, it is convenient to compare attenuation of the ridged guide to that of rectangular guide of identical cutoff frequency. The normalized attenuation is referred to a rectangular guide of aspect ratio b/a = 0.5, and evaluated at a frequency of

cff 3

The normalized attenuation in this graph must be multiplied by the rectangular guide attenuation at this frequency.

Double-ridge Waveguide Normalized Attenuation for b/a = 0.5

0

2

4

6

8

10

12

14

16

18

20

22

24

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9

Ridge width - S/a

Atte

nuat

ion

- db/

m

5.04.5

4.03.5

3.02.7

2.5

Bandwidth

Figure C.1-14 Attenuation of double ridged rectangular waveguide with aspect ratio b/a = 0.5, as a function of ridge width and for various ridge height d/b values..

Rectangular guide attenuation at cff 3 is shown in Figure C.1-15, for b/a = 0.5 at the same

frequency.



463

Standard Rectangular Waveguide Attenuation vs Waveguide Width

Blue = Published loss values for Copper w/gRed = Best fit loss values

0.001

0.010

0.100

1.000

0.1 1 10 100

Waveguide Width - centimeters

Atte

nuat

ion

- db/

met

er

330300 0.3Frequency - GHz

110100

Figure C.1-15 Standard rectangular waveguide attenuation vs waveguide size. Further, nominally the top of the ridge has sharp edges, contributing to the propensity for voltage breakdown. To reduce this phenomenon, the edges must be rounded. How much rounding ?? Some guidance is offered in Figure C.1.16.[2]

Figure C.1.16 Effects of rounding the edges of ridges. The same approach can be applied for the rounding of tuning elements encountered in more complex waveguide components such as phase shifters and couplers and filters.



464

Power handling of rectangular ridged guide Power handling for rectangular ridged waveguide is given by [2 ]. The special interest in ridged waveguide is the rapid increase in band width with the introduction of ridges - either single of double ridges. Because of the reduction in spacing between top and bottom of the waveguide, the power handling will be decreased when compared with standard rectangular waveguide. This is expressed with the following expression.

kkk

k

b

d

kkb

d

kkm

k

EP co

go

o

4

sin4

1

/2sin

/cos2sin

4

1

22lncoseccos

2 2

22

2

... (C.1.26)

where

cc pa

ka

sas

a

d

a

b

;;;

2

/1;;

m 1 for double ridged guide

m 2 for single ridged guide

oE Breakdown voltage = 30,000 volt/cm in air at standard temperature and pressure.

Inside non-ridged rectangular waveguide with TE10 mode, the behaviour of maximum power that can be transmitted without breakdown is shown in Figure C.1-17 for the case s = 0, d = 0

cccc

o

go

o aa

a

bm

EP

2

sin4

1

2/sin

1

2 2

2

(C.1.27)

CW Power handling in Rectangular Waveguide

1

10

100

1000

0 5 10 15 20 25 30 35 40 45 50

Typical Transmit Frequency Bands - GHz

CW

Pow

er -

kWat

ts WR

-159

WR

-75

WR

-62

WR-28WR-22

WR

-284

WR

-430

WR

-137

Maximum

Safety factor = 2

Standard rectangular waveguide commonly utilized for high powerearth station transmit functions.

Maximum power determined by voltage breakdown in the w/g.

Safety factor = 2 chosen in casesof waveguide systems with practicalheat dissipation cooling mechanisms.

Figure C.1.17 Power handling capacities of rectangular waveguide as calculated with (C.1.27) References: [1] Cohn, S., "Properties of Ridge Waveguide", Proc IRE vol 35, No. 8 Aug. 1947, p 783-788 [2] Hopfer, S. "Design of Ridged Waveguides", IRE vol MTT-3 No. 10, Oct 1955, p 20-29 [3] Markuvitz, N., "Waveguide Handbook", MIT Radiation Laboratory Series



465

C.2 Aperture Patterns C.2.1 Rectangular or Square Aperture For a rectangular or square aperture the approximate narrow angle pattern will be given by

cos

cossin

cos

cossin,

b

b

a

a

u

u

u

ug

sina

ua and

sinb

ub

Case 1: Uniform field distribution across the "b" dimension, as represented by the E-plane.

u

uug

sin

sin

sinsin

,b

b

g ; 0 (E-plane) (C.2.1)

Gain factor = 1; bdb

88.03 ; First null in the pattern = b

; First sidelobe level = 14db

Case 2: Rectangular aperture with a tapered field distribution, as represented by the H-plane.

2

21

cos2

u

ua

ug ; 2

sin4

1

sincos2

,

a

aa

g ; 90 (H-plane) (C.2.2)

Gain factor = 0.88; bdb

2.13 ; First null in the pattern = a

5.1 ; First sidelobe level = 23db

C.2.2 Rectangular waveguide aperture with higher order modes Radiation pattern from an open waveguide aperture involving higher order modes nm, employs slightly

more complicated expressions. [1],[2]. TE modes: Definitions: xz plane = H-plane = phi = 0; yz plane = E-plane = phi = 90

22mnmn k ... (1.3.4);

222

b

n

a

mmn

... (1.4.3); 2

k ... (1.3.2)

E-plane pattern, 90

,,cossincos1sin22

DCb

n

a

mB

kAE mnE

eE

...(C.2.3)

where

23

2

2

21

mn

Ee R

abA

amplitude factor

cos1

kB mnE

e reflection factor in the aperture



466

the aperture reflection coefficient

2222

2sinsin

2sinsinsin

2cossin

2cossinsin

nb

nb

ma

ma

C pattern function

jeD

21sincossin

nmbakR phase factor

R distance from the aperture plane xy.

H-plane pattern, 0

,,,coscossinsin DCBk

AE mnEh

E

(C.2.4)

where

R

abAE

h 3

2

2

21

kB mnE

h

cos

TM modes: E-plane pattern

,,,cos1sin DCBk

AE Me

mn

Me

M

(C.2.5)

where 22

3

4 mn

mnMe R

abmnA

cos1mn

Me

kB

H-plane pattern

0ME (C.2.6)

For the special case TE10 mode, E-plane is defined as 90 , and neglecting the phase factor ,C

and the aperture reflection factor B

E-plane pattern 90

sin

sinsin

cos1 102

221

b

b

kR

baE E

(C.2.7)



467

H-plane pattern 0

4sin

sincos

cos2 2

10

2

221

a

a

kR

baE E (C.2.8)

where, using (1.3.2), (1.3.4) and (1.4.3),

2

22

10

21

2

2

a

a

k g

(C.2.9)

The open ended waveguide working TE10 mode displays a wide beam width, but displays a high reflection coefficient at the aperture. In order to reduce the reflection, the aperture must be flared to larger dimensions. The first pattern null will occur at approximately

E-plane b

Enull

arcsin2 and H-plane a

HNull 2

3arcsin2

Wide angle pattern details will diverge from those given in these expressions because no account is taken for aperture edge diffraction. Diffraction causes currents to exist on the aperture edge and the surface outside the waveguide near the aperture. C.2.3 Circular waveguide aperture The more accurate radiation pattern from an open circular waveguide aperture in the presence of

nm, modes can be calculated with the following relationships. [1].

TE modes E-plane pattern 90

jkRmmnm

mnmnm emkaJ

aJkkR

majE

sin

sin

sincos11

21 (C.2.10)

where = aperture plane reflection coefficient H-plane pattern 0

jkR

mn

mmnm

mnmnm emk

kaJaJ

kkR

kajE

cos

sin1

sincoscos

2 2

'1 (C.2.11)



468

TM modes E-plane pattern, 90

jkR

mn

mnmm

mnmnmnm em

k

aJkaJ

kkR

kajE

cos

sin1

sincoscossin2 2

'1

...(C.2.12) H-plane pattern, 0

0E

For the TE11 mode, the position for the first pattern null is given by the approximations

E-plane: anull

2

83.3arcsin and H-plane:

anull

2

33.5arcsin

E-plane 3db beamwidth: a

Edb

7.143 and H-plane 3db beamwidth: a

Hdb

6.183

E-plane 10db beamwidth: a

Edb

0.2510 and H-plane 10db beamwidth: a

Hdb

2.3210

The far-field gain:

25.10

apertureofarea

G for the aperture reflection coefficient 0 .

C.2.4 Diagonal horn with square aperture [3]. For the diagonal horn with side dimensions d , the field is developed as shown in Figure 3.4-1 and 3.4-2 from Chapter 3.

sind

u ;

22

2

2

cos4

1

coscos

sin

sinsin2,

u

u

u

udE y

(C.2.13)

22

2

2

sin4

1

sincos

cos

cossin2,

u

u

u

udE x

(C.2.14)

The total field will be

22 yx EEE (C.2.15)

For the principal planes of the diagonal horn, o45 or o135 planes, and we can write

2

221

2cos

2

2sin

22

u

u

u

u

E

(C.2-16)

If we now consider the 45 deg planes of the diagonal horn by setting 0 and 180o, we obtain

expressions similar to (C.2.7) and (C.2.8).



469

2

2

2

41

cos2

u

udE y

(C.2.17)

u

udE x sin2 2

(C.2.18)

substituting (C.2.17) and C.2.18) into (C.2.15),

the Co-pol pattern is

2

2

2

41

cossin2

2

u

u

u

udEEE

yx

co (C.2-19)

and the cross-pol pattern is

2

2

2

41

cossin2

2

u

u

u

udEEE

yx

co (C.2.20)

For the TE10 mode, the position for the first sidelobes and nulls and sidelobe levels are given by the approximations shown here: X and Y Principal Planes Diagonal 45 and 135 deg Planes

3db beamwidth: ddb

5.583 ddb

583

10db beamwidth: ddb

10110 ddb

9810

Position of 1st null: dnull

81 dnull

70

Position of 1st sidelobe: d

stSL

961 d

stSL

921

Level of the 1st sidelobe: 31db 19db

Position of 2nd null: d

ndnull

1222 d

ndnull

1222

Position of 2nd sidelobe: d

ndSL

1392 d

ndSL

1472

Level of the 2nd sidelobe 41db 24db Points of interest: 1. Rectangular/square apertures with uniform illumination possess a pattern with 1st sidelobe of about 14db. 2. Tapered illuminations prompt lower 1st sidelobe, and slightly wider main beam. 3. Circular apertures with uniform illumination possess a pattern with 1st sidelobe of about 17.5db. References: [1] S. Silver, "Microwave Antenna Theory and Design", MIT Radiation Lab. Series 1948 [2] F. Hyjazie, and R.Paknys, IEEE Antennas and Propagation Magazine, vol 44, No. 6, Dec 2002, pp 98-100. [3] A. W. Love, "Electromagnetic Horn Antennas", IEEE Press, 1976



470

D. General Information D.1 Exponentials, Logarithms, and db D.1.1 Concept of exponents Examples: 10 x 10 = 102 = 100 10 x 10 x 10 = 103 = 1000 Law of exponents: 102 x 103 = 102+3 = 105

1323

2

1010

110

10

10

63222232 1010101010)10( x

10001010)10( 366 21

D.1.2 Concept of inverse functions Consider the expression

x

xy

1 when 2

1,1 yx

Suppose we know what y is, but need to calculate what x is, then this expression needs to be rearranged

to solve for x .

y

yx

yyx

xxyy

xxy

1

1

)1(

When 21y , 1x ; also 2y , 2x

Plotting these two expressions on a graph:

Comparison of an Inverse Function Pair

-10

-8

-6

-4

-2

0

2

4

6

8

10

-6 -4 -2 0 2 4 6

Variable

Func

tion

y = x/(1+x) y = f(x)

x = y/(1-y) x = f -1(y)

By definition, the function )(1

xfx

xy

and the inverse is )(

11 yf

y

yx



471

D.1.3 Exponential function Suppose we consider xy 10 when 2x and 100y

If we did not know what the value of x was, we would need to write the inverse of this exponential

expression. This is written as yx 10log , the common logarithm to base 10.

Exponential form Logarithmic form 103 = 1000 log 1000 = 3 102 = 100 log 100 = 2 101 = 10 log 10 = 1 10o = 1 log 1 = 0 10-1 = 0.1 log 0.1 = -1 10-2 = 0.01 log 0.01 = -2 10-3 = 0.001 log 0.001 = -3 The log of a number between 1 and 10 will lie between 0 and 1. e.g., log 2 = 0.3010, and log 0.5 = -0.3010. How did we get these values for the log of 2 ?? Let us look at the results of investigation into sequences of numbers. Some functions are expressible as a series of terms. For example:

...!6!4!2

1cos642

xxx

x

...!5!3

sin53

xx

xx

...!6!4!2

1

...!5!3

cos

sintan

642

53

xxx

xxx

x

xx

and finally,

...!4!3!2

1432

xxx

xe x

For 71828182.2,1 1 eex

Writing xeN , the inverse of this function is known as Nx elog , or Nx ln where elog or ln is

referred to as the "natural logarithm" to base e . This means, if we have a number N , we can find its natural log as x , by looking into a tabulation of the

function xe for various x . Suppose we wish to operate with common logarithms only, then we can write xeN , take logarithms to base 10 of both sides of this equation

exeN x101010 logloglog

Reverse this logarithm procedure, or take the anti-logarithm

]434294482.0[log 1010 10 xexN



472

Let's perform a test: For 0.43429 ... x = 3.16

therefore 27617.7...43429.0

16.3x

Then proceed to calculate

34.1445...!3!2

132

27617.7 xx

xeeN x

Therefore 34.144510 16.3 or 16.334.1445log10

The "3" is called the characteristic, and the ”.16" is called the mantissa. Note that the magnitude of the characteristic is 1 less than the number of digits in the number N . Now we can handle "exponentiation" and its inverse operation "logarithm". So what do we do with all this ?? Suppose we have a series of numbers to multipy - 3.163 x 0.001297 x 0.9138 x 10.3674 = M Using "logs", we can write P = log 3.163 + log 0.01297 + log 0.9138 + log 10.3674 And the answer will be M = 10P Calculators have long since relegated "logarithm tables" to the library shelf. But let us look at the components again, and imagine they represent power levels of four different signals. The largest is 10.3674 watts The smallest is 0.001297 watts log 3.163 = 0.5001 or +0.5 Bells 5 deciBel or db log 0.001297 = -2.8871 or -2.9 B -29 db log 0.9138 = -.0391 or-.04 B -0.4 db log 10.3674 = +1.0157 or 1.0 B +10 db This means that the maximum level (10.3674 watts) is 10 - (-29) = +39 db larger than the smallest signal, or

4.7993001297.0

3674.10

watts

watts times larger.

db394.7993log10

Try plotting these power levels graphically - it becomes difficult to do on an ordinary linear scale. The db scale is much easier. If we wish to make a comparison with a reference 1 Watt power level, then 10.3674 Watts is 10.3674 times larger

i.e. 3674.101

3674.10

W

W and 10log 10.3674 = +10.15 dbW, and the smallest signal is -29 dbW.

Another commonly used "reference" is milliwatts. = mWWatts

1000

.

The largest signal is +40 dbm; the smallest signal is +1 dbm; the difference = 39db, as determined above.



473

D.2 Bessel Function Polynomial Approximations For some applications, the solution to circular waveguide aperture patterns becomes essential to the conceptual design. This will require use of the Bessel function. The following excerpt from the Handbook of Mathematical Functions [1] offers an easy to use approximation to many of the problems.

[1] M. Abramowitz and I. A. Stegun, "Handbook of Mathematical Functions", NBS Applied Mathematics Series", 55, June 1964



474

E. Reference Performance Documents E.1 Regulatory specifications for antenna pattern performance Excerpts of the most prominent and important of the independent requirements are provided here, for the simple reason that they are not readily available without paying a lot of money. They are subject to change, but for the moment they will provide adequately the general essence of performance requirements. ITU R S.580 Near-in radiation pattern sidelobe envelope ITU R S.465 Wide-angle radiation pattern sidelobe envelope ITU R S.732 Processing of sidelobe peaks exceeding the envelope FCC Document 47 CFR ch1 para 25-209 MIL Std 188-164 The MIL std sidelobe envelope requirement is identical to that indicatedd by the ITU. However, additional requirement is given on the matter of interference by intermodulation products. E. 2 Recommendation ITU-R S.580- 6

Radiation diagrams for use as design objectives for antennas of earth stations operating with geostationary satellites

(Question ITU-R 42/4)

(1982-1986-1990-1992-1993-1994-2003)

The ITU Radiocommunication Assembly,

considering a) that efficient utilization of the radio spectrum is a primary factor in the management of the geostationary-satellite orbit (GSO); b) that the side-lobe characteristic of earth-station antennas is one of the main factors in determining the minimum spacing between satellites and therefore the extent to which the radio spectrum can be efficiently employed; c) that the radiation diagram of antennas directly affects both the e.i.r.p. outside the main radiation axis and the power received by the side lobes; d) that the construction of antennas with improved side-lobe characteristics may be envisaged using current design techniques but that their practical applications may involve increase in cost; e) that the Radiocommunication Study Groups are studying the potential advantages of using antennas with improved side-lobe characteristics for a better utilization of the GSO,

recommends 1 that new antennas of an earth station operating with a geostationary satellite should have a design objective such that the gain, G, of at least 90% of the side-lobe peaks does not exceed:

dBilog25–29 G

(G being the gain relative to an isotropic antenna and being the off-axis angle in the direction of the GSO referred to the main-lobe axis). This requirement should be met for between 1° or (100 D) whichever is the greater and 20° for any off-axis direction which is within 3° of the GSO;



475

2 for an off-axis angle, , greater than the limits specified above, Recommendation ITU-R S.465 should be used as a reference (see Note 5);

0580-01

S

20°

20°

–3°

+3°

GSO(equatorial plane)

Antennamain-lobe axis

Earthstation

Satellitelongitude

Affectedzone

FIGURE 1

Example of a zone around the GSO to which the design objectivefor earth-station antennas applies

1° (or 100 D )

3 that the following Notes should be considered part of this Recommendation. NOTE 1 – This Recommendation primarily addresses the GSO sharing criteria. However, it must be emphasized that the application of this Recommendation should not prejudice the antenna characteristics concerned with frequency coordination between the FSS and terrestrial services (see Recommendation ITU-R S.465). NOTE 2 – When asymmetric beam or asymmetric aperture antennas are used, the side-lobe radiation in the direction of the GSO can be reduced if the minor axis of the beam (major axis of the antenna aperture) is oriented so that it is parallel to the GSO arc. In this case, the alignment of the antenna aperture axes relative to the GSO arc would facilitate the compliance with recommends 1 in the affected zone around the GSO arc as indicated in Fig. 1:

– for the aperture minor axis plane, Recommendation ITU-R S.465 should be complied with for any off-axis angle beyond 1° or (100 De), whichever is the greater but not exceeding 3°, where De is provisionally defined as the circular equivalent diameter using the aperture area of the asymmetric aperture antenna as given below:



476

/4ADe

where A is the aperture area of the asymmetrical antenna;

– for the aperture major axis plane, recommends 1 should be complied with for any off-axis angle beyond 1° or (100 De), whichever is the greater but not exceeding 2°, where De is provisionally defined above.

NOTE 3 – This Recommendation applies to antennas with D/ greater than or equal to 50. Further studies are required to determine a design objective for circular aperture antennas having a D/ less than 50, and also to confirm the definition of De for the asymmetric aperture antennas. NOTE 4 – The method of statistical processing of side-lobe peaks is dealt with in Recommendation ITU-R S.732. NOTE 5 – In those cases where there is discontinuity between this design objective Recommendation and the reference radiation patterns of Recommendation ITU-R S.465, the gain, G, of at least 90% of the side-lobe peak is defined as follows:

3.2620fordBi5.3–G

NOTE 6 – For the analysis of an antenna pattern for angles not specified in this Recommendation, additional mathematical expressions from Appendix 7 of the Radio Regulations may be used as a reference to represent the radiation pattern limits for less than 1° or (100 D), whichever is the greater. Further study is required to define the most adequate expressions for this purpose. NOTE 7 – Small earth-station antennas with improved main beam and side-lobe characteristics are being developed. It is indicated that the efficient use of the GSO may necessitate reflecting these improved characteristics in the ITU Radiocommunication Assembly texts and Recommendations. NOTE 8 – The performance objectives in § 1 have been met by off-set-fed type antennas operating in the 10-14 GHz with D/ 35 and by off-set-fed type receive only antennas operating in the 10.7-11.7 GHz band with D/ 22. NOTE 9 – Theoretical calculations supported by preliminary test results of the side-lobe radiation pattern, in the diagonal plane, for square microstrip array antennas with D/ 26 meet the current design objective of § 1. These tests were performed on an active array in the 14 GHz band. Further studies are required to confirm that this design objective can be applied to square microstrip phased array antennas.



477

E.3 Recommendation ITU-R S.465-5



478



479

E.4 Excerpt from FCC Document 47 CFR Ch. (10-1-97 Edition) containing para 25.209 and 25.134



480



481



482

E.5 Recommendation MIL Std 188-164a



483

E.6 EIA- 411- A Electrical and Mechanical Characteristics of Earth Station Antennas for Satellite Communications Chapter 6.8 Measurement Accuracy The accuracy of the measurement methods discussed here depend upon: a. The frequency of operation. The higher the frequency of operation, the larger the expected measurement error will be. b. The availability of accurately calibrated radio source at the test site - satellite or radio star/sun/planet c. The accuracy of reference loads d. The calibration of the feed network and connecting transmission line e. The type of receiver used for the measurement f. The effect of various mismatches, e.g., VSWR changes caused by the test equipment Reflector surface inaccuracies Antenna pointing/alignment errors g. Clear, calm weather Because these factors are, in general, different for each antenna installation, it is imposisible to set specific accuracy limits without specifying the details and location of the test antenna. However, in order to provide some insight into the error magnitudes, Table 6.8-1 shows typical estimated 3-sigma measurment errors that can be expected when using state of the art test equipment. The important constraint in this assessment of errors is given under "conditions". Over/under-stepping these conditions of measurement generally leads to rapid increase in error. Important Note: The following error budgets are not intended to provide freedom from the intent of a given specification. EIA - 411 Page 6-77



484

Table 6.8-1(a) Typical Measurement Accuracy for Earth Station Antennas Operating up to 15 GHz Parameter Method Condition Main Source of Error Measurement Notes 1. Pattern sidelobe envelope

Satellite pattern measurement

1. C/N as large as possible 2. Clear calm weather 3. Zero scintillation condition

4. N

NC

correction necessary

1. Antenna pointing accuracy _ 0.05db 2. C/N calibration 0.25db 3. Relative power level measurement error in range 0 to 70db 1.0db 4. Carrier level stability for the duration of the measurement 0.10db 5. Calibration of angular motion of the antenna 6. Calibration of the angular scale of the pattern recording 7. Receiver/analyzer system stability for duration of measurement 8. Polarization match errors

1. Take note of possible adjacent satellite interference 2. Refer to manufacturer's handbook for analyzer operation errors 3. Beware of near-field obstructions. These will degenerate pattern envelope and can be considered the main source of error 4. Azimuth pattern angle corrections are required 5. Take care of angle scale calibrations where linear drive mechanisms are involved

Table 6.8-1(b) Typical Measurement Accuracy for Earth Station Antennas Operating up to 15 GHz Parameter Method Condition Main Source of Error Measurement Notes 2. Gain Satellite

substitution See EIA-411 paragraph 6.4.1

1. For C/N <15db, correction required 2. Clear, calm weather conditions 3. Zero satellite-earth path scintillation conditions

1. Uncertainty in satellite flux density at test station _ 1.0db 2. Aspect ratio 0.25db 3. Path length loss 0.20db 4. Antenna pointing _ 0.05db 5. Signal generator accuracy 0.10db 6. Connecting waveguide calibration 0.05db 7. VSWR 0.20db 8. C/N calibration 0.25db Possible rss error 1.09db

1. Far field range with small ground effects 2. Dependence upon cooperation of SSM* equipment operating under dissimilar conditions 3. No freedom to choose frequency and power level 4. EIRP likely to be lower than expected, caused by aging TWTA on board satellites * SSM = Satellite System Monitor station

EIA - 411 Page 6-78



485

Table 6.8-1(c) Typical Measurement Accuracy for Earth Station Antennas Operating up to 15 GHz Parameter Method Condition Main Source of Error Measurement Notes 3. Gain Standard Gain

Horn See EIA-411 paragraph 6.4.2

1. For C/N <15db, correction required

1. Calibration of attenuator and connecting waveguide 0.20db 2. Calibration of SGH 0.30db 3. C/N calibration 0.25db 4. SGH pointing _ 0.05db 5. Antenna pointing accuracy 0.05db Possible rss error 0.44db

1. Variation in the downlink signal seen by both test and reference antennas, and therefore not affecting comparison measurement 2. Implementation difficult, since SGH and test aperture may need to be separated by large distance 3. The larger the gain difference between the test and reference antennas, the greater the error incurred

Table 6.8-1(d) Typical Measurement Accuracy for Earth Station Antennas Operating up to 15 GHz Parameter Method Condition Main Source of Error Measurement Notes 4. Gain Pattern

beamwidth See EIA-411 paragraphs 6.4.3 and 6.4.5

1. For C/N <30db, correction required Requires mandatory complementing in-plant pattern measurement (type test acceptable) Applicable for 65% to 70% efficiency antennas

1. Antenna pointing accuracy _ 0.05db 2. Calibration of angular scale 0.25db 3. Calibration of relative pattern power levels 0.25db 4. Error in approximation _ 0.40db 5. Surface accuracy calibration 0.10db 6. Feed loss calibration 0.05db Possible rss error 0.55db

1. Part of normal pattern measurement routine 2. Requires no extra/special equipment 3. Requires separate measurement of feed loss(use inplant test data) and reflector system surface accuracy 4. Method applicable only for high efficiency antennas 5. Azimuth pattern correction necessary See EIA-411 paragraph 6.2.2

EIA - 411 Page 6-79



486

Table 6.8-1(e) Typical Measurement Accuracy for Earth Station Antennas Operating up to 15 GHz Parameter Method Condition Main Source of Error Measurement Notes 5. Transmit uplink Gain

Satellite link power See EIA-411 paragraph 6.4.2

1. For C/N <20db 2. Clear, calm weather conditions 3. Zero satellite - earth path scintillation conditions

1. Uncertainty in satellite flux density at SSM* _ 1.00db 2. SSM* gain calibration 0.50db 3. Aspect ratio SSM* 0.25db 4. Aspect ratio test antenna 0.25db 5. Path length loss test antenna 0.20db 6. Antenna pointing accuracy 0.20db 7. Antenna pointing _ 0.05db test antenna 8. Antenna pointing _ 0.05db test antenna 9. D/L power measurement SSM* 0.50db 10. U/L power measurement test antenna 0.50db 11. C/N measurement analyzer at SSM* 0.25db Possible rss error 0.44db

1. Far-field range measurement with low level ground effects 2. Dependence upon cooperation of SSM* equipment, operating under dissimilar conditions 3. No freedom to choose frequency or power level 4. Low latitude test sites generally suffer satellite - earth link scintillation, causing additional uncertainty 5. Because two antennas are involved, number of error sources doubled * SSM = Satellite System Monitor station

Table 6.8-1(f) Typical Measurement Accuracy for Earth Station Antennas Operating up to 15 GHz Parameter Method Condition Main Source of Error Measurement Notes 6. LNA Noise Temperature

Hot/Cold load See EIA-411 paragraph 6.5.1

1. Th - Tc = large Generally desirable to have LNA y-factor yp > 2.5db Requires mandatory complementing in-plant pattern measurement (type test acceptable) Applicable for 65% to 70% efficiency antennas

1. Calibration of cold load 1.0 K 2. Measurement of Th 2.0 K 3. VSWR 1.0 K 4. y-factor 3.4 K Possible rss error 4.2 K

1. Cold load generally consisting of a cryogenically cooled termination 2. Due to drift in the mixer/preamplifier, an average of several measurements at each frequency needs to be made

EIA - 411 Page 6-80



487

Table 6.8-1(g) Typical Measurement Accuracy for Earth Station Antennas Operating up to 15 GHz Parameter Method Condition Main Source of Error Measurement Notes 7. Antenna system noise temperature Ts

Hot load/Sky See EIA-411 paragraph 6.5.2

1. Dependence on clear calm weather 2. Measurements at least 5o above local horizon

1. Measurement of Th 2.0 K 2. Sky noise interference 4.0 K 3. y-factor 3.4 K Possible rss error 5.6 K

1. Sky noise temperature interference highly site dependent 2. Dependence on relative humidity at the test station

Table 6.8-1(h) Typical Measurement Accuracy for Earth Station Antennas Operating up to 15 GHz Parameter Method Condition Main Source of Error Measurement Notes 8. Antenna system noise temperature Ts

Hot load/Sky See EIA-411 paragraph 6.5.2

1. Dependence on value of Tp and Ts

1. Calibration of LNA 4.2 K 2. Measurement of Ts 5.6 K Possible rss error 7.0 K


Table 6.8-1(i) Typical Measurement Accuracy for Earth Station Antennas Operating up to 15 GHz Parameter Method Condition Main Source of Error Measurement Notes 9. G/T Satellite C/N

See EIA-411 paragraph 6.6.1

1. For C/N < 15db correction is required 2. Bandwidth as narrow as possible

1. SSM and Test 0.05db antenna pointing 0.05db 2. EIRP measurement _ 1.00db 3. Aspect ratio 0.25db 4. Path loss 0.20db 5. C/N calibration 0.25db Possible rss error 1.17db


EIA - 411 Page 6-81



488

Table 6.8-1(j) Typical Measurement Accuracy for Earth Station Antennas Operating up to 15 GHz Parameter Method Condition Main Source of Error Measurement Notes 10. G/T Radio star

See EIA-411 paragraph 6.6.2 Note: Not applicable for frequencies above 6 GHz communication band

1. For C/N <20db 2. Clear, calm weather conditions 3. Elevation angle >15o for star y-factor (ystar) measurement

1. y-factor 0.05db 2. Radio star flux density 0..43db 3. Source shape and polarization 0.02db 4. Atmospheric loss 0.08db 5. Antenna deformation 0.05db 6. Antenna pointing accuracy _ 0.05db 7. Temperature calibration 0.06db 8. Relative gaIn calibration 0.025db 9. G/T extrapolation 0.25db Possible rss error 0.47db

1. Large errors possible unless many points are measured to allow reasonable statistical evaluation 2. If sufficient data is taken, this method will also provide information about calibration of antenna readouts a. Pointing accuracy b. Gain variation as a function of antenna pointing

Table 6.8-1(k) Typical Measurement Accuracy for Earth Station Antennas Operating up to 15 GHz Parameter Method Condition Main Source of Error Measurement Notes 11. G/T A. Gain

(Method No.1) and noise temperature (No.6) measured separately B. Gain (Method No.2) and Ts C. Gain (Method No. 3) and Ts

1. Assume Ts ~ 100K 2. As many points as possible on frequency and satellites

1. Ts 0.24db 2. G 1.09db Possible rss error 1.12db Possible rss error 0.50db Possible rss error 0.74db

A. Direct satellite measurements characterized by large errors B. The standard gain antenna method provides measurement with least error C. If 180o patterns in at least three polarization planes have been measured, pattern integration may be carried out for G and T with reduced errors, estimated at 0.4db

EIA - 411 Page 6-82



489

6.9 Comments The important aspect of these measurements is to realize that satellite-based meassurements, usually performed on one satellite only, give limited data about the performance of the antenna. This is because of the fact that the antenna is tested while looking only into one part of the sky and a limited number of discrete frequencies. For immediate operational purposes, this is perfectly acceptable, even desirable. However, in many instances operational requirments may force the use of another satellite with the antenna pointed into a different part of the sky, and it is possible that performance changes will become apparent. These changes can be attributed to: 1. Deformations in the reflector system 2. Changed system noise temperature caused by a variable sky and atmospheric absorption 3. Polarization adjustment Measurements on several widely spaced satellites would be desirable, but probably not possible. Some of this difficulty can be overcome by using a radio star as independent boresight to characterize the antenna under various potential operational conditions. The G/T measurement described here allows measurements at any frequency and a large range of antenna pointing angles. The effects of reflector deformations caused by varying gravitational and light wind loads, and in the case of beam waveguide feeds, the influence of reflector alignment inaccuracies as a function of antenna pointing will all be included. In fact, when compared with the accurately known optical positions of the radio sources, the antenna pointing can be calibrated. Again the cautions listed in paragraph 6.6.2 as to which radio stars/sun/planet may be used for a given antenna system must be borne in mind. EIA - 411 Page 6-83 End of EIA - 411 document

Index


490

Air Supported Radomes 388 Angular extent 437 Antenna Axis Configurations 285 elevation over azimuth 285 X-Y 287 cross-elevation over elevation 287 declination over hour angle 288 Antenna Configurations 282 Antenna Efficiency Components 49 diffraction loss 51 feed blockage 50 performance features 51 subreflector blockage 50 subreflector support structure blockage 50 Antenna Noise Temperature 179,358,361 sky y-factor 358 Antenna Noise Temperature Components 182 antenna noise temperature 185 noise in reflector and feed system 186 sky noise 182 sky noise temperature vs frequency and elevation angle 184-185,190 Antenna Patterns, Characteristics of 69 beamwidth - 3db, 10db, ndb 72,76 sidelobe envelope 70 sidelobe location 72,73 Antenna Pattern Gain 73 approximate beamwidth gain formula 74 beamwidth constant 76 gain variation 75 pattern integration 73 rms surface accuracy 76 Antenna Patterns - Sum, Difference, Cross-pol 360 Antenna Site Interference Issues 401 interfacility links 402 RF leakage 402 terrestrial interference 401 Antennas with Simultaneous Multi-band Feeds 250 Antenna System G/T, Noise Temperature, and Gain 182,362 Aperture patterns 465 Array Analysis and Design 241 4-horn “cross” Array 231 4-horn “corner” Array 233 corner array 243 cross array 243 difference between array element pairs 242 five horn monopulse array 245 sum of array elements 242 Array, Integrated 5-horn 233 Aspects of Cross-polarization in Antennas 161 cross-pol under the 1db points 166 far field 162 near field 161 polarization sensitivity 162 variation of cross-pol with pol angle 164 Attenuation in waveguide 445 conductivity 446 resistivity 445 skin depth 445 Beam-waveguide 259 Bessel Function Polynomial Approximations 473

Boltzmann constant 177, 416 Cassegrain and Gregorian Configurations 46 equations parabola 40,47 hyperbola 47,48 ellipse 47,48 look angle 48 optical magnification 48 subreflector 48 Cavity-backed Dipole 101 backfire feed 101 dual band application 104 dual mode 102 dual polarized 103 splash-plate feed 101 sum and difference mode 104 Celestial coordinate system and time 431 celestial coordinates 432 celestial sphere 431,433 declination 428 ecliptic 434 epoch 433 first point of Aries 434 local hour angle 431 Newcombe equation of time 433 precession 433 right ascension 431 sidereal time 431 solar time 431 star positions 433 vernal equinox 434 Coaxial Lines 14 Combined CP and LP Tx/Rx Feed Configuration 141 Combined Dual Polarized Tx/Rx Feed Configuration 139 Concentric Aperture Horn 104,254 Conical Scan 216 Correction for atmospheric attenuation 440 Correction for star polarization 441 Corrugated Horn 92 comparison with multimode horn 93 corrugation groove geometries 93-96 Circular waveguide aperture patterns 467 TE and TM modes E and H plane 467-468 Circular waveguide attenuation features of waveguide loss 449 TEmn modes 449 TMmn modes 449 Cross-pol Matched Feed System for Single Off-set Reflector Applications 173 cross-pol compensation 174 Customer Site Preparations 345 Declination–over–Hour Angle antenna 427 hour angle 427 declination 428 Design of Reflector Panels 299 Determination of Antenna Gain and G/T Correction factors angular extent of radio stars 418 atmospheric absorption 418 beamwidth correction 419 polarization correction 419

Index


491

time dependence of the star flux density 418 Data anlysis basis for measurement 416 radio star flux densities 417 final expression for G/T 420 antenna system noise temperature 420 antenna system gain 421 correction due to receiver noise 422 using calibrated radio stars 411 Diagonal horn with square aperture 89,468 co-pol and cross-pol 468-469 Difference Patterns 354 Dragonian 69 Dual Aperture Feeds with FSS 255 Dual Linear Polarization - Receive Only 116 Feed Design and Configurations 116 Linearly Polarized Tx/Rx 116 Linear Polarized Rx and Tx 120 diplexers 121 Two Orthogonal Rx and One Tx 117 symmetrical OMT 118 Dual Offset Antennas - Cassegrain and Gregorian 66 design equations 66,68 minimum cross-pol 68 Earth Station Site Planning 397 Effects of Reflector Errors 335 polarization twist Elevation-over-Azimuth pattern angle correction 428 Elevation-over-Azimuth antenna 424 equatorial radius 424 geostationary orbit 425 local horizon 426 local zenith 426 mean radius of earth 424 meridian of satellite 426 polar radius 424 EIRP and Power Density 210 Electronic Conical Scan 216 Equivalent Noise Temperature 177 Exponentials, logarithms, and db 470 exponential function 471 exponents 470 inverse functions 470 Factory Testing 324 Feed Horn 79 E-plane 80 H-plane 80 Feed Horn, Rudimentary Design Considerations 105 Feed Horn Window Considerations 366 Feed insertion loss determination 409-410 Feed Pressurization Principles 367 cycle time for pressurization system 370 Feed Protection hydrophobic coating 376 Rain, Mist, Snow and Ice, and Birds 374 rainblower 374 sensor 375 window 375 Feed System – Sample Measurements 328-331 Feed System 2-Port Circularly Polarized Rx/Tx 131

performance features 132 Feed System 4-port CP 133 OMT with Rectangular Horn 130 performance features 130 Septum OMT 129 performance features 129 Feed System axial ratio 326 dimensional check 327 feed patterns 325 insertion loss 326 mechanical details 327 passive intermodulation – PIM 327 Performance Features 324 polarization control 327 polarization discrimination 326 port-to-port isolation 326 pressurization leak 327 return loss 326 RF leak rate 327 time or group delay 327 Formal On-site RF Antenna Tests 360 Finned Horn 97 Gain 357 Gain, Concept of 34 aperture pattern 35 beam 36 collimated beam 36 degree of bundling 36,37,77 open-ended waveguide aperture 35 Gain, Determination of 36 Gain Relative to Isotropic 37 isotropic source 37 pattern gain 38 Horn reflector 66,78 IFL Signal Path Integrity 346 Influences of Weather 318 Interference in Antennas 191 corrective filter 192 sources of interference 191 Interference by the Transmitter 192 Interference by Tx Signal Power 194 transmit rejection filter, TRF 194 Interference due to Tx Noise Power 196 decrease in G/T 196 receive band rejection filter RRF 198 Large Antenna Beam Waveguide 259 beam waveguide reflector geometries 262 quasi beam waveguide 265 pol rotation 261 Link Analysis 205 C/N 207 eirp 206 path loss 206 Uplink Analysis 205 Downlink Analysis 208 C/N 209 Main Reflector Fabrication 300 fiberglass and carbon fiber lay-ups 305 machined panels 305

Index


492

stretched panels with “zees” 300 stretched panels with precision profiled radials 303 stretched panels with honeycomb 303 spinnings 304 Maximum signal “Search and Track” Methods 215 Measurement Accuracy 365,483-488 Mechanical Layout Concepts Complex Feed Systems 319 sample feed design problem 319 Mitzugutch condition 68 Monopulse Detection Methods 237 pseudo monpulse 237-239 Monopulse tracking sensitivity 361 Transmit Uplink Gain and eirp Stability 365 Multi-beam Antennas 267 declination over hour angle 267-268 Multi-frequency Corrugated Horn 94 groove depth constraints 95-96 groove designs 96-97 Noise in Antennas 176 Noise in a Satellite – Earth Station Link 181 Noise Figure 178 Noise Mechanisms 176 Noise Power 176 Obstructions and Safety 397 Radiation Hazard 393 beam broadening 394,395 far field 393 Fraunhofer 393 Fresnel 393 Fresnel-Fraunhofer transition point 394 near field 393 power density curve 396 Off-set Reflector Antennas 61 Outdoor Test Range 337 advantages of range measurements 341 ground reflections 338 length 337 Panel Alignment 316 microwave interferometry (holography) 318 photogrammetry and precision reference scale 317 theodolite and precision tape panel setting 316 Passive Intermodulation in Antennas 199 amplitude of PIMs 202 causes of PIMs 203 second order PIM 200 specific cases of PIM frequencies 201 third order PIM 200 Pedestal Alignment Check 345 Phase-amplitude Monopulse monopulse 219 tracking modes 220 TM01 + TE01 mode 219,220 TE21 mode 221 Phase Fronts and Phase Errors 82 phase center 82,84 phase error 83 propagation velocity 83 Pointing Accuracy 306 beam deviation factor 309 beam tilt due to

feed translation 313 main reflector translation 310 main reflector rotation 311 subreflector translation 311 subreflector rotation 312 defocussing due to axial displacement of the feed 314 subreflector axial displacement 314 position encoder error 308 reflector deformation 308 thermal and loads 308 Pointing Angles to Geosynchronous Satellites 424 Pointing Angles to Radio Star Positions 431 Polarization Requirements for Monopulse Functions 237 Polarization 149 axial ratio addition 156-161 circular polarization 150 cross-pol vector addition 157 discrimination 27 elliptical polarization 153 differential amplitude 153 differential phase shift 154 linear polarization 149 Polarization in Offset Antennas 166 CP beam displacement (squint) 168-169 dual offset reflector 170 cancellation of cross-pol single offset with prime focus feed 167 Polarization Rotation and Switching 133 90 deg Differential Phase Shifter 134 CP/LP Selection 134 CP Adjust 138 CP/LP Selection - 2-port Rx/Tx Feed 138 180 deg Differential Phase Shifter 135 CP/LP and LP Angle LP Angle Adjust Only 137 branch-line 180 deg phase shifter 135-136 branch-line 90 deg phase shifter 136 Polarization twist 428 Positional geometry of the sun over the earth 434 Power handling of waveguides 452 convective loss 454 effective conductivity 453 thermal limits 453 radiant loss 454 Stefan-Boltzmann constant 454 voltage breakdown 452 Preliminary RF Checks and example Difficulties 349 Pretest Preparations 347 angular range limits for antenna patterns 347 azimuth correction 347 applicability of radio star measurements 348 Prime-Focus Antenna Efficiency Components 41 blockage 43 feed terminal loss 45 illumination loss 42 phase error loss 42 polarization loss 43 reflection loss 45 spillover loss 43 reflector panel loss 45 Prime Focus Horn 100

Index


493

Protecting the Feed against the Elements 366 feed pressure leak rate 367-371 Pyramidal and Conical Horn 84 evaluation of feed horn patterns 85,86 aperture efficiency 87 general pattern requirements for feed 88 spillover efficiency 86 look angle 84 Quad-ridge Horn 99 Radiated Fields 6 circular polarization 6 elliptical polarization 7 linear polarization 6 reflection 8 reflection coefficient 11 return loss 10,11 vswr 10,11 Radio Star Information 435 flux density decay 435 Jansky 435 Star flux change with frequency spectral index 437 decay with time 435 Star flux densities 435 Radio Star Track Check 358 mode spikes 359 return loss 359 star y-factor 358 Radio Waves 1 charge 1 frequency 3 moving charges 1 moving fields 1 radiation 3 electric dipole 4 electric field 1,3,4 electromagnetic wave 4 magnetic dipole 5 magnetic field 1,3,4 wavelength 3 Radomes 377 attributes 391 comparative radome performance 391 reasons for use 390 transmission loss 377,390 types of radomes 377 Rectangular waveguide attenuation 446 dielectric constant 447 intrinsic impedance 447 magnetic permeability 447 Reflector Accuracy 297 half path length error 299 path length error 298 rms 299 Reflector Geometries 295 aperture area 296 parabolic arc length 296 parabolic profile 296 side projected area 296 total surface area 296 Reflector Support Structures 291

design of radials 292 equivalent steady state wind velocity 294 equivalent wind pressure 295 gust wind velocity 294 mean wind velocity 294 wind loads 293-295 Reflector System 331 Reflector and Feed System Mechanical Alignment Check 345 Regulatory specifications EIA-411- A 483 FCC 25.209 479 FCC 25.134 479 ITU-R S.580-6 474

ITU-R S.465-5 477 MIL Std 188-164 482

Ridged waveguide 460 attenuation 462 bandwidth 461 breakdown voltage 464 cut-off wavelength 461 cw power handling in rectangular waveguide 464 power handling in ridged waveguide 463 ridge rounding effects 463 standard rectangular waveguide attenuation 463 Ring-Focus Antenna 58 performance features 60 Sandwich Radomes 381 Selectable Multi-feed Systems 256 Signal-to-Noise Ratio 176 Signal velocity in waveguide 442 cut-off wavelength 442,443 group velocity 442-443 guide wavelength 442 phase velocity 443-445 Single Aperture Feed Horn 250 corrugated horn groove depth 251-252 exclusion zones 252 Single Circular Polarization Receive Only Feed Configurations 122 cross-pol 122 polarization discrimination 122 voltage axial ratio 122 OMT + 90 deg Power Divider 123 performance features 124 Differential Phase Shifter with OMT 124 differential phase shifter 124,125 performance features 124,125,126 Single Linearly Polarized Example Satellite Link 110 Linear Polarization - with Polarization Rotation 114 Rx Feed Design and Configurations 110 Single QJ and Magic Tee Feed Network Layout 140 Sky Noise Temperature Variation with Ambient Temperature and Humidity 190 Smooth-walled Multimode Horn 90 comparison of E and H plane patterns 88 Potter horn 91 Solid Laminate Radomes 386 Space Frame Radomes 381 Single Offset Reflector Antenna 60

Index


494

beam squint 64 cross-pol 65 features 62 Single Reflector Antenna 39 aperture angles 40 angular field of view 40 effective magnification 40 F/D 40 focus 39,40 parabola 39 parabolic reflector 39 radiating aperture 39 Shaped Reflector Design Considerations 52 performance features 58 Standard waveguide features and characteristics 455 mode diagrams 456-459 Stefan-Boltzmann constant 454 Step Track 215 Structural Alignment 315 orthogonality 316 azimuth axis verticality 315 structural deformation 314 causing degradation in gain 315 Subreflector Fabrication 306 Sum Patterns 349 Sun Outage 430 diameter of the sun’s disk 430 outage time 430 TE21 mode Coupler Design Concepts 221 case study 225 circular polarization 223 linear polarization 222 Location, Setup, and Function Check system performance study 227 reference path 228 error path 228 tracking slope in the presence of noise 230 tracking slope 224 tracking jitter 225 Test Equipment 349 Transmit Uplink Gain and eirp Stability 365 Terminal Characteristics, Feed System 143 Axial Ratio and Cross-pol 146 Insertion Loss 146 Polarization Discrimination 146 Port-to-Port Isolation 146 Signal Delay Time 147 VSWR - Effect of Multiple Contributions 144 Practical Matching Techniques 145 Torus 270 beam deviation factor 273 declination difficulty 272 declination beam shift 273 off-axis feed settings 272 performance 276 no scan loss 279,280 with scan loss 279,280 phase aberrations 274

siting the torus to other latitudes 275 Transmission Line 11 development of waveguide 12 free space propagation 11 propagation in transmission lines 13 TEM-mode waves 13 TE-mode waves 13 TM-mode waves 14 Twin QJ Feed System Layout 140 Types of Transmission Line 14 Waveguide flange design 18,19 propagation modes 16 surface current distributions 17 Waveguide Characteristics Circular 28,449 Waveguide Modes TE-modes 29,449 TM-modes 30,449 attenuation 448-449 cut-off wavelength 29,449 Rectangular 15,445 Waveguide Modes TE-modes 16 TM-modes 17 attenuation 445-447 cut-off wavelength 16,17,445 skin depth 18 Waveguide Components Circular 31 circular to rectangular transition 31 Quadrature Junction – QJ 33 symmetrical coupler 31 symmetrical OMT 32 Waveguide Components Rectangular 19 bends 20 cross-guide coupler 25 directional coupler 23,24 OMT 25 frequency selective 28 performance features isolation 27 polarization isolation 27 return loss 27 transformers 21 90 deg hybrid 22 magic tee 21 power divider 21 symmetrical OMT 32 septum OMT 128 unbalanced OMT 26 Y-junction OMT 26 Waveguide System Dehydration 372 dehydrator 373 Wideband Feed Horn 254 Zero Signal Track Methods 219