Practical Issues of Using Negative Impedance Circuits as ... · Practical Issues of Using Negative Impedance Circuits as an Antenna Matching Element by Fu Tian Wong B.E. (Electrical

Practical Issues of Using Negative Impedance Circuits

as an Antenna Matching Element

by

Fu Tian Wong

B.E. (Electrical & Electronic, First Class Honours),

The University of Adelaide, Australia, 2011

Thesis submitted for the degree of

MMaasstteerr ooff EEnnggiinneeeerriinngg SScciieennccee

In

School of Electrical and Electronic Engineering

The University of Adelaide, Australia

June 2011

Copyright © 2011 by

Fu Tian Wong

All Rights Reserved

Page i

Contents

Contents ............................................................................................................................. i

Abstract ............................................................................................................................ iii

Statement of Originality .................................................................................................... v

Acknowledgments ........................................................................................................... vii

Thesis Conventions .......................................................................................................... ix

List of Figures .................................................................................................................. xi

List of Tables.................................................................................................................. xiii

1 Introduction and Motivation ..................................................................................... 2

1.1 Introduction ........................................................................................................ 2

1.1.1 Limitations of small antennas ..................................................................... 2

1.1.2 Other potential methods .............................................................................. 3

1.2 Motivation .......................................................................................................... 4

1.2.1 Broadband matching network ..................................................................... 4

1.3 Thesis Overview ................................................................................................. 7

2 Negative Impedance Converters ............................................................................. 10

2.1 Introduction ...................................................................................................... 10

2.2 Linear analysis .................................................................................................. 10

2.2.1 NIC Realisation ......................................................................................... 11

2.2.2 Analysis with and without parasitic capacitance ...................................... 17

2.3 Matching Performance Using a Simple Negating Capacitor ........................... 22

2.4 Three element negation network ...................................................................... 26

2.5 Chapter summary ............................................................................................. 30

3 Stability concerns .................................................................................................... 32

3.1 Introduction ...................................................................................................... 32

3.2 NIC characteristic ............................................................................................. 32

3.3 Stability Analysis ............................................................................................. 34

3.4 Circuit Modification ......................................................................................... 42

3.5 Chapter Summary ............................................................................................. 56

4 Effects of Non-idealities ......................................................................................... 58

4.1 Transistor Mismatch and Hfe Variations .......................................................... 58

4.2 Temperature Variations .................................................................................... 62

4.3 Supply Voltage Variations ............................................................................... 63

4.4 Sensitivity Analysis .......................................................................................... 66

4.5 Chapter Summary ............................................................................................. 70

5 Noise Considerations .............................................................................................. 72

5.1 Introduction ...................................................................................................... 72

5.2 Internal noise .................................................................................................... 72

5.3 External noise ................................................................................................... 76

5.4 Chapter summary ............................................................................................. 82

6 Non-linear Analysis ................................................................................................ 86

6.1 Introduction ...................................................................................................... 86

6.2 Intermodulation Distortion and Numerical Modelling ..................................... 87

6.3 Broadcast Stations ............................................................................................ 96

6.4 Theoretical or Expected IMD Noise Levels ..................................................... 98

6.5 Comparison with External Noise...................................................................... 99

6.6 Chapter summary ........................................................................................... 101

7 Conclusion ............................................................................................................ 104

Page ii

7.1 Results and Conclusions ................................................................................. 104

Appendix A ................................................................................................................... 109

Appendix B ................................................................................................................... 111

References ..................................................................................................................... 113

Page iii

Abstract

In the design of antenna systems, it is well known that there are trade-offs between

bandwidth and size. As the size of an antenna reduces, in proportion to wavelength,

there is a reduction in bandwidth. Wavelength at HF is of the order of tens of meters

and so practical HF antennas either have narrow bandwidth or are very large in size.

This conclusion holds when passive matching circuits are used, but it is possible that

active circuits could provide improved bandwidth. Negative Impedance Converters

(NICs) are active circuits that provide a promising avenue for achieving a high

bandwidth with electrically small HF antennas. This thesis focuses on tackling the

practical issues of using NIC based matching networks for HF reception.

The work presented in this thesis contributes to the research on NICs as HF matching

networks in several ways: (i) the interaction of the environment with the non-linearity in

the NIC circuit; (ii) a comparison between the external and internal noise effects; and

(iii) the stability of the NICs when operated as matching circuits at HF frequencies.

In this thesis, a brief introduction is presented to the previous work to reduce the size of

antennas. This includes a short summary on the development of the NIC and its

application as a matching network. The thesis then continues with a theoretical analysis

of the NIC and its application as an antenna matching circuit.

The thesis also provides an investigation on various practical issues namely the stability

of the circuit, device variations, noise and the effects of non-linearity. It was found that

device variations, noise and non-linearity did not pose a serious problem. Stability,

however, was found to be an important issue and that the NIC circuit had to be carefully

loaded to maintain stability. This research is a contribution towards the use of NICs in

HF receive systems and could help bring to fruition the dream of small sized HF

antennas with high bandwidth. In particular, HF radios for domestic purposes could

benefit from such a research outcome.

Page iv

Page v

Statement of Originality

I, Fu Tian Wong, certify that this work contains no material that has been accepted for

the award of any other degree or diploma in any university or other tertiary institution

and, to the best of my knowledge and belief, contains no material previously published

written by another person, except where due reference has been made in the text.

I give consent to this copy of the thesis, when deposited in the University Library, being

available for loan and photocopying, subject to the provisions of the Copyright Act

1968.

I also give permission for the digital version of my thesis to be made available on the

web, via the University’s digital research repository, the Library catalogue, and also

through web search engines, unless permission has been granted by the University to

restrict access for a period of time.

_________________ ________________

Signed Date

Page vi

Page vii

Acknowledgments

I am privileged with the opportunity to undertake such a challenging but rewarding

Masters Research. It is indeed a gratifying experience to see this research through from

the beginning to the end. I extend my sincerest thanks to my family, friends, colleagues

and supervisors for their constant support.

I sincerely thank my supervisor, A/Prof Chris Coleman, for his constant guidance and

encouragement throughout my Masters candidature. I am immensely grateful for all the

time that he has dedicated for discussions on my work. I would also like to deeply thank

my research co-supervisor, Dr Said Al-Sarawi, for reviewing my research and providing

fruitful insights during our discussions. Further, I would like acknowledge the staff of

the School of Electrical and Electronic Engineering at the University of Adelaide,

particularly Mr Danny Di Giacomo and Mr Pavel Simcik and the administrative team

for their assistance.

For my friends who have seen my ups and downs, encouraged and prayed for me

throughout this journey, thank you very much. I thank my family for their unconditional

love, support and prayers. This research could not have been completed without them. I

would like to thank God for providing me with wisdom and help from all the people

listed above, and many others whom have been a great support in many ways.

Fu Tian Wong (June 2010)

Page viii

Page ix

Thesis Conventions

Typesetting

This thesis is typeset using Microsoft Word 2007.

The fonts used in this thesis are Times New Roman and Arial.

Referencing

The referencing and citation style adopted in this thesis are based on the Institute of

Electrical and Electronics Engineers (IEEE) Transaction style.

For electronic references, the last accessed date is shown at the end of a reference.

Units

The units used in this thesis are based on the International System of Units (SI units).

Prefixes

In this thesis, the commonly used numerical prefixes to the SI units are “p” (pico; 10-12),

“n” (nano; 10-9), “µ” (micro; 10

-6), “m” (milli; 10

-3), “k” (kilo; 10

3), “M” (mega; 10

6)

and “G” (giga; 109).

Spelling

The Australian English spelling is adopted throughout this thesis

Page x

Page xi

List of Figures

Figure 1 : Non-Foster circuit reactance cancellation ........................................................ 5

Figure 2 : Time harmonic analysis of antenna system. Antenna represented by a series

RC component and a voltage source. .............................................................................. 10

Figure 3 : (a) Basic NIC circuit as proposed by Sussman-Fort [20] (b) Bipolar Junction

Transistor equivalent circuit. ........................................................................................... 11

Figure 4 : Small signal analysis (excluding rπ) ............................................................... 12

Figure 5 : Small signal analysis (including rπ) ................................................................ 14

Figure 6 : Small signal analysis (Including parasitic capacitance) ................................. 18

Figure 7 : A BJT implementation of the negative ‘capacitor’ ........................................ 24

Figure 8 : Simulation results of a 2 meter dipole by 4NEC2+ program ......................... 25

Figure 9 : Equivalent capacitor representing the antenna's reactance (Using a first order

approximation) ................................................................................................................ 25

Figure 10 : Equivalent resistor representing the antenna's resistor (Using a first order

approximation) ................................................................................................................ 25

Figure 11 : Simple three element network to represent antenna's reactance across 3-

20MHz ............................................................................................................................ 27

Figure 12 : The reactance of the three element network (blue curve) reasonably

resembles the reactance of the antenna (red curve) ........................................................ 29

Figure 13 : NIC’s two ports terminated by ZL1 and ZL2. One port will be Open Circuit

Stable while the other will be Short Circuit Stable (adopted from [24]). ....................... 33

Figure 14 : Circuit setup for Rollet Factor simulation ................................................... 35

Figure 15 : Rollet Factor simulation result .................................................................... 35

Figure 16 : Reflection coefficient (S11) as seen from the receiver................................ 36

Figure 17 : Circuit setup for antenna port reflection coefficient (S11) simulation ........ 37

Figure 18 : Reflection coefficient (S11) as seen from the antenna ................................ 38

Figure 19 : Circuit setup for transistor base reflection coefficient (S11) simulation ..... 39

Figure 20 : Reflection coefficient (S11) as seen the receiver side transistor’s base and

the antenna side transistor base respectively ................................................................... 40

Figure 21 :(a) Transient Analysis and (b) Fourier Series of the voltage at the receiver

(labelled Vout in the circuit) ........................................................................................... 41

Figure 22 : Modified NIC circuit ................................................................................... 43

Figure 23 : Reflection coefficient (S11) as seen from the receiver (a) and antenna (b)

respectively ..................................................................................................................... 44

Figure 24 : Reflection coefficient (S11) as seen the receiver side transistor’s base (a)

and the antenna side transistor base (b) respectively ...................................................... 45

Figure 25 : Transient Analysis (a) and its Fourier Series (b) of the voltage at the

receiver ............................................................................................................................ 46

Figure 26 : Transient Analysis circuit setup .................................................................. 47

Figure 27 : Transient Analysis (a) and its Fourier Series (b) of the voltage at the

receiver ............................................................................................................................ 48

Figure 28 : Imaginary part of the input impedance of the NIC with 1:1 transformer .... 49

Figure 29 : Reactance curve of an ideal negative 27pF capacitor.................................. 50

Figure 30 : Imaginary part of the input impedance of the NIC with a transformer as

seen from the receiver ..................................................................................................... 50

Figure 31 : Real part of the input impedance of the NIC as seen from the receiver ...... 51

Figure 32 : Circuit setup for stability sensitivity due to receiver load ........................... 52

Page xii

Figure 33 : Reflection coefficient as seen from antenna with varying receiver load (Rx)

......................................................................................................................................... 53

Figure 34 : Reflection coefficient as seen from the base of the antenna-side transistor

with varying receiver load (Rx) ...................................................................................... 53

Figure 35 : Source Follower Circuit Design (note: Vbuff = 7.0 V) ............................... 54

Figure 36 : Real part of the input impedance of the overall NIC circuit ....................... 55

Figure 37 : (a) Reactance (without buffer circuit) and (b) stability, when both transistor

betas are varied ................................................................................................................ 59

Figure 38 : (a) Reactance (without buffer circuit) and (b) stability, when only the

antenna side transistor is varied ...................................................................................... 60

Figure 39 : (a) Reactance (without buffer circuit) and (b) stability, when only the

receiver side transistor is varied ...................................................................................... 61

Figure 40 : (a) Reactance (without buffer circuit) and (b) stability when temperature is

varied for military applications ....................................................................................... 63

Figure 41 : (a) Reactance (without buffer circuit) and (b) stability when the voltage

source at the collectors are varied ................................................................................... 64

Figure 42 : (a) Reactance (without buffer circuit) and (b) stability when the voltage

source at the bases are varied .......................................................................................... 65

Figure 43 : Sensitivity Analysis for the NIC circuit ...................................................... 67

Figure 44 : Reactance (without buffer circuit) sensitivity analysis across 0.1 to 40 MHz

......................................................................................................................................... 67

Figure 45 : Reactance sensitivity analysis across (a) 3-10 MHz , (b) 10-12 MHz and (c)

12-40 MHz respectively .................................................................................................. 68

Figure 46 : Sensitivity of the reflection coefficient as seen from antenna across 0.1 to 40

MHz. ............................................................................................................................... 69

Figure 47 : ADS circuit to analyse internal noise ........................................................... 74

Figure 48 : Noise Figure of the NIC circuit .................................................................... 75

Figure 49 : Minimum Noise Figure of the NIC circuit ................................................... 75

Figure 50 : Noise voltage at the output of the NIC circuit due to internal noise ............ 76

Figure 51 : Median values for man-made noise power (adopted from [41]) .................. 78

Figure 52 : Noise voltage at the receiver end of the NIC due to environmental noise in

rural areas ........................................................................................................................ 81

Figure 53 : Noise voltage at the receiver end of the NIC due to environmental noise in

the cities .......................................................................................................................... 82

Figure 54 : Noise voltage at the receiver end of the NIC circuit due to environmental

noise and internal noise. .................................................................................................. 82

Figure 55 : NIC two tone harmonic balance analysis ..................................................... 88

Figure 56 : Vout spectrum arising from input frequencies of 15.17 MHz and 15.72 MHz

......................................................................................................................................... 89

Figure 57 : Surface plots for MATLAB’s least squares quadratic fit to the coefficients

of (a) 2

1α and (b) 0

1α (as described in Equation 6.3). ........................................................ 92


of (a) 2w2 (i.e. a4) and (b) w2-w1 (i.e. a6) (as described in Equation 6.1). .................... 93


of (a) w2+w1 (i.e. a5) and (b) 3w1 (i.e. a7) (as described in Equation 6.1). ................... 94


of (a) 2w1+w2 (i.e. a9) and (b) 2w1-w2 (i.e. a10) (as described in Equation 6.1). .......... 95

Page xiii

List of Tables

Table 1: Input Impedance (Real and Imaginary) and the Voltage Standing Wave Ratio

(VSWR) of the NIC output as obtained using ADS ....................................................... 26

Table 2 : Antenna reactance as represented by an equivalent capacitor ......................... 27

Table 3 : Reactance of three element network ................................................................ 28

Table 4 : VSWR and impedance characteristics of a three element negated NIC circuit

......................................................................................................................................... 29

Table 5: Signal level at receiver given a fixed input voltage level ................................. 55

Table 6: Temperature durability range according to the context of application ............. 62

Table 7: Man Made Noise according to location. A noise figure of 39.5 dB (bolded) was

used for a electric field calculation in Equation 5.7. ....................................................... 79

Table 8: Least squares quadratic fit for first 6 coefficients (c.f. Equation 6.1; The

relationship between coefficients an and bn is described by Equation 6.2) ..................... 90

Table 9: Least squares quadratic fit for next 6 coefficients (c.f. Equation 6.1; The

relationship between coefficients an and bn is described by Equation 6.2) ..................... 91

Table 10: MRF949’s IMD modelled and simulated performance when the 15.17MHz

signal at 0.00652V interacts with the 15.72MHz signal at 0.00255V). .......................... 91

Table 11: Typical shortwave broadcast stations’ signals, as received in Adelaide,

Australia. ......................................................................................................................... 96

Table 12: Highest 2w1-w2 or 2w2-w1 components due to the different two tone

combinations. (The highest value was bolded) ............................................................... 99

Table 13: Comparison between IMD levels with environmental noise in rural areas and

cities. ............................................................................................................................. 100

Table 14: Transistor IMD performance comparison. The 2w1-w2 component represents

the most significant IMD problem (as bolded). ............................................................ 100

Table 15: MRF949 Die Gummel Poon Parameters ...................................................... 111

Page xiv

Page 1

Chapter 1

Introduction and

Motivation

HIS chapter presents some brief information on the efforts on minimizing

the size of antennas, the limitations in achieving this and the emergent

Negative Impedance Converters (NICs) that offer promising results to

achieve the previously defined limits on its bandwidth and some claim that NICs have

the potential to exceed those limits. The chapter also provides a summary of the

organisation of this thesis and its contributions.

Introduction and Motivation

Page 2

1 Introduction and Motivation

With the advance of science and technology, electronic components have been

miniaturised over the years. However, the size of antennas remains limited by the fact

that a traditional design needs a size in an order of a quarter to half a wavelength, thus

giving a limit in minimum size. This limitation is most evident in antennas operating on

a relatively low frequency band. High Frequency (HF) communications are in the

frequency range 3-30 MHz which, contrary to their name, are relatively low frequencies

compared with frequencies used for present day communication systems. Such

frequencies, however, are still much in use. The size of an antenna is related to its

wavelength of operation and thus HF antennas have sizes in the range from 10-100

meters. Therefore, the size of a HF antenna is physically large. This causes spatial

inefficiency and would be a hindrance for further development of HF antennas,

especially for broadcast reception. For example, spatial inefficiency could be an

obstacle for the implementation of Multiple Input and Multiple Output (MIMO) HF

antennas. Consequently, this obstacle highlights the need to find methods to reduce the

size of HF antennas.

1.1 Introduction

This chapter introduces some of the approaches to improve small antenna performance

and discusses the motivation and practical issues in utilizing a class of network circuits

called non-Foster circuits to achieve this. A non-foster network is a network which

contains non-Foster elements. These elements have an imaginary immitance at all real

frequencies and the derivative of their reactance is zero or negative [1]. This is

elaborated further in section 1.2.1. The structure of this thesis and a concise summary of

the novel contributions represented by this work are given.

1.1.1 Limitations of small antennas

Wheeler [2] and Chu [3] stated a fundamental limitation on the bandwidth and

efficiency (Q-limit) of small antennas. This is given by

(1.1)

where

(in radians/meter)

(1.2)

3)(

11

kakaQ +=

λπ2

=k

Chapter 1

Page 3

and a is defined as the radius of sphere enclosing the maximum dimension of the

antenna (in meters). λ is the wavelength of the electromagnetic wave.

This limit implies that for a 2 metre monopole antenna at 10 MHz, the maximum Q is

113.6 and the maximum bandwidth is approximately 88 kHz. This is not sufficient even

for a single side band signal and thus the circuit is used with a matching network.

Matching networks are said to be able to increase the (half-power) bandwidth by a

factor of 3.2 [4]. (It is to be noted that for a real antenna, additional loss is incurred and

thus the bandwidth could be increased above the factor of 3.2) Therefore, ever since the

formulation of the limitations on bandwidth and efficiency (Q-limit) of small antennas,

antenna engineers and scientists have worked on overcoming these limitations. A

myriad of methods have been tried over the past few decades to achieve a Q value

which is close to the Q-limit. In general, these methods can be categorised into two

major categories which are wire engineering and material loading. Firstly, wire

engineering involves rearranging the wires, and the structure, of an antenna in order to

reduce its length, yet maximise its efficiency and bandwidth. Some examples of wire

engineering are folded dipoles [5] and multiple folded arm spherical helix [6], amongst

others [7]. The purpose of wire engineering is to reduce the length of the antenna. The

second category of methods is material loading which involves adding passive reactive

loadings or active devices to help achieve self-resonance for the antenna (so that

conjugate matching is not required), improve bandwidth and to control the radiation

pattern of the antenna [7]. There is a trade-off between bandwidth and efficiency and

one quality is realised at the expense of the other. However, the Q-limit (Q = Quality

factor) has not yet been reached [4]. Therefore, further work needs to be done to achieve

a closer Q value to the Q-limit.

1.1.2 Other potential methods

The attempts in wire engineering and material loading have not been able to bring to

fruition an antenna anything close to the Q-limit. To achieve this limit, various

innovative ideas have been implemented, such as an antenna in a Negative Index

Metamaterial (NIM) [8]. This approach, however, turned out to be flawed as described


Page 4

by Hansen [4]. Nevertheless, with the advent of non-Foster circuits, a significant

improvement seems possible [4].

These non-Foster circuits give the possibility of circumventing the problem of reactance

cancellation for only a single frequency (the case when foster circuits are used [9]).

Mayes and Poggio [10] applied non-Foster circuits to antennas, whereby multiple-

loading was used with a log-periodic distribution of the active element impedances,

hence improving their previous work in which passive periodic loading was used [11].

1.2 Motivation

The desire for small antennas, hence making them easily portable, has long been an

ideal for antenna engineers. This is due to ecological, aesthetical, and economical

reasons. Extensive work had been done in this area, which has significantly reduced the

size of some classes of antennas. Nevertheless, size reduction has continued to be a

problem for High Frequency (HF) antennas. The Q-limit remains untouched, therefore,

it is realistic to expect improvements on the previous work. New dimensions are now

open with the advent of non-Foster circuits and efficient broadband matching circuits,

are a possibility.

1.2.1 Broadband matching network

More often than not, the impedance of the antenna is not matched to the transmission

line. Therefore, a matching network is required. Wheeler [2] rightly points out the fact

that the associated circuits of the antenna system have a significant effect on the overall

bandwidth of operation. Thus, it is vital to have a matching network which is

broadband. The topic of broadband matching is not a new one, and many engineers and

scientist have attempted for years to improve it. Fano [12] derived the fundamental

limitations of a matching circuit, and since then a plethora of techniques and algorithms

have been applied and can be found in various textbooks [13], [14]. A notable journal

article is by Dedieu [15] where the author describes how the prior art of designing and

optimizing a broadband matching circuit has evolved through the years. He later

proposed a novel method called ‘Recursive Stochastic Equalization,’ whereby this

stratagem circumvents the need to guess the initial equaliser parameter and reduces the

computational time. This however, has its drawback, as it requires an equaliser topology

to be imposed. Further improvements to overcome this were suggested by Rodríguez et

Chapter 1

Page 5

al. [16], their approach bypassing the need of prior knowledge of each network element,

and only requiring a definition for the generalised topology of the network. This

approach, which includes the utilization of Genetic Algorithms (GAs), also reduces the

computational time of the optimization process and may account for the non-idealities

of the network elements. Besides this, the prospect of using non-Foster circuits to

design broadband matching circuits is promising, as patented by Skahill et al [9]. Armed

with a barrage of techniques which have been tried through the years, a potential future

project would be to combine some of these methods using non-Foster circuits.

The emphasis of this thesis is on investigating a non-Foster matching network that

utilises a Negative Impedance Converter (NIC) and, in particular, its application at HF

frequencies (3 – 30 MHz). With NICs, a significantly more broadband matching for

small antennas is possible. NICs ‘creates’ negative inductors and negative capacitors

which then are able to cancel the reactance of an antenna over a wider range of

frequencies, and consequently extend the bandwidth of broadband matching. This is

illustrated in Figure 1 where Foster reactance curve describes elements, such as

capacitors and inductors, which has a positive reactance slope; as compared with the

non-Foster reactance curve produced by NICs.

Figure 1 : Non-Foster circuit reactance cancellation

The concept of Negative Impedance Converters was credited to Marius Latour for his

work on negative regenerative systems, though not much actual use was developed at

that time [17]. Then in the early 1930s, NICs were designed using vacuum tubes to be


Page 6

used in long-line telephony repeaters to provide negative resistance to offset line losses

and amplification of the signal. With the advent of transistors, they quickly replaced

vacuum tubes in NIC circuits. Linvill [18] designed, built and tested the first

transistorised NIC in 1953. From that time, there was appreciable effort to improve and

utilise the NIC. Applications include increasing the Q of filters, using the NICs as

negative elements at the arms of the antenna, and as a matching network. Of particular

relevance to this research is the work done by Harris and Myers [19], as they were the

first to apply NICs to match electrically small antennas according to Sussman-Fort [20].

Harris and Myers successfully designed and built a shunt negative capacitor. Op Amps

were then used by Perry [17] to realise a negative capacitance for antenna matching and

this was used as a series element. Hansen [21] pointed out that, although Op Amps are

easier to obtain, it has significant disadvantages due to parasitics, noise, poor efficiency

and dynamic range. More information regarding the history of NICs, applied as a

matching network, can be found in [20] and [21]. Furthermore, Sussman-Fort [22]

provided a catalogue of ten different transistorised NICs, that were designed and

published by a number of authors, among which only Linvill [18] and Yanagisawa’s

NIC [23] have been built and tested according to Sussman-Fort.

Among the NIC circuits published, the paper published in 2006 by Sussman-Fort is

particularly relevant. In that research, Sussman-Fort [24] implemented a NIC circuit and

managed to produce a broadband, stable, high Q, grounded negative capacitance. These

‘negative’ capacitors and ‘negative’ inductors are non-Foster circuits, i.e. circuits which

have a negative dX/df characteristic and traverse the Smith Chart in an anti-clockwise

manner. This is the opposite of passive circuits and antennas themselves, thus non-

Foster matching is able to cancel the reactance of an antenna over a wider range of

frequency. Aberle et. al. [25] followed on that work and simulated the NIC circuit with

ADS using a s-parameter model for the NE85630 BJT. His simulation shows that the

circuit was stable and achieves broadband matching. However, a perfect bias was used

and in [26] he showed that the circuit is not unconditionally stable at frequencies below

31 MHz. The stability of the NIC is a significant issue in its practical implementation

and will be discussed thoroughly in this thesis.

Non-Foster circuits involve the usage of active devices like BJTs and MOSFETs. These

active devices could contribute significantly to the noise level of the antenna system.

Chapter 1

Page 7

Further, a broadband antenna will accept many signals over a wide range of frequency

and the inherent nonlinearity of the active devices will cause intermodulation products

that could act as artificial noise and further degrade the performance of the antenna.

Besides Bahr [27], Krantz and Branner [28], no one has done a thorough noise analysis

on Negative Impedance Converters in the application as broadband matching networks

for antennas. Bahr concluded in his paper that the NIC contributes an undesirably large

amount of noise. However, he did indicate that he used a ‘simplified design approach’,

thus there is space for further development via computer aided techniques. Furthermore,

developments in transistors have led to a reduction of their noise figure. Krantz and

Branner [28] have done a comparative internal noise analysis between various classes of

FET filter implementations. These two papers however were not targeted towards NIC

antenna matching circuits and do not cover the HF frequency range.

If NICs are to be widely used in matching circuits, it is crucial that a study on the

impact of noise and nonlinearity upon a NIC circuit be undertaken to determine the

feasibility of NICs as a matching network for small antennas. In particular, it is

necessary to determine whether the additional noise caused by the NIC is below that of

the natural environmental noise (i.e. externally noise limited system). Non-ideal

Negative Impedance Converters are only conditionally stable and sensitive to their

loading. Therefore this thesis aims to verify the practicality of NIC implementation of

matching networks with regards to noise, non-linearity, stability and other practical

considerations. It is also interesting to see how the improvements in transistor

technology could contribute to the effectiveness of a non-Foster impedance matching

network for small antennas.

1.3 Thesis Overview

This research seeks to explore the feasibility of using Negative Impedance Converters

as a matching network for High Frequency antenna systems. This chapter has provided

a brief literature overview of the work done in order to reduce the size of antennas.

From the myriad of strategies attempted in the past, non-Foster matching or NIC

matching was chosen as it is an exciting area for improving the performance of small

antennas. This chapter has also provided an overview of some of the caveats in pursuing

this direction, many of which will be studied in detail in the following chapters.


Page 8

Chapter 2 introduces the mechanics of the negation process by using linear analysis.

This analysis also provides a platform to understand the parameters that affect the NIC

negation. A major issue in the practical implementation of an NIC is to keep the device

stable. Therefore, some simulations and testing regarding the stability characteristics of

NIC can be found in chapter 3. Then, the following chapter explores the effects of

device variation upon the performance and stability of the NIC circuit.

Chapter 5 considers the internal and external noise of an NIC circuit to ascertain if the

device is externally noise limited. As active devices are intrinsic in the functionality of

NICs, non-linearity could pose a threat to the practicality of a NIC matching network.

Consequently, a thorough non-linear analysis is detailed in chapter 6. A comparison

between the different contributors of noise for the NIC circuit can then be made.

Finally, chapter 7 concludes the thesis by bringing together the various factors

considered in this research and discussing the feasibility of NICs as a matching network

for HF antenna systems. Future work is suggested to advance this technology.

Chapter 2

Page 9

Chapter 2

Negative Impedance

Converters

HIS chapter provides a further introduction to the concept of Negative

Impedance Converters. This chapter includes a linear analysis to understand

the negating behaviour of an NIC circuit. Finally, the chapter shows how

the utilisation of an NIC matching network could improve the bandwidth of an antenna

system, and thus allow a greater usage of small antennas.

Negative Impedance Converters

Page 10

2 Negative Impedance Converters

2.1 Introduction

A negative impedance converter (NIC), as the name suggests, is a device which negates

a general impedance. This is done by inverting the polarity of the voltage across its

input and output terminals (VNIC) or inverting the current flow into and out of the

device (INIC). NICs are active devices, i.e. they need an external power supply. Such

devices do not follow Foster’s reactance theorem which states that the reactance

monotonically increases with frequency for passive devices. For NICs, the change of

reactance with respect to frequency can be negative. Therefore, in the design of a

matching network, NICs could greatly increase the frequency range of reactance

cancellation and thus they could be used to produce a higher bandwidth in an antenna

system. This could release the system from being bounded by Chu-Wheeler’s [2, 3]

limit on the bandwidth of small antennas. We will investigate the NIC applied to

matching a non-ideal antenna to a receiver.

2.2 Linear analysis

Firstly, a simple linear analysis on the circuit involving the NIC will be considered. This

linear analysis can be used as a basis for a non-linear analysis by using the perturbation

method (assuming that the NIC is weakly non-linear). Firstly, consider the simplified

model of Figure 2.

Figure 2 : Time harmonic analysis of antenna system. Antenna represented by a series RC

component and a voltage source.

Chapter 2

Page 11

We consider a time harmonic analysis of the above circuit, where ωjs = . By applying

Kirchhoff Voltage Law, and assuming that the NIC negates a general impedance of Z

perfectly, we get

(2.1)

then, rearranging to obtain the current through the device

X

A

A

S

RZsC

R

Vi

+−+=

1

(2.2)

From Ohm’s law,

X

A

A

XSX

RZsC

R

RViRV

+−+==

11 (2.3)

By choosing Z to be the capacitor CA, we obtain the maximum voltage possible at the

receiver. We have essentially removed the reactance of the antenna (represented by CA)

that can cause a massive reduction in receiver voltage at low frequencies.

2.2.1 NIC Realisation

(a)

(b)

Figure 3 : (a) Basic NIC circuit as proposed by Sussman-Fort [20] (b) Bipolar Junction Transistor

equivalent circuit.

0)()1

( =−−−+− X

A

AS iRZisC

RiV

NOTE: This figure is included on page 11 of the print copy of the thesis held in the University of Adelaide Library.


Page 12

In order to understand the factors that affect a NIC’s negation ability, a small signal

analysis was performed on a BJT implementation of a NIC circuit (as shown in Figure

3a). The transistor can be modelled as shown in Figure 3b. This circuit can be simplified

by representing the BJTs by current sources alone. This assumption means that the

parameter rπ is infinite and Cπ = Cµ=0.

2.2.1.1 rπ is assumed to be infinite and Cπ = Cµ=0

With infinite rπ, the following will represent the circuit of Figure 3a.

Figure 4 : Small signal analysis (excluding rπ)

Each current source is dependent on the voltage drop across its input resistance. Thus,

)( 11 Vfi ∆= (2.4)

where

121 VvV −=∆ (2.5)

and

)( 22 Vfii ∆==

(2.6)

where

212 VvV −=∆ (2.7)

The voltage drop across the general impedance Z is given by

iZvv =− 21 (2.8)

By using Kirchhoff Current Law, we know that current is conserved, thus

0)()( 12 =∆+∆ VfVf (2.9)

The voltage dependent current source (the transistor) can be represented by

Chapter 2

Page 13

...)( 3

3

2

21 +∆+∆+∆=∆ vgvgvgVf (2.10)

However, by assuming only weak non-linearity about the bias point, we can use the

linear transistor model of

vgVf ∆=∆ 1)( (2.11)

The current through the circuit, i.e. (2.6), can be expressed as a sum of two components

as given by

)(2

1)(

2

122 VfVfi ∆+∆= ,

(2.12)

then by substituting (2.9) into (2.12), we obtain

)(2

1)(

2

112 VfVfi ∆−∆= ,

(2.13)

and by substituting (2.5), (2.7) and (2.11) into this equation

)(2

1)(

2

1121211 VvgVvgi −−−=

(2.14)

which implies

)(2

1)(

2

1211211 VVgvvgi −−−=

(2.15)

Substituting this into (2.8) gives

)(2

1)(

2

121121121 VVZgvvZgvv −−−=−

(2.16)

from which

)(2

21

1

121 VV

Zg

Zgvv −

−=− .

(2.17)

Assuming that ∞→Zg1 ,

)( 2121 VVvv −−≈− (2.18)

and substituting (2.18) into (2.8)

)( 21 VVZi −=−

(2.19)

Since the impedance of the NIC is given by

=NICZ Current

dropVoltage

i

VV 21 −=

(2.20)

we have


Page 14

Zi

ZiZNIC −=

−=

(2.21)

This shows that, by making the appropriate assumptions, the ideal impedance negation

is achieved. The assumptions, however, are ideal and the consequence of real devices

will be analysed in the following sections.

2.2.1.2 For the case rπ is not infinite

Figure 5 : Small signal analysis (including rπ)

In any real Bipolar Junction Transistor, the parameter rπ is finite and the small signal

model of the transistors needs to include rπ, as shown in Figure 5.

By making the assumption, as in (2.11), we obtain

)()( 12111 VvgVfi −=∆= (2.22)

and

)()( 21122 VvgVfi −=∆=

(2.23)

A nodal analysis at the nodes labelled in Figure 5, yields at node B

2

21

1 iZ

vvib −

−=

(2.24)

On noting that

πr

Vvib

12

1

−=

(2.25)

and using (2.23), we obtain

Chapter 2

Page 15

)( 2112112 Vvg

Z

vv

r

Vv−−

−=

−

π

(2.26)

from which

211

112 )1

()11

( Vgr

V

Zgv

Zrv +=−++

ππ

(2.27)

At node A,

1

12

2 iZ

vvib −

−=

(2.28)

Then, noting that

πr

Vvib

212

−=

(2.29)

and by using (2.22), we obtain

)( 121

1221 VvgZ

vv

r

Vv−−

−=

−

π

(2.30)

from which

112

121 )1

()11

( Vgr

V

Zgv

Zrv +=−++

ππ

(2.31)

By subtracting (2.27) with (2.31), we get

)1

)(()111

)(( 121112 gr

VVZ

gZr

vv −−=+−+−ππ

(2.32)

From this, we can derive a more realistic assessment of the NIC.

2.2.1.3 Finite g1 and rπ

When the parameter g1Z and rπ are finite, we obtain a far more complex behaviour for

ZNIC. By rearranging (2.32), we obtain

Zg

r

gr

VVvv21

1

)()(

1

1

1212

+−

−−−=−

π

π

(2.33)

By simplifying the expression to include 2k , we have

)()( 12212 VVkvv −−=− (2.34)

where

Zg

r

gr

k21

1

1

1

2

+−

−

=

π

π

(2.35)


Page 16

In order to obtain the input impedance expression, a nodal analysis is performed at

nodes A and C

At Node C,

11 biii += (2.36)

then, by substituting (2.22) and (2.25) into the equation, we obtain

πr

VvVgi 1211 )(

−+∆=

(2.37)

Further, at Node A

213 biii += (2.38)

then, by substituting (2.22) and (2.29) into the equation, we have

πr

VvVgi 21113 )(

−+∆=

(2.39)

By subtracting (2.39) from (2.37), we obtain

πr

VVvvii 2112

3

+−−=−

(2.40)

Since Z

vvi 123

−=

(2.41)

by substituting 3i into (2.40) yields

ππ r

VV

Zrvvi 1212 )

11)((

−++−=

(2.42)

Using Equation (2.34) to substitute for )( 12 vv − yields

ππ r

VV

ZrVVki 12

122 )11

)((−

++−−=

(2.43)

or

)1

)(( 2212

ππ rZ

k

r

kVVi +−−−=

(2.44)

from which

Z

Zg

r

rZgr

ZrZNIC

−+−

+−

−=

21

))(1(

1

1

π

ππ

π

(2.45)

By applying a number of algebraic manipulations, the following expression

is obtained

Chapter 2

Page 17

1

2)1(

1

1

−−−−

=gr

rgrZZNIC

π

ππ

(2.46)

Since current gain factor, β, is given by

1grπβ =

(2.47)

Equation (2.46) is then simplified to the following

ββ π

+

+−==

1

2)1( rZZZ inNIC

(2.48)

It is to be noted that ZNIC is also the input impedance of the device.

From Equation (2.48), it can be seen that for a realistic device, the negation of

impedance could be compromised due to device characteristics. Figures 28 and 29 in

the next chapter show the difference between a realistic device and an ideal negative 27

pF capacitor. (It is to be noted that the circuit used to obtain the simulations in Figures

28 and 29 has been modified for the purposes of achieving stability). In establishing a

realistic analytical model, besides setting a finite rπ and gm, the parasitic effects should

be considered to understand its impact on the circuit.

2.2.2 Analysis with and without parasitic capacitance

At higher frequencies, Bipolar Junction Transistors tend to have parasitic effects

(capacitance in particular). In a BJT’s application as amplifiers, the parasitics reduces

the gain at high frequencies. In NIC circuits, these parasitic effects could impact the

accuracy of the reactance negation. Therefore, it is important to analyse its impact upon

NIC’s performance. Among the parasitic effects, only two of the main parasitic

capacitance will be considered, namely the capacitance across the base and emitter (Cπ)

and the capacitance across the base and collector of the transistor (Cµ). A circuit which

takes into account these parasitic capacitances is shown in Figure 6.


Page 18

Figure 6 : Small signal analysis (Including parasitic capacitance)

By using the linear transistor model, we obtain

)()( 121114 VvgVgi −=∆= (2.49)

)()( 211215 VvgVgi −=∆= (2.50)

The current passing through the two capacitors µC , is given by

µsCvvic )( 211 −= (2.51)

and

µsCvvic )( 122 −= (2.52)

From Ohm’s law,

Z

vvi 12

3

−=

(2.53)

Let the parallel impedance of rπ and Cπ be given by

Chapter 2

Page 19

ππ

ππ

sCr

sCrZRC 1

/

+=

(2.54)

Then, by assuming that both transistors are identical, Ohm’s law yields the

following equations

RC

bZ

Vvi 212

−=

(2.55)

RC

bZ

Vvi 121

−=

(2.56)

Nodal analysis at the nodes labelled in Figure 6, yields at node A

03214 =−++ iiii c (2.57)

Substituting (2.49), (2.51) and (2.53) into the equation gives

0)()( 12

221121 =−

−+−+−Z

vvisCvvVvg µ

(2.58)

from which

Z

vvsCvvVvgi 12

121212 )()(−

+−+−−= µ

(2.59)

A nodal analysis at node C gives

0222 =−+ bc iii (2.60)

Then, by substituting (2.52) and (2.55) into the equation yields

0)( 21122 =

−−−+

RCZ

VvsCvvi µ

(2.61)

from which

RCZ

VvsCvvi 21

212 )(−

+−= µ

(2.62)

By equating (2.59) and (2.62),

RCZ

VvsCvv

Z

vvsCvvVvgi 21

2112

121212 )()()(−

+−=−

+−+−−= µµ

(2.63)

from which

RCZ

VvVvg

ZsCvv 21

12112 )()1

2)((−

=−−+− µ

(2.64)

At node B, we have

01325 =+++ iiii c (2.65)


Page 20

Substituting (2.50), (2.52) and (2.53) into the equation gives

0)()( 12112211 =

−++−+−

Z

vvisCvvVvg µ

(2.66)

from which

)1

)(()( 211211Z

sCvvvVgi +−+−= µ

(2.67)

Further, nodal analysis at node C gives

111 cb iii −= (2.68)


µsCvvZ

Vvi

RC

)( 2112

1 −−−

=

(2.69)

By equating (2.67) and (2.69), yields

µµ sCvvZ

Vv

ZsCvvvVgi

RC

)()1

)(()( 2112

211211 −−−

=+−+−=

(2.70)

from which

RCZ

VvvVg

ZsCvv 12

12121 )()1

2)((−

=−++− µ

(2.71)

By subtracting (2.64) with (2.71), we obtain

RCZ

VvVvvVgVvg

ZsCvv 1221

12112112 )()()1

2)((2+−−

=−−−−+− µ

(2.72)

By grouping the voltage terms together and some rearrangements, we have

RC

RC

Zg

ZsC

gZ

VVvv12

4

1

)()(

1

1

1212

+−+

−−−=−

µ

(2.73)

This is simplified into

)()( 12412 VVkvv −−=− (2.74)

where

RC

RC

Zg

ZsC

gZ

k12

4

1

1

1

4

+−+

−=

µ

(2.75)

A nodal analysis at node E gives

14 biii += (2.76)

Substituting (2.49) and (2.56) into the equation gives

Chapter 2

Page 21

RCZ

VvVvgi 12121 )(

−+−=

(2.77)

Further, at node F

25 biii −−= (2.78)

Substituting (2.50) into the equation gives

221 biVgi −∆−= (2.79)

Then by substituting (2.7) and (2.55) into the equation, we obtain

RCZ

VvVvgi 21211 )(

−−−−=

(2.80)

By adding (2.77) and 2.75, we obtain

RCZ

VVvvVVvvgi 121212121 )(2

−+−+−+−=

(2.81)

By applying Kirchhoff current law at node C and node D respectively, we obtain

222 cb iii −= (2.82)

111 bc iii −= (2.83)

A nodal analysis at node A gives

2143 iiii c ++= (2.84)


221113 )( cbc iiiVgi −++∆= (2.85)

Further, at node B

1253 iiii c −−−= (2.86)

Then, by substituting (2.50) and (2.83), we obtain

112213 bcc iiiVgi −+−∆−= (2.87)

Then, by adding (2.85) and (2.87), we have

1221211213 22)(2 bbcc iiiiVvVvgi −+−++−−= (2.88)

By subtracting (2.81) with (2.88) and by dividing it by half, we obtain

22

1 1221

12123

bbcc

RC

iiii

Z

VVvvii

−+−+

−+−=−

(2.89)

By substituting (2.51), (2.52), (2.55) and (2.56) into the equation, we obtain

RCRC Z

VvVvsCvvsCvv

Z

VVvvii

2)()(

2

1 21121221

12123

+−−+−−−+

−+−=− µµ

(2.90)

from which


Page 22

µsCvvZ

VVvvii

RC

)(2 121212

3 −−−+−

=−

(2.91)

Then, by substituting (2.53) into the equation

)1

)(()211

)(( 1212

RCRC ZVVsC

ZZvvi −+−+−= µ

(2.92)

Then by substituting (2.74) into the equation, the following is obtained.

)21)(( 4

4412 µsCk

Z

k

Z

kVVi

RC

−−−

−=

(2.93)

Then, by using (2.20), the input impedance is now given by

14

44 )21( −−−−

= µsCkZ

k

Z

kZ

RC

in

(2.94)

where k4 and ZRC are given by Equations (2.75) and (2.54), respectively.

Equation (2.94) provides a more thorough description on the input impedance of the

NIC, when negating a general impedance, as compared to Equation 2.48. However, the

BJTs used in this thesis are MRF 949, which have a maximum parasitic capacitance of

200 fF, thus the effects of these parasitic capacitances are negligible at the HF

frequency range. A simulation performed in ADS comparing two transistor models,

with and without the parasitic capacitances, yielded a difference in reactance of less

than 1.5% at 10 MHz. Thus Equation (2.48) is deemed to be sufficient in describing the

NIC’s impedance negation properties.

In this section, the linear analysis performed could provide a better understanding on the

non-ideal behaviour of NICs with regard to its negation ability upon a general

impedance. Its performance in relation to the transistor parameters and (indirectly) its

biasing conditions could be inferred. In the following section, we consider the

performance of the NIC when used as a matching network for a HF antenna.

2.3 Matching Performance Using a Simple Negating Capacitor

It is the purpose of this research, to utilise a negative impedance converter circuit, to

create a matching network to cancel the reactance of an electrically small antenna. The

figure of merit in matching antennas is the Voltage Standing Wave Ratio (VSWR) of

the antenna system. This measures the amount of reflection or loss in the system which

is a result of how well the circuit is matched. An ideal antenna system’s VSWR is 1:1.

However, for practical receive antenna systems, a VSWR of 4:1 or below is an

Chapter 2

Page 23

acceptable level for a matched circuit. This section, two programs namely Numerical

Electromagnetic Code (NEC) and Agilent’s Advanced Design System (ADS 2009),

were used to simulate the antenna system performance. NEC simulates the impedance

characteristics of the antenna, while ADS utilises the antenna impedance result, from

NEC, to simulate the NIC matching circuit.

Building on the work by Aberle et. al. [25], which used a form of Linvill’s NIC design

[18], a circuit (shown in Figure 7) was implemented using a pair of MRF 949 transistors

in order to cancel the reactance in an unloaded 2 metres monopole for a large range of

frequencies. A 2 meter antenna exhibits capacitive behaviour (over the target frequency

range from 3 to 20 MHz) that can be represented by a lumped capacitor in series with a

resistor. The antenna’s impedance values (as shown in Figure 8) vary with frequency

and these values were simulated using the NEC2 (Numerical Electromagnetics Code)

antenna modelling program. The NEC model treated the antenna as a dipole and so

calculated values of impedance that were halved in order to obtain those of the intended

monopole. These values were then used to obtain equivalent series capacitance and

resistance that represent the antenna (Figures 9 and 10 ). A value of 29 pF capacitor was

chosen to represent the antenna (internal capacitance of the NIC provided about 2 pF

and so the value in the NIC circuit was set at 27 pF). Table 1 shows the resultant

VSWR, at the output of the NIC circuit, obtained over the frequency range of 3 – 20

MHz.


Page 24

Figure 7 : A BJT implementation of the negative ‘capacitor’

(Note: A first order approximation of real inductors, given by a series resistor and parallel

capacitor, was included in the simulation circuit as a data block labelled Antenna2)

Vout

S_Para

m

SP1

Ste

p=1 M

Hz

Sto

p=20 M

Hz

Sta

rt=3 M

Hz

S-P

AR

AM

ETE

RS

Zin

Zin

2

Zin

1=zin

(S11,P

ortZ1)

Zin

N

VAR

VAR

48

Rm

id=6.5

Lto

p=470

Lbot=

220

Rbot=

2.6

Rto

p=6.5

Cb=2

Lm

id=470

Eqn

Var

VSW

R

VSW

R2

VSW

R1=vs

wr(

S11)

VSW

R

BJT_M

odel

MR

F949

Term

Term

2

Z=50 O

hm

Num

=2

Term

Term

1

Z=50 O

hm

Num

=1

C C33

C=27 p

F

S1P

Ante

nna2

1Re

f

VAR

VAR

49

VD

C=10

Vb=10

Re=1600

R2=150000

R1=20000

Rc=200

Eqn

Var

R R43

R=R

2 O

hm

R R42

R=R

2 O

hm

BJT_N

PN

BJT4

Model=

MR

F949

BJT_N

PN

BJT3

Model=

MR

F949

V_D

C

SR

C21

Vdc=Vb V

R R44

R=R

1 O

hm

C C37

C=0.1

uF

V_D

C

SR

C20

Vdc=Vb V

R R41

R=R

1 O

hm

R R40

R=R

e O

hm

R R39

R=R

e O

hmC C

36

C=0.1

uF

V_D

C

SR

C19

Vdc=VD

C

R R38

R=R

c O

hm

R R37

R=R

c O

hm

V_D

C

SR

C18

Vdc=VD

C

L L29

R=R

top

L=Lto

p u

H

L L33

R=R

mid

L=Lm

id u

H

L L34

R=R

mid

L=Lm

id u

H

L L31

R=R

bot

L=Lbot uH

L L30

R=R

bot

L=Lbot uH

L L32

R=R

top

L=Lto

p u

H

C C34

C=C

b n

F

C C35

C=C

b n

F

Chapter 2

Page 25

Figure 8 : Simulation results of a 2 meter dipole by 4NEC2+ program

(Note: the antenna model used in ADS is a monopole and thus its impedance is to be halved)

Figure 9 : Equivalent capacitor representing the antenna's reactance (Using a first order

approximation)

Equivalent Radiation Resistance vs Freq

0

0.5

1

1.5

2

2.5

3

3.5

4

4.5

3 5 7 9 11 13 15Frequency (MHz)

Resistor (R)

Figure 10 : Equivalent resistor representing the antenna's resistor (Using a first order

approximation)


Page 26

Table 1: Input Impedance (Real and Imaginary) and the Voltage Standing Wave Ratio (VSWR) of

the NIC output as obtained using ADS

The VSWR at the output of the NIC is low over a bandwidth of 8 MHz (from 7 to 14

MHz). Traditional methods using passive circuits (i.e. a traditional antenna tuner) would

struggle to achieve such results across a similar bandwidth. This was achieved using a

fixed capacitor in the NIC despite using a compromised value of 27 pF. The

capacitance, from this single capacitor, does not model the reactance of the antenna over

the entire frequency range and therefore the reactance cancellation would not be

complete. However, by designing a network of elements, which is modelled upon the

reactance of the antenna, there could be significant improvements in the reactance

cancellation.

2.4 Three element negation network

The NIC in Figure 7 utilised the negation of a single capacitor of 27 pF. However, the

reactance of an unloaded short antenna can only be represented well if the capacitance

can vary with frequency. Negating the reactance of the antenna with a single capacitor

has its limitation. This implies that there could be further improvements in the VSWR

performance if we could generate frequency dependent capacitance.

By taking the reactance of the antenna at five spot frequencies, 3, 5, 10, 15 and 20 MHz,

it can be represented by equivalent capacitors as shown in Table 2. A simple 3 element

Freq

3.000 MHz4.000 MHz5.000 MHz6.000 MHz7.000 MHz8.000 MHz9.000 MHz10.00 MHz11.00 MHz12.00 MHz13.00 MHz14.00 MHz15.00 MHz16.00 MHz17.00 MHz18.00 MHz19.00 MHz20.00 MHz

Real(Zin1)

1905.612483.579 114.728 47.129 27.942 21.256 18.775 17.929 17.754 17.840 18.001 18.167 18.335 18.547 18.869 19.378 20.143 21.208

Imag(Zin1)

628.871-581.396-258.183-124.047-61.823-27.862-6.8987.370

17.906 26.225 33.215 39.422 45.205 50.780 56.293 61.805 67.333 72.840

VSWR1

42.26523.71314.2818.4154.8793.1952.7222.8583.2223.6574.1214.6105.1285.6716.2256.7627.2497.655

Chapter 2

Page 27

LC network, as shown in Figure 11, was designed to match, as closely as feasible, to the

reactance of the antenna at the chosen spot frequencies.

Table 2 : Antenna reactance as represented by an equivalent capacitor

Frequency (MHz)

Reactance Resistance Equivalent capacitor

(F)

3 -1903.4 0.042496 2.7872E-11

5 -1130.1 0.28351 2.8167E-11

10 -536.95 2.2551 2.9641E-11

15 -326.76 3.8279 3.2471E-11

20 -207.85 6.5957 3.8286E-11

C

C2

L

LC

C1

Figure 11 : Simple three element network to represent antenna's reactance across 3-20MHz

The input impedance of the network is given by

21

1//)

1(

sCsCsLZ in +=

(2.95)

from which

21

21

2

2

11

1

sCsCsL

CCssC

sL

Z in++

+=

(2.96)

Noting that

jws = (2.97)

and substituting (2.97) into (2.96) yields

21

21

2

2

1

wC

j

wC

jjwL

CCwC

L

Z in−−

−=

(2.98)


Page 28

By grouping the imaginary terms together, we obtain

−+

−=

wLwCwC

CCwC

L

jZin

21

21

2

2

11

1

(2.99)

Equation (2.99) describes the impedance of the LC network. A MATLAB program was

then written, utilizing the imaginary part of the input impedance equation, to optimise a

choice of L, C1 and C2 in order to match the reactance of the frequency dependent

capacitor. The optimised values are: L= 3.5198 µH, C1=12.186 pF, C2=12.473 pF. Table

3 shows the resultant reactance values across the desired frequency range. By

comparing Table 3 and Table 2, we see that there is a reasonable match across this

frequency range for this simple network. Figure 12 illustrates this match with a plot

which compares the antenna reactance and the three element network.

Table 3 : Reactance of three element network

Freq


Imag(Zin1)

-2135.082-1591.654-1263.251-1042.269-882.571 -761.066 -664.905 -586.355 -520.469 -463.923 -414.384 -370.149 -329.928 -292.705 -257.641 -224.010 -191.147 -158.398

Chapter 2

Page 29

4 6 8 10 12 14 16 182 20

-2000

-1500

-1000

-500

-2500

0

freq, MHz

imag(Z

in3) (H

)

H

Figure 12 : The reactance of the three element network (blue curve) reasonably resembles the

reactance of the antenna (red curve)

By using a LC network as the negation element, the VSWR performance of the antenna

matching network has improved considerably as shown in Table 4, which lists the input

impedance and resultant VSWR, at the output of this NIC circuit.

Table 4 : VSWR and impedance characteristics of a three element negated NIC circuit

Whilst a complex network might appear to give an improved performance, resonance

within the network could have implications for the stability of the NIC. Consequently,

for the purposes of this thesis, a single capacitor of 27 pF is used as the element to be

negated. A detailed discussion on the instability of NICs is given in chapter 3.

Freq


Real(Zin1)

1734.377399.11696.24640.77225.37920.24518.48617.99417.99018.14818.32218.46518.58618.73118.97019.38220.03520.969

Imag(Zin1)

583.313-409.387-152.359-56.329 -18.579 -2.8743.1184.2922.826-0.257-4.419-9.384

-15.025 -21.347 -28.427 -36.454 -45.701 -56.555

VSWR1

38.61416.4457.1283.2952.3182.4802.7172.8022.7892.7552.7542.8182.9683.2203.5884.0944.7725.679


Page 30

2.5 Chapter summary

The preceding sections have broadly explained the mathematics behind the negation

ability of Negative Impedance Converters. It has given an analytical formula, which

provides a platform for understanding the linear characteristics of the NIC. It was also

shown that, by negating a capacitor, considerable reactance cancellation of the antenna

occurs in the circuit. This improves the VSWR of the system across a wide range of

frequencies. Less than 4:1 VSWR over a range of 4 MHz was obtained. By designing

and negating a network of elements, the bandwidth was increased to about 11 MHz.

This is a very large bandwidth for the HF frequency range and would be a good result.

This potential, however, is clouded by the possibility of instability in the NIC and this

problem will be explored in the next chapter.

Page 31

Chapter 3

Stability Concerns

EGATIVE Impedance Converters have significant promise in the

application of antenna matching, as shown in the previous chapter.

However, concerns arise regarding the stability of the NICs as they are only

conditionally stable. This chapter seeks to understand the nature of NIC stability and

the methods to achieve stability.

Stability Concerns

Page 32

3 Stability concerns

3.1 Introduction

In the design of a matching network it is imperative that the stability of the circuit, i.e.

its resistance to oscillate, is thoroughly considered. This is because oscillations would

nullify the functionality of the matching network. The stability of a network is

frequency dependent and has to be stable across all frequencies, not only at the design

frequencies.

There are two types of stability as defined by Pozar [29]:

1) Unconditional stability: “The network is unconditionally stable if |τin|<1 and

|τout|<1 for all passive source and load impedances”

2) Conditional stability: “The network is conditionally stable if |τin|<1 and |τout|<1

only for a certain range of passive source and load impedances. This case is

also referred to as potentially unstable.”

Note: τin and τout are the input and output reflection coefficient of the network or circuit.

Unconditional stability is the ideal goal in the design of an active matching network.

However, due to the nature of the NIC, it is at best only conditionally stable. This

chapter will describe the characteristics of NICs, the methods of predicting stability and

investigate the conditions at which the NIC is stable and the modifications that were

necessary to achieve stability.

3.2 NIC characteristic

The Negative Impedance Converter design chosen has similarities with an astable

multivibrator as the transistors’ bases are coupled to the other transistor’s collector

using a capacitor. This cross-couple similarity provides insight into the instability issue

that NIC circuits face. A BJT based NIC, which has emitters at the NIC’s input-output

ports, has an Open Circuit Stable (OCS) characteristic (OCS means that for any passive

load on one port, the device is stable with an open circuit on the other port [24]. Short

Circuit Stable (SCS) BJT based NIC circuits, however, have collectors at the input and

Chapter 3

Page 33

output terminal pair. (SCS means that for any passive load on one port, the device is

stable with a short circuit on the other port [24]). Open Circuit Stable NICs are to be

used as series elements, while SCS NICs are to be used as shunt elements. OCS circuits

are stable only if they are terminated with relatively large impedances, while SCS

circuits are stable only if they are terminated with significantly lower impedance as

compared with the input impedance of the NIC.

Sussman-Fort [24] further explains that the inherent conditional stability of an NIC sets

a limitation on the magnitude of the impedances at its respective terminations. This

limitation is given by the following two equations,

11 || inL ZZ >

(3.1)

and

22 || inL ZZ <

(3.2)

where ZL1 and ZL2 are the load impedances on the left hand side and right

hand side respectively, and Zin1 and Zin2 are the input impedance looking in

from the left hand side and right hand side respectively (as shown in Figure

13).

Figure 13 : NIC’s two ports terminated by ZL1 and ZL2. One port will be Open Circuit

Stable while the other will be Short Circuit Stable (adopted from [24]).

Sussman-Fort recommends that Inequalities 3.1 and 3.2 be satisfied by at least a factor

of two. However, he stated that there is no general answer for this and that it has to be

evaluated according to its context. Therefore, the loading of a NIC has to be carefully

analysed, according to its context, as its stability is crucial for it to function as a

matching network for HF antennas. In the current work, an emitter input / output type

NIC will be considered as this is appropriate to the antenna matching problem at HF. A

Stability Concerns

Page 34

number of stability analysis methods will be used in the next section to analyse the

conditions at which the NIC is stable. It is to be noted that other stability prediction

methods (aside from those used in this thesis) are applicable, namely Middlebrook’s

technique [30] and Rollet’s proviso [31, 32].

3.3 Stability Analysis

This research include two main methods of predicting stability in the NIC circuit,

namely Reflection Coefficient (or S-parameters) Analysis and Transient Analysis. By

setting the conditions for the circuit, the stability of a particular port can be analysed by

considering the S11 (S-parameter input port reflection coefficient) of a one port

network. If the reflection coefficient of a port (reflection coefficient is shown as S11) is

found to be greater than 1, the port may oscillate at that frequency given the appropriate

excitations. This analysis will be performed at the input of the receiver and at the output

of the antenna (the other port being appropriately load by either the antenna or the

receiver). However, as there could be circuit noise and power supply transients, this

analysis was found to be necessary at the bases of the transistors also. In order to

confirm the results on stability, a transient analysis of the output voltage (at the

receiver) was performed as a secondary method in predicting stability of the circuit.

Firstly, the circuit was tested to obtain its Rollet Factor [33] to check for unconditional

stability. A requirement for unconditional stability is to have a Rollet Factor greater

than one across all frequencies. The circuit setup as shown in Figure 14 was used and

the results can be found in Figure 15. The results confirm that unconditional stability

was not achieved with this circuit as the Rollet Factor is less than one at frequencies

below 3 MHz. This fits in the hypothesis for this chapter as NICs are known to be at

best conditionally stable. Thus S11 analysis at the relevant ports (receiver port, antenna

port and the transistor bases) were performed to test for conditional stability.

Chapter 3

Page 35

Vout

VAR

VAR48

Rmid=6.5

Ltop=470

Lbot=220

Rbot=2.6

Rtop=6.5

Cb=2

Lmid=470

EqnVar

Tran

Tran1

MaxTimeStep=1.0 nsec

StopTime=100.0 usec

TRANSIENT

StabMeas

StabMeas1

StabMeas1=stab_meas(S)

StabMeas

StabFact

StabFact1

StabFact1=stab_fact(S)

StabFact

Zin

Zin2

Zin1=zin(S11,PortZ1)

Zin

N

VSWR

VSWR2

VSWR1=vswr(S11)

VSWR

BJT_Model

MRF949

Term

Term2

Z=50 Ohm

Num=2

Term

Term1

Z=50 Ohm

Num=1

S_Param

SP1

Step=0.01 MHz

Stop=20 MHz

Start=0.01 MHz

S-PARAMETERS

C

C33

C=27 pF

S1P

Antenna2

1 Re f

VAR

VAR49

VDC=10

Vb=10

Re=1600

R2=150000

R1=20000

Rc=200

EqnVar

R

R43

R=R2 Ohm

R

R42

R=R2 Ohm

BJT_NPN

BJT4

Model=MRF949

BJT_NPN

BJT3

Model=MRF949

V_DC

SRC21

Vdc=Vb V

R

R44

R=R1 Ohm

C

C37

C=0.1 uF

V_DC

SRC20

Vdc=Vb V

R

R41

R=R1 Ohm

R

R40

R=Re Ohm

R

R39

R=Re Ohm

C

C36

C=0.1 uF

V_DC

SRC19

Vdc=VDC

R

R38

R=Rc Ohm

R

R37

R=Rc Ohm

V_DC

SRC18

Vdc=VDC

L

L29

R=Rtop

L=Ltop uH

L

L33

R=Rmid

L=Lmid uH

L

L34

R=Rmid

L=Lmid uH

L

L31

R=Rbot

L=Lbot uH

L

L30

R=Rbot

L=Lbot uH

L

L32

R=Rtop

L=Ltop uH

C

C34

C=Cb nF

C

C35

C=Cb nF

Figure 14 : Circuit setup for Rollet Factor simulation

Figure 15 : Rollet Factor simulation result

In order to perform the reflection coefficient analysis at the receiver side, the antenna

was directly shorted to ground (i.e. the 50 Ohm S-parameter termination was short

circuited). Figure 16 shows the results of the S11 or reflection coefficient simulation as

seen from the receiver. It is observed that the circuit is not stable at low frequencies as

the S11 is less than one.

2 4 6 8 10 1 14 1 10 2

-0.5

0.0

0.5

1.0

-1.0

1.5

freq, (MHz)

Stability Concerns

Page 36

2 4 6 8 10 12 14 16 180 20

0.6

0.7

0.8

0.9

1.0

1.1

0.5

1.2

freq, MHz

mag(S

(1,1

))

Figure 16 : Reflection coefficient (S11) as seen from the receiver

Chapter 3

Page 37

Figure 17 : Circuit setup for antenna port reflection coefficient (S11) simulation

Next, the same analysis was done to check the reflection coefficient as seen from the

Antenna. In this analysis, the receiver was replaced by a 50 Ohm resistor, as shown in

Figure 17. The simulation results are given in Figure 18, and show that the antenna port

is stable.

Vout

Term

Term

1

Z=50 O

hm

Num

=1

R R45

R=50 O

hm

S_Para

m

SP1

Ste

p=0.0

1 M

Hz

Sto

p=20 M

Hz

Sta

rt=0.0

1 M

Hz

S-P

AR

AM

ETE

RS

C C33

C=27 p

F

S1P

Ante

nna2

1R

ef

VAR

VAR

48

Rm

id=6.5

Cm

id=0.0

86235

Lto

p=470

Lbot=

220

Rbot=

2.6

Rto

p=6.5

Cbot=

0.1

124

Cb=2

Cto

p=0.0

86235

Lm

id=470

Eqn

Var

VAR

VAR

49

VD

C=10

Vb=10

Re=1600

R2=150000

R1=20000

Rc=200

Eqn

Var

Zin

Zin

2

Zin

1=zin

(S11,P

ortZ1)

Zin

N

VSW

R

VSW

R2

VSW

R1=vs

wr(

S11)

VS

WR

BJT_M

odel

MR

F949

R R43

R=R

2 O

hm

R R42

R=R

2 O

hm

BJT_N

PN

BJT4

Model=

MR

F949

BJT_N

PN

BJT3

Model=

MR

F949

V_D

C

SR

C21

Vdc=Vb V

R R44

R=R

1 O

hm

C C37

C=0.1

uF

V_D

C

SR

C20

Vdc=Vb V

R R41

R=R

1 O

hm

R R40

R=R

e O

hm

R R39

R=R

e O

hmC C

36

C=0.1

uF

V_D

C

SR

C19

Vdc=VD

C

R R38

R=R

c O

hm

R R37

R=R

c O

hm

V_D

C

SR

C18

Vdc=VD

C

L L29

R=R

top

L=Lto

p u

H

L L33

R=R

mid

L=Lm

id u

H

L L34

R=R

mid

L=Lm

id u

H

L L31

R=R

bot

L=Lbot uH

L L30

R=R

bot

L=Lbot uH

L L32

R=R

top

L=Lto

p u

H

C C34

C=C

b n

F

C C35

C=C

b n

F

Stability Concerns

Page 38

Figure 18 : Reflection coefficient (S11) as seen from the antenna

Next, the reflection coefficient analysis was performed at the bases of the transistors.

Figure 19 shows the circuit setup for the reflection coefficient analysis at the base of the

antenna-side transistor. Similarly, the other transistor base is tested by moving the S-

parameter termination along with a DC blocking capacitor in Figure 19, to the base of

the receiver side transistor. This blocking capacitor is required so that it does not affect

the DC bias of the circuit. The results of these two simulations are shown in Figure 20.

The result of Figure 20, where the reflection coefficient is greater than 1, indicates that

the circuit could oscillate at low frequencies.

2 4 6 8 1 12 1 16 180 20

0.2

0.4

0.6

0.8

0.0

1.0

freq, MHz

Chapter 3

Page 39

Figure 19 : Circuit setup for transistor base reflection coefficient (S11) simulation

Vout

C C38

C=0.1

uF

R R45

R=50 O

hm

Term

Term

1

Z=50 O

hm

Num

=1

S_Para

m

SP1

Ste

p=0.0

1 M

Hz

Sto

p=20 M

Hz

Sta

rt=0.0

1 M

Hz

S-P

AR

AM

ET

ER

S

C C33

C=27 p

F

S1P

Ante

nna2

1Ref

VAR

VAR

48

Rm

id=6.5

Cm

id=0.0

86235

Lto

p=470

Lbot=

220

Rbot=

2.6

Rto

p=6.5

Cbot=

0.1

124

Cb=2

Cto

p=0.0

86235

Lm

id=470

Eqn

Var

VAR

VAR

49

VD

C=10

Vb=10

Re=1600

R2=150000

R1=20000

Rc=200

Eqn

Var

Zin

Zin

2

Zin

1=zin

(S11,P

ortZ1)

Zin

N

VSW

R

VSW

R2

VSW

R1=vs

wr(

S11)

VSW

R

BJT_M

odel

MR

F949

R R43

R=R

2 O

hm

R R42

R=R

2 O

hm

BJT_N

PN

BJT4

Model=

MR

F949

BJT_N

PN

BJT3

Model=

MR

F949

V_D

C

SR

C21

Vdc=Vb V

R R44

R=R

1 O

hm

C C37

C=0.1

uF

V_D

C

SR

C20

Vdc=Vb V

R R41

R=R

1 O

hm

R R40

R=R

e O

hm

R R39

R=R

e O

hmC C

36

C=0.1

uF

V_D

C

SR

C19

Vdc=VD

C

R R38

R=R

c O

hm

R R37

R=R

c O

hm

V_D

C

SR

C18

Vdc=VD

C

L L29

R=R

top

L=Lto

p u

H

L L33

R=R

mid

L=Lm

id u

H

L L34

R=R

mid

L=Lm

id u

H

L L31

R=R

bot

L=Lbot uH

L L30

R=R

bot

L=Lbot uH

L L32

R=R

top

L=Lto

p u

H

C C34

C=C

b n

F

C C35

C=C

b n

F

Stability Concerns

Page 40

(a)

(b)

Figure 20 : Reflection coefficient (S11) as seen the receiver side transistor’s base and the antenna

side transistor base respectively

Lastly, a transient analysis is performed as a secondary test for stability and to

understand the characteristics of instability. A transient analysis using a maximum step

size of 1 ns and a stop time of 100 us were found to be sufficient for this case. The

results in Figure 21 show that the circuit is unstable and its oscillations grow with time.

The Fourier series of the waveform shows that oscillations occur at a number of

frequencies. Therefore, if this circuit is to be utilised as a matching network for HF

antennas, some major changes would be required to stabilise this circuit without

2 4 6 8 10 12 14 16 180 20

0.6

0.8

1.0

1.2

1.4

1.6

1.8

0.4

2.0

freq, MHz

2 4 6 8 10 12 14 16 18 0 20

1

2

3

4

0

5

freq, MHz

Chapter 3

Page 41

nullifying its ability to negate impedances. This will be discussed in the following

section.

(a)

10 20 30 40 50 60 70 80 900 100

-200

-100

0

100

200

-300

300

time, usec

Vout, m

V

(b)

1E61E5 1E7

20

40

60

80

100

120

0

140

freq, Hz

fs(V

out), m

V

Figure 21 :(a) Transient Analysis and (b) Fourier Series of the voltage at the receiver (labelled Vout

in the circuit)

Stability Concerns

Page 42

3.4 Circuit Modification

The simulation results in section 3.3 confirm that the circuit is not stable. Therefore,

modifications to the circuit are necessary. The circuit was biased using standard

amplifier biasing methodology. Since stability is the main problem, the circuit was re-

biased to produce better stability factors by designing the NIC such that the voltage at

the base of the transistor is 1/10th that of the voltage of the supply as suggested by

Gonzales [34].

Literature review of the work done by Linvill and Sussman-Fort, at the beginning of this

chapter, explained that this circuit is only open circuit stable (as the input and output of

the NIC are at the emitter ends of the transistors). For this circuit setup, the impedance

of the receiver (50 Ohms) was found to be not sufficiently large as compared to the

input impedance of the NIC. Thus a transformer with a turns ratio of 1:10 was placed

before the receiver, such that the receiver impedance would appear to be 100 times

larger to the NIC. It is to be noted that this solution is not ideal, as it reduces the already

small antenna voltage.

The reflection coefficient results (Figures 16 and 20) suggest that a large proportion of

the instability occurs at low frequencies. This could be circumvented by adding filters

into the circuit. However, a careful selection and placement of filters were necessary in

order to avoid grounding a large proportion of the signal and thus nullify the

functionality of the circuit. After much experimentation and analysis, it was found that

by implementing a band-stop filter and two resistively loaded notch filters, the circuit

could be stabilised. The modified circuit is shown in Figure 22. By following the same

steps in section 3.3, the circuit was tested for its reflection coefficient across a number

of points and a transient analysis was performed. The results are shown in Figures 23 to

25.

Chapter 3

Page 43

Figure 22 : Modified NIC circuit

Vin

Vout

R R76

R=5 O

hm

L L47

R=

L=5 n

H

C C66

C=0.0

01 u

F

C C63

C=5 u

F

L L43

R=

L=1 u

H

Zin

Zin

2Zin

1=zi

n(S

11,P

ortZ1)

Zin

N

VS

WR

VS

WR

2V

SW

R1=vs

wr(S

11)

VSW

R

BJT

_M

odel

MR

F949

L L31

R=R

bot

L=Lbot uH

R R40

R=R

e O

hm

C C36

C=0.1

uF

S1P

Ante

nna2

1Ref

S_P

ara

m

SP

1

Ste

p=0.1

MH

z

Sto

p=40 M

Hz

Sta

rt=0.1

MH

z

S-P

AR

AM

ETER

S

Term

Term

1

Z=50 O

hm

Num

=1

TF

TF2

T=0.1

0

C C101

C=0.1

uF

VA

RV

AR

61

Rsta

b=1

Eqn

Var

VA

R

VA

R51

VD

C=20

Vb=20

Re=100

R2=4200

R1=59800

Rc=2900

Eqn

Var

VA

R

VA

R48

Rm

id=6.5

Cm

id=0.0

86235

Lto

p=200

Lbot=

470

Rbot=

2.6

Rto

p=6.5

Cbot=

0.1

124

Cb=1

Cto

p=0.0

86235

Lm

id=470

Eqn

Var

BJT

_N

PN

BJT

3M

odel=

MR

F949

R R69

R=R

sta

b O

hm

R R68

R=R

sta

b O

hm

L L39

R=

L=Lto

p u

H

R R37

R=R

c O

hm

V_D

C

SR

C18

Vdc=V

DC

L L30

R=R

bot

L=Lbot uH

R R39

R=R

e O

hm

L L56

R=

L=10 u

H

C C77

C=0.1

055 n

F

R R75

R=95 O

hm

C C106

C=1.0

nF

C C105

C=1.0

nF

BJT

_N

PN

BJT

4

Model=

MR

F949

R R44

R=R

1 O

hm

V_D

C

SR

C21

Vdc=V

b V

R R43

R=R

2 O

hm

R R42

R=R

2 O

hm

V_D

CS

RC

20

Vdc=V

b V

R R41

R=R

1 O

hm

C C33

C=27 p

F

R R38

R=R

c O

hm

V_D

C

SR

C19

Vdc=V

DC

L L38

R=

L=Lto

p u

H

Stability Concerns

Page 44

(a)

5 10 15 20 25 30 350 40

0.97

0.98

0.99

0.96

1.00

freq, MHz

mag(S

(1,1

))

m8

m8freq=mag(S(1,1))=0.9972207755Max

29.320000000MHz

(b)

5 10 15 20 25 30 350 40

0.65

0.70

0.75

0.80

0.85

0.90

0.95

0.60

1.00

freq, MHz

mag(S

(1,1

))

m8

m8freq=mag(S(1,1))=0.9999998369Max

30.000000000kHz

Figure 23 : Reflection coefficient (S11) as seen from the receiver (a) and antenna (b) respectively

Chapter 3

Page 45

(a)

10 20 30 40 500 60

0.4

0.5

0.6

0.7

0.8

0.9

0.3

1.0

freq, MHz

mag(S

(1,1

))

m8

m8freq=mag(S(1,1))=0.9990352243Max

33.940000000MHz

(b)

10 20 30 40 500 60

0.6

0.7

0.8

0.9

0.5

1.0

freq, MHz

mag(S

(1,1

))

m8

m8freq=mag(S(1,1))=0.9963402964Max

10.000000000kHz

Figure 24 : Reflection coefficient (S11) as seen the receiver side transistor’s base (a) and the

antenna side transistor base (b) respectively

Stability Concerns

Page 46

(a)

0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6 1.80.0 2.0

-20

-15

-10

-5

0

5

10

-25

15

time, msec

Vout, fV

(b)

Figure 25 : Transient Analysis (a) and its Fourier Series (b) of the voltage at the receiver

Figures 23 to 25 show that the circuit is stable under this set of conditions. Transient

analysis, adding a transient voltage step at the power supply and some initial conditions

(+0.1 V at receiver-side transistor base) confirmed this result. The circuit setup used is

shown in Figure 26.

Chapter 3

Page 47

Figure 26 : Transient Analysis circuit setup

Vsu

p

Vou

tV

in

Tra

n

Tra

n1

Max

Tim

eSte

p=0.

5 ns

ecS

topT

ime=

100

usec

TR

AN

SIE

NT

V_D

CS

RC20

Vdc

=Vb

V

VtS

tep

SR

C3

Vlo

w=0 V

Vhig

h=-1

V

Dela

y=10 n

sec

Ris

e=1 n

sec

t

InitC

ond

InitC

ond1

V=0.1

V

Init

Co

nd

NodeSet

NodeSet1

V=0.1

V

No

de

Se

t

S1P

Ant

enna

2

1Re

f

TF

TF

1T

=0.

1

Ter

mT

erm

1

Z=

50 O

hm

Num

=1

C C66

C=

0.00

1 uF

L L47

R=

L=5

nH

R R78

R=

1.5

Ohm

R R75

R=

5 O

hm

C C77

C=0.

1055

nF

L L56

R=

L=10

uH

R R68

R=R

stab

Ohm

L L43

R=

L=1

uH

C C63

C=C

1 uF

R R69

R=

Rst

ab O

hmB

JT_N

PN

BJT

3M

odel

=M

RF

949

VA

RV

AR61

Rst

ab=

1

Eqn

Var

C C78

C=

1 nF

C C79

C=

1 nF

C C33

C=

27 p

F

S_P

aram

SP1

Ste

p=0.

01 M

Hz

Sto

p=40

MHz

Sta

rt=

0.1

MH

z

S-P

AR

AM

ET

ER

S

VA

RV

AR60

C3=

0.47

C1=

5

Eqn

Var

BJT

_Mod

el

MR

F94

9

VA

RV

AR48

Rm

id=

6.5

Cm

id=

0.08

6235

Ltop

=20

0

Lbot

=47

0R

bot=

2.6

Rto

p=6.

5

Cbo

t=0.

1124

Cb=

1C

top=

0.08

6235

Lmid=

470

Eqn

Var

C C36

C=

0.1

uF

BJT

_NP

N

BJT

4M

odel

=M

RF

949

C C37

C=0.

1 uF

R R42

R=

R2

Ohm

Zin

Zin

2Z

in1=

zin(

S11

,Por

tZ1)

Zin

N

VS

WR

VS

WR

2VS

WR

1=vs

wr(

S11

)

VS

WR

L L31

R=

Rbo

tL=

Lbot

uH

R R40

R=

Re

Ohm

R R39

R=

Re

Ohm

L L30

R=

Rbo

t

L=Lb

ot u

H

L L40

R=

Rbo

tL=

Lbot

uH

L L41

R=

Rbo

t

L=Lb

ot u

H

R R43

R=

R2

Ohm

R R41

R=R

1 O

hm

L L39

R=

L=Lt

op u

H

L L38

R=

L=Lt

op u

H

VA

RV

AR51

VD

C=

20

Vb=

20R

e=10

0R

2=42

00

R1=

5980

0R

c=29

00

Eqn

Var

V_D

CS

RC

21

Vdc

=V

b V

R R44

R=

R1

Ohm

V_D

CSR

C19

Vdc

=V

DC

R R38

R=

Rc

Ohm

R R37

R=

Rc

Ohm

V_D

C

SR

C18

Vdc

=VD

C

Stability Concerns

Page 48

The additional parameters were necessary as to simulate a perturbation that could

trigger oscillation. In the case, when the circuit is unstable, a spurious signal that grows

with time will be produced by the transient analysis. The transient analysis was run for

1 ms with a maximum step size of 0.5 ns. The result in Figure 27 shows a spike at the

start due to the voltage step input for the transient analysis, but the spurious signal does

not grow with time and the Fourier Series of the signal does not indicate oscillation.

This transient and reflection coefficient analysis confirms that the circuit is stable.

(a)

0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6 1.80.0 2.0

0

10

20

30

40

-10

50

time, msec

Vout, m

V

(b)

Figure 27 : Transient Analysis (a) and its Fourier Series (b) of the voltage at the receiver

Chapter 3

Page 49

However, the solution applied to achieve a stable circuit has come at cost of a slight

degradation in performance. This was expected because a number of filters were

introduced into the NIC itself and a 0.1 turns ratio transformer was used at the receiver

end.

With regards to the negation ability of the NIC, the inclusion of the filters has reduced

the performance of reactance negation. This is because a notch filter designed for 4.9

MHz was used due to instability at that frequency. This notch filter, however, includes a

95 Ohm resistor to reduce the effects of the attenuation to a sufficient level for stability.

The reactance negation of the NIC circuit upon a 27 pF capacitor is shown in Figure 28.

For simplicity in reading the simulation, the result was obtained using a 1:1 turns ratio

transformer and the antenna was shorted. This result is to be compared with the

reactance curve of an ideal negative 27 pF capacitor as simulated by ADS in Figure 29.

The overall imaginary impedance of the circuit is shown in Figure 30.

5 10 15 20 25 30 350 40

-1000

-500

0

500

-1500

1000

freq, MHz

imag(Z

in1)

m1m2

m3m4m5

m6m7

m1freq=imag(Zin1)=665.259Max

6.450MHz m2freq=imag(Zin1)=532.369

10.00MHzm3freq=imag(Zin1)=306.330

15.00MHz

m4freq=imag(Zin1)=188.007

20.00MHz


22.00MHz


3.000MHz


5.000MHz

Figure 28 : Imaginary part of the input impedance of the NIC with 1:1 transformer

and without the antenna

Stability Concerns

Page 50

2 4 6 8 10 12 14 16 180 20

1000

2000

3000

4000

5000

0

6000

freq, MHz

imag(Z

in1)

m1

m2m3 m4 m5




10.00MHz



20.00MHz

Figure 29 : Reactance curve of an ideal negative 27pF capacitor

By comparing Figures 28 and 29, it is observed that at lower frequencies, below 6.15

MHz, the reactance curve of the NIC has been severely affected by the filters. However,

at higher frequencies the accuracy improves. Some discrepancies in the reactance

negation are to be expected, but the overall circuit reactance cancellation, has a

moderately good performance as can be seen in Figure 30. It will be noted, however,

that the transformer has reduced the reactance to 1/100 of its value at the output of the

NIC.

10 20 30 40 500 60

-1.5

-1.0

-0.5

0.0

-2.0

0.5

freq, MHz

imag(Z

in1)

m1m2

m3m4m5m6

m7

m1freq=imag(Zin1)=0.449Max

10.50MHz


10.00MHz

m3freq=imag(Zin1)=-0.213

15.00MHz


20.00MHz


22.00MHz



5.000MHz

Figure 30 : Imaginary part of the input impedance of the NIC with a transformer as seen from the

receiver

Chapter 3

Page 51

Another disadvantage with this solution, as briefly mentioned earlier in this section, is

that the introduction of the 1:10 transformer also reduces the already small antenna

voltage. In addition, the real resistance becomes even smaller in magnitude and thus

causing the impedance that is seen by the receiver to be further from the ideal of 50

Ohm. The real part of the input impedance of the matching network, and antenna, as

seen from the receiver is shown in Figure 31.

10 20 30 40 500 60

0.2

0.4

0.6

0.8

1.0

0.0

1.2

freq, MHz

real(Zin

1)

m10

m11

m10freq=real(Zin1)=1.016Max

11.25MHz

m11freq=real(Zin1)=0.070Min

29.32MHz

Figure 31 : Real part of the input impedance of the NIC as seen from the receiver

In order to improve on this solution, an understanding on what impedance values are

necessary for stability would be helpful. Thus a stability analysis on the effect of

impedance loading on the receiver side is performed by using a batch analysis

(parameter sweep) of the receiver impedance and its effect on stability. The circuit setup

is shown in Figure 32. The reflection coefficient of the antenna port and transistor base

port is shown in Figure 33 and Figure 34.

Stability Concerns

Page 52

Figure 32 : Circuit setup for stability sensitivity due to receiver load

Vout

Vin

Batc

hSim

Contr

olle

r

Batc

hSim

1

Rem

oveD

ata

sets

=no

Merg

eD

ata

sets

=no

UseSepara

tePro

cess=no

SweepA

rgum

ent=

SweepM

odule=

""

UseSw

eepM

odule=

no

Analysis

[1]=

"SP

1"

UseSw

eepP

lan=

yes

Var=

"Rx"

Sta

rt=50.0

Sto

p=50000.0

Dec=1.0

Log=

BA

TC

H S

IMU

LA

TIO

N

VA

R

VA

R62

Rx=

500

Eqn

Var

Term

Term

1

Z=

50 O

hm

Num

=1

S1P

Ante

nna2

1Re

f

R R77

R=

Rx O

hm

VAR

VAR

51

VDC

=20

Vb=20

Re=100

R2=4200

R1=59800

Rc=2900

Eqn

Var

Zin

Zin

2

Zin

1=zin

(S11,P

ortZ

1)

Zin

N

VSW

R

VSW

R2

VSW

R1=

vsw

r(S

11)

VSW

R

R R76

R=5 O

hm

R R75

R=95 O

hm

L L56

R=

L=10 u

H

C C77

C=

0.1

055 n

F

S_P

ara

m

SP

1

Ste

p=

0.0

1 M

Hz

Sto

p=

20 M

Hz

Sta

rt=0.1

MHz

S-P

AR

AM

ET

ER

S

C C66

C=

0.0

01 u

F

L L47

R=

L=5 n

H

BJT

_NP

N

BJT

3

Model=

MRF

949

VA

R

VA

R61

Rsta

b=

1

Eqn

Var

C C78

C=

1 n

F

C C79

C=

1 n

F

R R69

R=

Rsta

b O

hm

C C63

C=C

1 u

F

L L43

R=

L=1 u

H

R R68

R=R

sta

b O

hm

C C33

C=27 p

F

VA

R

VA

R60

C3=

0.4

7

C1=

5

Eqn

Var

BJT_M

odel

MR

F949

VAR

VAR

48

Rm

id=

6.5

Cm

id=

0.0

86235

Lto

p=200

Lbot=

470

Rbot=

2.6

Rto

p=6.5

Cbot=

0.1

124

Cb=

1

Cto

p=0.0

86235

Lm

id=470

Eqn

Var

C C36

C=0.1

uF

BJT_N

PN

BJT4

Model=

MR

F949

C C37

C=

0.1

uF

R R42

R=R

2 O

hm

L L31

R=

Rbot

L=

Lbot

uH

R R40

R=

Re O

hm

R R39

R=

Re O

hm

L L30

R=R

bot

L=

Lbot

uH

L L40

R=R

bot

L=

Lbot

uH

L L41

R=

Rbot

L=

Lbot

uH

R R43

R=

R2 O

hm

V_DC

SRC

20

Vdc=V

b V

R R41

R=

R1 O

hm

L L39

R=

L=

Lto

p u

H

L L38

R=

L=

Lto

p u

HV

_D

C

SRC

21

Vdc=

Vb V

R R44

R=

R1 O

hm

V_D

C

SRC

19

Vdc=

VD

C

R R38

R=R

c O

hm

R R37

R=R

c O

hm

V_D

C

SR

C18

Vdc=

VD

C

Chapter 3

Page 53

2 4 6 8 10 12 14 16 180 20

0.88

0.90

0.92

0.94

0.96

0.98

1.00

1.02

1.04

1.06

0.86

1.08

freq, MHz

mag(S

(1,1

))

mag(S(1,1))

Rx=50.000000

Rx=500.000000

Rx=5000.000000

Rx=50000.000000

Figure 33 : Reflection coefficient as seen from antenna with varying receiver load (Rx)

2 4 6 8 10 12 14 16 180 20

0.55

0.60

0.65

0.70

0.75

0.80

0.85

0.90

0.95

0.50

1.00

freq, MHz

mag(S

(1,1

))

mag(S(1,1))

Rx=50.000000

Rx=500.000000

Rx=5000.000000

Rx=50000.000000

Figure 34 : Reflection coefficient as seen from the base of the antenna-side transistor with varying

receiver load (Rx)

From Figures 33 and 34, we can conclude that the NIC requires a loading of at least

5000 Ohms at the receiver side for the circuit to be stable. This re-affirms the number of

turns chosen for the transformer used. However, as previously discussed, the

transformer does not match the circuit to 50 Ohms. An alternate solution is to

incorporate a buffer amplifier between the NIC and the receiver. A buffer circuit has a

Stability Concerns

Page 54

significant advantage over the 1:10 transformer solution, as it does not cause a drop in

antenna voltage. Its disadvantage, however, is that it could add additional noise.

There are two main choices for a buffer circuit design for this application, namely an

emitter follower and a source follower. A source follower was chosen as it provides

larger input impedance as compared to an emitter follower.

A simple source follower circuit was designed and shown in Figure 35. The source

follower was designed to provide an input impedance of 500k Ohms and an output

impedance of 50 Ohms. The high input impedance would cause a greater proportion of

the signal voltage to occur across the receiver impedance and yet fulfil the stability

requirements. The result of including the buffer into the circuit is shown in Figure 36,

where the real part of the input impedance was successfully matched to 50 Ohms.

NIC_Output

VoutTerm

Term1

Z=50 Ohm

Num=1

C

C102

C=0.1 uF

R

R117

R=Rbuf kOhm

VAR

VAR63

Rbuf=1000.0

EqnVar

ap_nms_2N6660_19930601

M2

R

R118

R=Rbuf kOhm

R

R115

R=665 Ohm

C

C101

C=0.1 uF

V_DC

SRC34

Vdc=Vbuff

Figure 35 : Source Follower Circuit Design (note: Vbuff = 7.0 V)

Chapter 3

Page 55

2 4 6 8 10 12 14 16 180 20

10

20

30

40

50

0

60

freq, MHz

real(Zin

3)

Figure 36 : Real part of the input impedance of the overall NIC circuit

In order to compare the performance of the different circuits, a transient analysis was

performed using a 1 mV voltage source, placed within the antenna circuit and its

frequency was varied. The resultant voltage across the receiver input is listed in Table 5.

Table 5: Signal level at receiver given a fixed input voltage level

Freq

(MHz)

Buffer

(2N6660) &

NIC (V)

Buffer (2N6660)

(V)

NIC & 1:10

transformer

(V)

3.00 6.975E-5 4.623E-4 1.508E-5

5.00 5.847E-5 4.624E-4 1.274E-5

10.00 0.002 4.624E-4 4.328E-4

11.24 0.004 4.320E-4 6.331E-4

15.00 0.002 4.624E-4 3.383E-4

20.00 0.001 4.624E-4 2.596E-4

From Table 5 we can observe that the NIC circuit with the buffer (column 2) shows a

marked improvement in performance for frequencies above 10 MHz over standard

active antenna matching that uses the buffer alone (column 3). Sussman-Fort, in his

recent work [35], confirm that a buffer circuit enhances the performance of the NIC and

surpasses traditional active antenna matching. This circuit also has a substantial

Stability Concerns

Page 56

decrease in signal loss as compared with the NIC circuit containing the transformer

(column 4).

3.5 Chapter Summary

NICs are, at best, conditionally stable. By applying a reflection coefficient analysis at

various points within the circuit and by utilizing transient analysis, the circuit’s stability

can be tested. The NIC’s stability is particularly dependent on its loading. For emitter

based NICs, it is Open Circuit Stable and require a high impedance load. Besides that,

for an NIC to be stable, it was found that the DC bias of the transistors needs to be

carefully chosen, such that the voltage at the base is relatively low (1/10th or smaller) as

compared with the supply voltage. Last but not least, there were inherent instabilities at

low frequencies in this circuit which could be removed by band-stop filters and notch

filters. It is to be noted that the design of the filters is a complicated matter as the filters

themselves could interact with the circuit and cause a different set of instabilities. The

solutions applied to stabilise the NIC circuit have caused deterioration in the bandwidth

of the NIC. Further work could be explored in order to minimise this loss in

performance.

By introducing a source follower at the output of the NIC, substantial improvements

were made in the matching of the real resistance of the antenna to the 50 Ohms of the

receiver. This combination has improved the voltage level received at the receiver while

maintaining circuit stability. Over the appropriate bandwidth of the NIC, its

performance is better than traditional active matching. Future work could include other

methods of stability prediction that may provide a better understanding of the conditions

for stability. This could improve the efficiency of the design process of NICs. In the

practical implementation of the NIC circuit, device variation could have a detrimental

effect on the circuit. The following chapter explores some of the common

manufacturing variations and its consequence upon the NIC circuit.

Page 57

Chapter 4

Effects of Non-idealities

N this chapter, the effects of non-idealities upon the performance of the

NIC will be analysed. Some of the non-idealities considered are parameter

variations, environmental changes and supply voltage fluctuations. A

sensitivity analysis was also performed to understand the sensitivity of the parameters

chosen and its impact on the NIC performance.


Page 58

4 Effects of Non-idealities

In the preceding chapter, we have seen that stability is a significant issue to be

considered for NIC circuits. We have established, through reflection coefficient analysis

and transient analysis, that the NIC with the circuit conditions and loading in section

3.4, is stable. However, in the practical implementation of NIC circuits, device

variations and other non-idealities could affect stability and other aspects of

performance. The parameters that will be considered are transistor beta value,

temperature, supply voltage and some of the lumped components used in the circuit. In

particular, asymmetry in transistor properties could be a problem. The effect of

variations upon factors such as stability and impedance negation performance will be

analysed.

4.1 Transistor Mismatch and Hfe Variations

The NIC circuit, in this research, has a degree of symmetry and includes two identical

transistors. However, in the manufacturing of these transistors, there could be

differences in their beta or hfe values. Hence, it is important to consider the impact of a

mismatch in the two BJTs.

The BJTs’ (MRF949) datasheet specifies that it has a minimum beta value of 50. This

implies that there could be a fair degree of variance about this value. Thus a batch

simulation in ADS2009 was performed, by varying the beta values for one and/or both

of the transistors. In Figure 37, both of the transistors’ beta values were varied

simultaneously and its reactance and the stability are simulated with a parameter sweep

of beta starting from 50 to 200. The stability parameter is taken by looking into the

antenna end of the NIC. It is to be noted that the reactance simulation, shown in this

chapter, does not include the buffer circuit and is seen from the 50 Ohm receiver.

Similarly, asymmetric beta is analysed by varying only one transistor’s beta value at a

time, fixing the other at 175 (a typical beta value for this transistor). The results are

given in Figures 38 and 39. This shows the effect of transistor mismatch upon the

important performance parameters of the circuit.

Chapter 4

Page 59

beta=50.000000

beta=75.000000

beta=100.000000

beta=125.000000

beta=150.000000

beta=175.000000

beta=200.000000

beta=50.000000

beta=75.000000

beta=100.000000

beta=125.000000

beta=150.000000

beta=175.000000

beta=200.000000

(a)

2 4 6 8 10 12 14 16 180 20

-60

-40

-20

0

20

40

60

-80

80

freq, MHz

imag(Z

in1)

(b)

2 4 6 8 10 12 14 16 180 20

0.95

0.96

0.97

0.98

0.99

0.94

1.00

freq, MHz

S(1

,1)

Figure 37 : (a) Reactance (without buffer circuit) and (b) stability, when both transistor betas are

varied


Page 60

beta=50.000000

beta=75.000000

beta=100.000000

beta=125.000000

beta=150.000000

beta=175.000000

beta=200.000000

beta=50.000000

beta=75.000000

beta=100.000000

beta=125.000000

beta=150.000000

beta=175.000000

beta=200.000000

(a)

2 4 6 8 10 12 14 16 180 20

-40

-30

-20

-10

0

10

20

30

40

-50

50

freq, MHz

imag(Z

in1)

(b)

2 4 6 8 10 12 14 16 180 20

0.95

0.96

0.97

0.98

0.99

0.94

1.00

freq, MHz

S(1

,1)

Figure 38 : (a) Reactance (without buffer circuit) and (b) stability, when only the antenna side

transistor is varied

Chapter 4

Page 61

beta=50.000000

beta=75.000000

beta=100.000000

beta=125.000000

beta=150.000000

beta=175.000000

beta=200.000000

beta=50.000000

beta=75.000000

beta=100.000000

beta=125.000000

beta=150.000000

beta=175.000000

beta=200.000000

(a)

2 4 6 8 10 12 14 16 180 20

-60

-40

-20

0

20

40

60

-80

80

freq, MHz

imag(Z

in1)

(b)

2 4 6 8 10 12 14 16 180 20

0.95

0.96

0.97

0.98

0.99

0.94

1.00

freq, MHz

S(1

,1)

Figure 39 : (a) Reactance (without buffer circuit) and (b) stability, when only the receiver side

transistor is varied

The results of Figures 37 to 39 show that beta variation has little effect on the

performance of the NIC. However, it is interesting to note that the performance of the

NIC is more sensitive to the beta value of the receiver end transistor. The following

section will explore the impact of temperature variations on the performance of the NIC.


Page 62

4.2 Temperature Variations

HF systems are used in a number of different environmental conditions. The durability

of the NIC circuit is important to be able to withstand non-ideal environmental

conditions. One environmental variation that could have a significant impact is

temperature changes. In this section, we will test the NIC’s performance under a range

of temperatures. There are standards which specify the temperature durability of a

circuit, depending on the application context of the circuit. One of them is the United

States Military Standard, MIL-STD-810, which details the required circuit durability

under a wide range of temperature variation. Table 6, as obtained from Altera

Corporation [36] , shows the temperature variations that the circuit design should take

into account, such that the circuit fulfils the specified performances.

Table 6: Temperature durability range according to the context of application

Application Temperature Range

Civilian 0 to 85 ˚C

Industrial -44 to 100 ˚C

Military -55 to 125 ˚C

The most stringent temperature durability range, namely the one for military

applications, was chosen and an ADS simulation was performed, by varying the

circuit’s temperature, in order to simulate the performance of the NIC circuit under

these harsher conditions. This temperature variation test was applied to the lumped

components and transistors of the NIC. It is to be noted that high temperature stability

capacitors with a temperature coefficient of 30ppm/˚C were used. The results, as shown

in Figure 40, lead to an understanding that the stability and negation performance of the

circuit is not significantly affected by temperature variation of the transistors.

Chapter 4

Page 63

T1=-55.000000

T1=-10.000000

T1=35.000000

T1=80.000000

T1=125.000000

T1=-55.000000

T1=-10.000000

T1=35.000000

T1=80.000000

T1=125.000000

(a)

2 4 6 8 10 12 14 16 180 20

-40

-30

-20

-10

0

10

20

30

40

-50

50

freq, MHz

imag(Z

in1)

(b)

2 4 6 8 10 12 14 16 180 20

0.95

0.96

0.97

0.98

0.99

0.94

1.00

freq, MHz

S(1

,1)

Figure 40 : (a) Reactance (without buffer circuit) and (b) stability when temperature is varied for

military applications

4.3 Supply Voltage Variations

Variations in the power supply for the NIC circuit, could directly affect the collector

current and hence affect NIC’s performance. There are three DC voltage sources in the

NIC circuit namely the voltage at the transistors’ collector (VCC), bases (VBB) and at the

MOSFET’s drain (labelled as Vbuff in the circuit). Variations at the Voltage source of

the Buffer would not analysed as they do not affect the negation ability and stability of

the circuit. ADS simulations were performed to analyse the impact of minor supply

voltage variations (less than ±10%) for the other two voltage sources.


Page 64

Firstly, the voltage at the transistors’ collector is varied from 18 V to 22 V, and its

impact upon reactance (without buffer circuit), and the stability as seen from the

antenna are shown in Figure 41. The same simulations were performed by varying the

base voltage source instead and its results are shown in Figure 42. The results obtained

show that minor supply voltage variations, for both collector and base voltage, do not

affect the performance of the NIC.

(a)

5 10 15 20 25 30 350 40

-40

-30

-20

-10

0

10

20

30

40

-50

50

freq, MHz

imag(Z

in1)

Vcc=18.000000

Vcc=18.500000

Vcc=19.000000

Vcc=19.500000

Vcc=20.000000

Vcc=20.500000

Vcc=21.000000

Vcc=21.500000

Vcc=22.000000

(b)

2 4 6 8 10 12 14 16 180 20

0.95

0.96

0.97

0.98

0.99

0.94

1.00

freq, MHz

S(1

,1)

Vcc=18.000000

Vcc=18.500000

Vcc=19.000000

Vcc=19.500000

Vcc=20.000000

Vcc=20.500000

Vcc=21.000000

Vcc=21.500000

Vcc=22.000000

Figure 41 : (a) Reactance (without buffer circuit) and (b) stability when the voltage source at the

collectors are varied

Chapter 4

Page 65

(a)

5 10 15 20 25 30 350 40

-40

-30

-20

-10

0

10

20

30

40

-50

50

freq, MHz

imag(Z

in1)

Vbb=18.000000

Vbb=18.500000

Vbb=19.000000

Vbb=19.500000

Vbb=20.000000

Vbb=20.500000

Vbb=21.000000

Vbb=21.500000

Vbb=22.000000

(b)

2 4 6 8 10 12 14 16 180 20

0.95

0.96

0.97

0.98

0.99

0.94

1.00

freq, MHz

S(1

,1)

m1

m1freq=S(1,1)=0.9999997587 / -0.0932602033Vbb=22.000000Max

100.00000000kHz

Vbb=18.000000

Vbb=18.500000

Vbb=19.000000

Vbb=19.500000

Vbb=20.000000

Vbb=20.500000

Vbb=21.000000

Vbb=21.500000

Vbb=22.000000

Figure 42 : (a) Reactance (without buffer circuit) and (b) stability when the voltage source at the

bases are varied


Page 66

4.4 Sensitivity Analysis

Besides the variation found in section 4.1, there are other process variations that occur

for the other practical elements used in the NIC circuit. A simple example is the

tolerance in resistor values and other lumped components. Little variations in the

values, or parasitics, of these elements could contribute to a poorer performance for the

NIC. ADS provides a method for sensitivity analysis, in order to understand the impact

that is contributed by each of these elements.

A sensitivity analysis using ADS optimisation simulation was performed upon some of

the major elements in the circuit (as shown in Figure 43), namely the bias resistors,

chokes, capacitors and filters within the NIC circuit. This analysis was carried across

the frequency range 0.1 to 40 MHz. The result of the sensitivity analysis upon the

reactance of the NIC circuit (excluding the buffer circuit) is shown in Figure 44. ADS’

normalised sensitivities use the approximate gradient (single-point sensitivity) to predict

the percentage change in the response due to a 1 % change in the design variable. Figure

44 would then imply that, for a 1 % increase in inductor value at the left hand side notch

(Lnotch1), an increase of about 150 % in the magnitude of the reactance would occur.

This, however, is the maximum value recorded across the entire frequency range.

Chapter 4

Page 67

VAR

VAR50

T1=25

beta=175

EqnVarVAR

VAR66

Cnotch2=0.001 {o}

Lnotch2=5 {o}

Rnotch2=5 {o}

EqnVar

VAR

VAR65

Rbsf=1 {o}

Lbsf=1 {o}

Cbsf=5 {o}

EqnVar

VAR

VAR61

Lnotch1=10 {o}

Cnotch1=0.1055 {o}

Rnotch1=95 {o}

EqnVar

Goal

sensAbsImagZin

Weight=

Max=10

Min=0

SimInstanceName="SP1"

Expr="mag(imag(Zin1))"

GOAL

Goal

sensS11

Weight=

Max=10

Min=0

SimInstanceName="SP1"

Expr="mag(S(1,1))"

GOAL

S_Param

SP1

Step=0.01 MHz

Stop=40 MHz

Start=0.1 MHz

S-PARAMETERS VAR

VAR64

Rmid=6.5

Cmid=0.086235

Ltop=470 {o}

Lbot=220 {o}

Rbot=2.6

Rtop=6.5

Cbot=0.1124

Cb=1 {o}

Ctop=0.086235

Lmid=470 {o}

EqnVar

Optim

Optim1

UseAllGoals=yes

UseAllOptVars=yes

StatusLevel=4

OptimType=Sensitivity

OPTIM

ParamSw eep

Sw eep1

SimInstanceName[6]=

SimInstanceName[5]=

SimInstanceName[4]=

SimInstanceName[3]=

SimInstanceName[2]="SP1"

SimInstanceName[1]="Optim1"

PARAMETER SWEEPVAR

VAR51

VDC=20

Vb=20

Re=100 {o}

R2=4200 {o}

R1=59800 {o}

Rc=2900 {o}

EqnVar

Vout

Vin

C

C101C=0.1 uF

V_DCSRC34

Vdc=7

RR118R=Rbuf kOhm

VAR

VAR63Rbuf=1000.0

EqnVar

RR115R=665 Ohm

ap_nms_2N6660_19930601M2

RR117R=Rbuf kOhm

TermTerm1

Z=50 OhmNum=1

BJT_NPNBJT4Model=MRF950a

LL31

R=Rbot

L=Lbot uH

RR40R=Re Ohm

LL30

R=RbotL=Lbot uH

RR39R=Re Ohm

CC36C=0.1 uF

BJT_NPNBJT3Model=MRF949

CC63C=Cbsf uF

RR68R=Rbsf Ohm

RR69R=Rbsf Ohm

LL43

R=

L=Lbsf uH

RR76R=Rnotch2 Ohm

LL47

R=L=Lnotch2 nH

CC66C=Cnotch2 uF

S1PAntenna2

1 Ref

VARVAR60

C3=0.47

C1=5

EqnVar

LL56

R=L=Lnotch1 uH

CC77C=Cnotch1 nF

RR75R=Rnotch1 Ohm

BJT_ModelMRF949Bf=beta

BJT_ModelMRF950aBf=175

CC78

C=1 nF

CC79

C=1 nF

C

C33C=27 pF

RR42

R=R2 Ohm

LL40

R=Rbot

L=Lbot uH

LL41

R=RbotL=Lbot uH

RR43

R=R2 Ohm

V_DCSRC20Vdc=Vb V

RR41R=R1 Ohm

LL39

R=L=Ltop uH

LL38

R=L=Ltop uH V_DC

SRC21Vdc=Vb V

RR44R=R1 Ohm

V_DCSRC19

Vdc=VDC

RR38

R=Rc Ohm

RR37

R=Rc Ohm

V_DC

SRC18Vdc=VDC

Figure 43 : Sensitivity Analysis for the NIC circuit

R2

R1

Rc

Lto

p

Lbot

Cb

Lm

id

Lnotc

h1

Cnotc

h1

Rnotc

h1

Rbsf

Lbsf

Cbsf

Cnotc

h2

Lnotc

h2

Re

Rnotc

h2

0

50

100

150

-50

200

sensVariables

Reacta

nce S

ensitiv

ity

Figure 44 : Reactance (without buffer circuit) sensitivity analysis across 0.1 to 40 MHz


Page 68

The simulation was repeated for the range 3-10 MHz, 10-12 MHz and 12-40MHz in

order to identify the frequency for which the filter was problematic. Figure 45 (c) shows

the range 12-40 MHz for which the filter does not represent a problem. Figure 45 (a)

and Figure 45 (b) show that in the range 3 – 12 MHz, the tolerance of filter coefficients

must be as low as possible to achieve the expected negation performance.

(a)

R2

R1

Rc

Lto

p

Lbot

Cb

Lm

id

Lnotc

h1

Cnotc

h1

Rnotc

h1

Rbsf

Lbsf

Cbsf

Cnotc

h2

Lnotc

h2

Re

Rnotc

h2

0

10

20

30

-10

40

sensVariables

Reacta

nce S

ensitiv

ity

(b)

R2

R1

Rc

Lto

p

Lbot

Cb

Lm

id

Lnotc

h1

Cnotc

h1

Rnotc

h1

Rbsf

Lbsf

Cbsf

Cnotc

h2

Lnotc

h2

Re

Rnotc

h2

0

50

100

150

-50

200

sensVariables

Reacta

nce S

ensitiv

ity

(c)

R2

R1

Rc

Lto

p

Lbot

Cb

Lm

id

Lnotc

h1

Cnotc

h1

Rnotc

h1

Rbsf

Lbsf

Cbsf

Cnotc

h2

Lnotc

h2

Re

Rnotc

h2

-0.5

0.0

0.5

1.0

1.5

-1.0

2.0

sensVariables

Reacta

nce S

ensitiv

ity

Figure 45 : Reactance sensitivity analysis across (a) 3-10 MHz , (b) 10-12 MHz and (c) 12-40 MHz

respectively

Chapter 4

Page 69

A deviation of 10 % in Lnotch1 was found to cause a deviation of 30 Ohms in the overall

imaginary impedance of the circuit. Thus a minimum tolerance of 10% is recommended

for each the filter elements used. It is to be noted that the introduction of the filters

affected the input impedance across the 27pF capacitor. As a result, the sensitivity of the

negating capacitor might be affected. The sensitivity effect of the filters in relation to

the negating capacitor could be investigated further as a future research.

Next, we analyse the sensitivity of the reflection coefficient (as seen from the antenna)

due to variations in the lumped components. The sensitivity analysis result (shown in

Figure 46) shows the positive impact of the filters in improving stability. However, it

also suggests that there is a trade-off involved in the choice of filters, due to interaction

between the filters. This complicates the search to design the appropriate filters.

R2

R1

Rc

Lto

p

Lbot

Cb

Lm

id

Lnotc

h1

Cnotc

h1

Rnotc

h1

Rbsf

Lbsf

Cbsf

Cnotc

h2

Lnotc

h2

Re

Rnotc

h2

-0.20

-0.15

-0.10

-0.05

0.00

0.05

0.10

-0.25

0.15

sensVariables

Reflection C

oeffic

ient Sensitiv

ity

Figure 46 : Sensitivity of the reflection coefficient as seen from antenna across 0.1 to 40 MHz.

Figure 46 show that variations in the lumped components do not significantly impact

the stability performance of the NIC circuit.


Page 70

4.5 Chapter Summary

The impact of process variation, temperature changes and supply voltage variation upon

the performance of the NIC circuit was discussed and simulated in this chapter. It was

found that the NIC performance was not heavily affected by these variations. The

exception, however, is the variations in the filter component values. A sensitivity

analysis indicates that the reactance cancellation ability is severely affected by variation

in the filter components. The stability of the circuit, however, is not sensitive to these

variations. For the present, however, the filter solution is a workable option, providing

filter components are carefully chosen. Since the NIC consists of active circuits, the

intrinsic noise in the circuit could pose threats, as it may be at a higher voltage level

than the signals received, and thus diminish the usefulness of the NIC matching

network. The following chapter explores some of these issues.

Page 71

Chapter 5

Noise Considerations

OISE is an important consideration in the design of an antenna system. In

this chapter, a noise analysis will be performed for a receive antenna system

utilizing the NIC circuit in this thesis. Two main categories of noise,

namely environmental noise and internal noise will be considered and compared, in

order to understand if the device is externally or internally noise limited. The ideal goal

for an antenna matching network designer is that the circuit be externally noise limited.


Page 72

5 Noise Considerations

5.1 Introduction

Noise is an important parameter to consider in the design of an active matching network

for an antenna system. Noise generated by active matching circuits can be at a relatively

high level and hence ‘drown’ the signals of interest, and thus diminish the benefits of

having a NIC circuit which successfully negates the reactance of the antenna. Noise is,

essentially, undesired signals. Noise could be segmented into two major categories,

namely internal and external noise. External noise arises from sources such as

atmospheric noise, man-made noise, etc. From the circuit designer’s perspective, not

much could be done about the environmental noise. Internal noise, however, has its

origin in circuit imperfections, some components creating more noise than others. Thus,

in designing a matching network, it is a goal of the circuit design to mitigate the internal

noise of the circuit such that the device is environmentally noise limited. This chapter

seeks to understand the impact of the different sources of internal, and external noise

and to estimate the typical noise levels contributed by these sources. We can thus

conclude whether typical NIC circuits are externally noise limited or whether the

internal noise dominates.

5.2 Internal noise

Circuits create noise internally. This noise originates in the electronic components

themselves. There are three types of internal noise namely Thermal noise, Shot noise

and Flicker. Thermal noise (or Johnson-Nyquist noise, as it is sometimes known) is

generated from the motion of charge carriers inside an electrical conductor at

equilibrium. With or without any applied voltage, there is a random movement of

electrons which will produce a noise voltage. This is independent of frequency and thus

it is also known as ‘white noise’. Shot noise is produced by active devices. This occurs

when the current flow is discontinuous, or when there is a ‘jump’ in current. Shot noise

particularly occurs across the junctions of the BJT. It increases when the bias current is

increased. It should be noted that flicker noise also appears in active devices, but its

effect is negligible at HF frequencies (its amplitude is inversely proportional to

frequency).

Chapter 5

Page 73

As the NIC implementation in this research consists of 2 Bipolar Junction Transistors, a

MOSFET and numerous lumped components, only thermal noise and shot noise are to

be considered. Advanced Design System 2009’s Harmonic Balance simulation was used

to perform a non-linear noise simulation to analyse the internal noise of the circuit. The

circuit was setup as in Figure 47. It is to be noted that the temperature was set to 16.85

˚C in order to achieve the highest accuracy for noise analysis as suggested by ADS’

documentations [37]. Figures 48 and 49 give the specified noise figure and the

minimum noise figure of the circuit respectively. The voltage at the receiver (as shown

in Figure 50) shows a maximum voltage level of 4.40 nV. This is significantly smaller

than typical signals generated by the receiver antenna (c.f. Table 5 in section 3.4). This

level, however, must be compared with the environmental noise in order to understand

which noise source is limiting its Signal to Noise ratio (SNR).


Page 74

Figure 47 : ADS circuit to analyse internal noise

Vout

Vin

C C109

C=0.1

uF

Term

Term

2

Z=50 O

hm

Num

=2

Harm

onic

Bala

nce

HB

2

Oth

er=

Ord

er[

1]=

ord

er

Fre

q[1

]=fr

eq1 M

Hz

MaxO

rder=

3HAR

MO

NIC

BALAN

CE

V_D

C

SR

C35

Vdc=V

DC

R R122

R=R

c O

hm

Options

Options1

Tnom

=25

Tem

p=16.8

5

OPTIO

NS

Nois

eC

on

NC

1

Nois

yTw

oP

ort=ye

sN

ois

eN

ode[1

]=V

out

HB N

OIS

E C

ON

TR

OLLER

C C104

C=0.0

01 u

F

L L58

R=

L=5 n

H

R R119

R=5 O

hm

L L61

R=

L=10 u

H

C C106

C=0.1

055 n

F

R R124

R=95 O

hm

VA

RV

AR

3

freq1=15

ord

er=

3

Eqn

Var

SN

R

SN

R1

SN

R1=snr(V

out,V

out.nois

e,{1})

BJT

_M

odel

MR

F949

P_nT

one

PO

RT

1

P[1

]=pola

r(dbm

tow

(-117.6

5),0)

Fre

q[1

]=freq1 M

Hz

Z=50 O

hm

Num

=1

VA

RV

AR

66

Rm

id=6.5

Cm

id=0.0

86235

Lto

p=200

Lbot=

470

Rbot=

2.6

Rto

p=6.5

Cbot=

0.1

124

Cb=1

Cto

p=0.0

86235

Lm

id=470

Eqn

Var

VA

RV

AR

65

VD

C=20

Vb=20

Re=100

R2=4200

R1=59800

Rc=2900

Eqn

Var

VA

RV

AR

64

Rsta

b=1

Eqn

Var

L L63

R=

L=Lto

p u

H

V_D

CS

RC

39

Vdc=V

DC

R R133

R=R

c O

hm

C C111

C=27 p

F

R R132

R=R

1 O

hm

V_D

C

SR

C38

Vdc=V

b V

R R131

R=R

2 O

hm

R R130

R=R

2 O

hm

V_D

C

SR

C37

Vdc=V

b V

R R129

R=R

1 O

hm

R R128

R=665 O

hm

V_D

C

SR

C36

Vdc=7

R R127

R=R

buf kO

hm

C C110

C=0.1

uF

VA

R

VA

R63

Rbuf=

1000.0

Eqn

Var

ap_nm

s_2N

6660_19930601

M3

R R126

R=R

buf kO

hm

R R125

R=R

e O

hm

L L62

R=R

bot

L=Lbot uH

BJT

_N

PN

BJT

4M

odel=

MR

F949

C C108

C=1.0

nF

C C107

C=1.0

nF

R R123

R=R

e O

hm

L L30

R=R

bot

L=Lbot uH

C C105

C=0.1

uF

S1P

Ante

nna3

1Ref

L L60

R=

L=Lto

p u

H

R R121

R=R

sta

b O

hm L L

59

R=

L=1 u

H

R R120

R=R

sta

b O

hm

BJT

_N

PN

BJT

3

Model=

MR

F949

C C103

C=5 u

F

Chapter 5

Page 75

4 6 8 10 12 14 16 182 20

5

10

15

20

25

0

30

noisefreq, MHz

nf

Figure 48 : Noise Figure of the NIC circuit

4 6 8 10 12 14 16 182 20

2

3

4

5

6

7

1

8

noisefreq, MHz

NFm

in

Figure 49 : Minimum Noise Figure of the NIC circuit


Page 76

4 6 8 10 12 14 16 182 20

1

2

3

4

0

5

noisefreq, MHz

Vout.nois

e, nV

m1

m1noisefreq=Vout.noise=4.403E-9Max

11.00MHz

Figure 50 : Noise voltage at the output of the NIC circuit due to internal noise

5.3 External noise

In the design and planning of any RF communication system, it is important to compare

the wanted signal levels with the background signal level, i.e. its external noise. This is

because the natural background noise could set a limit on the sensitivity of receiver

system (antenna plus radio receiver). A good receiver system is one which its internal

noise is below the external noise. i.e. the system is externally noise limited. In the

preceding section, we have considered the internal noise sources and its overall noise

contribution to the NIC circuit. In this section, we seek to understand the sources of

external noise and its impact on the noise level of the NIC. The sources of external

noise consist of atmospheric, galactic and man-made noise. The significance or

magnitude of these noise sources varies according to the frequency range of the

communications system.

Atmospheric noise is generated by a number of sources that are distributed worldwide.

They are impulsive in nature and thus span a large frequency and are caused by

radiation from lightning discharges, emissions from atmospheric gases and the earth’s

surface. Their impact is especially strong at frequencies at and below HF (less than 30

MHz). Lightning across the globe can be ‘heard’ as it travels across continents using the

Chapter 5

Page 77

Earth’s ionosphere as a waveguide. Furthermore, there is almost continuous lightning

activity around the world, approximately 100 lightning strokes happen per second [38].

Thus the impact of atmospheric noise is significant in raising the external noise floor

and will thus set a limit on the sensitivity of radio systems.

In the design of an antenna system, there is no need to achieve sensitivity of the system

that is better than the external noise. It is therefore important to quantify the external

noise according to the operating frequency range targeted. As atmospheric noise is a

random process and has variation across localization, time and season, a comprehensive

probabilistic model is required. With these consideration, CCIR, or Comité Consultatif

International pour la Radio (currently known as ITU) has produced several atmospheric

noise models, taken from 16 measurement stations worldwide across a period of 4 years

[39]. This model can be used by radio engineers when designing a receive system.

Another source of external noise is galactic or cosmic noise which arises from the sun

and other stars. Its impact on earth is dependent on the ionospheric shielding and varies

with frequency. In the HF band, its impact is considerably lower than atmospheric and

man-made noise and thus can be neglected.

Last but not least, mankind has contributed to an increasing amount of external noise.

Man-made radio noise is caused by a variety of sources of which the most significant

noise contributor is from electrical equipment. These consist of electrical machinery,

spark ignition systems, switching transients, discharge lighting and etc. Since man-made

noise originate from man-made technologies, it is dependent on the distance of the noise

sources to the antenna system and it occurs at random time with a short duration and

random magnitude. Bianchi [40] states that distance, frequency, emitted power,

continuous or impulsive nature of the emitted waves, its polarization and modulation are

important characteristics that describe man made noise.

Bianchi proceeds further and claims that man made noise has been increasing steadily

for the past century or so. This makes sense as devices which utilises Electromagnetics

are becoming increasing available, affordable and in a wider range of applications.


Page 78

International Telecommunication Union Radiocommunication sector (ITU-R), formerly

known as CCIR, has produced numerous recommendations regarding radio noise level.

The ITU recommendations include information on noise figures from the different noise

sources in order for radio designers to estimate system performance. This information is

obtained empirically in different locations in the world at different times. ITU Radio

Noise Recommendation P.372-9 [41] provides a noise figure versus frequency graph for

the Noise Figure estimation of man-made noise (as shown in Figure 51)

Figure 51 : Median values for man-made noise power (adopted from [41])

From Figure 51, we see that the noise figure of man-made noise increases as frequency

decreases. In the HF region, the level is significant and varies depending on localization.

NOTE: This figure is included on page 78 of the print copy of the thesis held in the University of Adelaide Library.

Chapter 5

Page 79

In comparison with atmospheric noise level, man-made noise’s impact varies with time.

At night time, natural noise level is considerably higher than the noise contributed by

artificial noise sources. However, during daytime, the atmospheric noise level is

significantly lower than man-made noise (25 dB or more). In terms of probability, the

external noise of the antenna is dominated by man-made noise most of the time

(99.5%).

In the design of an antenna system, the aim is to limit the level of internal noise to

below that of its external noise. Here, according to the figure above, a probable estimate

for the spot frequency of 10 MHz in rural areas, gives approximately an external noise

figure of 40 dB. The precise values are given in Table 7.

Table 7: Man Made Noise according to location. A noise figure of 39.5 dB (bolded) was used for a

electric field calculation in Equation 5.7.

Freq (MHz) City (dB) Residential (dB) Rural (dB) Quiet Rural (dB)

3 63.58 59.28 53.98 39.95

4 60.12 55.82 50.52 36.38

5 57.44 53.14 47.84 33.61

6 55.25 50.95 45.65 31.34

7 53.39 49.09 43.79 29.43

8 51.78 47.48 42.18 27.77

9 50.37 46.07 40.77 26.31

10 49.10 44.80 39.50 25.00

11 47.95 43.65 38.35 23.82

12 46.91 42.61 37.31 22.74

13 45.94 41.64 36.34 21.74

14 45.05 40.75 35.45 20.82

15 44.22 39.92 34.62 19.96

16 43.45 39.15 33.85 19.16

17 42.72 38.42 33.12 18.41

18 42.03 37.73 32.43 17.70

19 41.38 37.08 31.78 17.03

20 40.76 36.46 31.16 16.39


Page 80

Then, a calculation is required to obtain the voltage induced on the antenna by the

external noise, which then could be compared against its internal noise and

Intermodulation effects.

The following formulas as obtained from [41] applies

bkt

pf na

0

= (5.1)

where af : external noise factor

np : available noise power from an equivalent lossless antenna

k : Boltzmann’s constant = 1.38 X 10-23 J/K

0t : reference temperature (K) taken as 290 K

b : noise power bandwidth of the receiving system (Hz)

Equation (5.1) can also be written as:

204−+= BFP an dBW (5.2)

where

nn pP log10= (5.3)

bB log10= (5.4)

and

204log10 0 −=tk (5.5)

Note that Equation (5.2) is based on the assumption that noise is incident on the antenna

uniformly in all directions. (This is a reasonable assumption for a small antenna.)

For the case where a short monopole is used along with a perfecting conducting ground

plane, the vertical electric field strength is given as below [41]:

5.95log20 −++= BfFE MHzan dB (µV/m) (5.6)

where

En : field strength in bandwidth b, and

fMHz : centre frequency (MHz).

For the HF frequency range, aF = 39.5 dB (rural area), 10=MHzf , and B = 10 log (3000

Hz) for the receiver noise bandwidth.

Substituting these into Equation (5.6) gives

23.1−=nE dB (µV/m) (5.7)

The voltage induced at the antenna is given by the following formula

Chapter 5

Page 81

effhEV .= (5.8)

Substituting (5.7) into (5.8), and assuming that the 2 meters length antenna is

perfectly aligned with the noise signals (to obtain the worst case estimate).

µV736.1210. 20

23.1

=×==−

effhEV (5.9)

The voltage induced then would be 1.736 µV.

By placing this voltage as a noise source (with the same magnitude across the 3 – 20

MHz range) at the antenna end, and ‘switching’ off internal noise effects, the voltage at

the receiver end of the NIC was simulated and found to have a voltage of 1.797 µV at

10MHz. This calculation and simulation is repeated for every 1 MHz and the noise at

the receiver end of the NIC is shown in Figure 52. The results show that man made

noise could range from 85.12 nV to 2767 nV depending on the frequency. This value

could then be compared with the internal noise simulated in Figure 50. It is to be noted

that these values are relevant to rural area application. In cities, however, the man made

noise is different and is shown in Figure 53. A comparison would lead to a conclusion

that the noise contribution due to environmental noise sources, for both rural or city

areas, is higher than the internal noise of the circuit. It is to be noted that the shape of

the curve was affected by the filters introduced to achieve stability (Chapter 3).

Figure 52 : Noise voltage at the receiver end of the NIC due to environmental noise in rural areas


Page 82

Figure 53 : Noise voltage at the receiver end of the NIC due to environmental noise in the cities

5.4 Chapter summary

This chapter has described the different noise sources for the NIC circuit, namely its

intrinsic internal noise and the environmental noise. This is crucial in order to

understand the limitation of the NIC’s noise performance. The results obtained in this

chapter leads to an understanding that the circuit’s noise performance is limited mainly

by the environmental noise. Figure 54 confirms that conclusion by comparing the

internal noise of the circuit with the voltage at the receiver caused by external sources

(man-made noise as measured from rural areas), across 3 to 20 MHz.

Figure 54 : Noise voltage at the receiver end of the NIC circuit due to environmental noise and

internal noise.

Chapter 5

Page 83

The simulated internal noise gives a maximum of 4.40 nV at the receiver which is

significantly smaller as compared to the voltage induced by environmental sources

which gives a minimum voltage of 85.12 nV at the receiver. However, in order to

confirm that the circuit is externally noise limited, the remaining noise component needs

to be considered, namely noise from the Intermodulation distortion (IMD) of the signals

that enter the antenna system. This is the effect of non-linearity due to the presence of

active devices in the circuit. The non-linear behaviour of the NIC and its IMD effects

are discussed in the next chapter.


Page 84

Page 85

Chapter 6

Non-linear Analysis

HE ultimate goal of the NIC matching network is to increase the bandwidth

of the system and to enable a higher voltage level for the received signals of

interest compared to the noise floor. However, a higher bandwidth implies

that more signals are received. Active devices which comprise the NIC circuit would

interact with these signals non-linearly and thus increase the noise floor or block the

signals of interest. In this chapter, a non-linear analysis was performed to model the

non-linear behaviour of the NIC and typical signals were used to understand the IMD

performance of the NIC.

Non-linear Analysis

Page 86

6 Non-linear Analysis

6.1 Introduction

“In these circuits (small signal amplifiers), non-linearities are responsible for

phenomena that degrade system performance and must be minimised” – Stephen A.

Maas [42]

In the preceding chapters, the NIC was shown to be able to provide a broadband match

in the HF frequency range and that its noise performance is only limited by the

environmental noise. However, NIC circuits utilise active devices in order to achieve

positive feedback to negate reactance. Active devices are inherently non-linear and

hence this introduces a whole set of non-linear problems which needs to be carefully

considered in determining the practicality and usefulness of the NIC matching circuit. In

particular, we need to analyse whether Intermodulation products have the potential to

mask the signals that we seek to receive.

Non-linear circuits are circuits whereby the superposition principle does not apply. This

is due to the non-linear terms in the transfer characteristics of BJTs. This gives rise to

problems like Intermodulation distortion, co-channel distortion, desensitization,

harmonics and etc. Consequently, frequency domain techniques are unable to provide

an acceptable analysis of the circuit behaviour. Agilent Advanced Design System 2009

Harmonic Balance simulation was chosen as the tool to analyse the non-linear

behaviour of the NIC circuit.

This chapter examines the non-linear behaviour of the NIC circuit and its consequences.

It provides the reader with a numerical model to approximate the NIC’s non-linear

response towards incoming signals. This numerical model can then be utilised to

estimate the intermodulation products received from broadcast stations. Typical levels

of broadcast signals are derived and then used to estimate the expected magnitude of

Intermodulation products. These products are then compared with the other unwanted

signals described in chapter 5 (i.e. noise).

Chapter 6

Page 87

6.2 Intermodulation Distortion and Numerical Modelling

The NIC, as shown in chapters 2 and 3, successfully matches an antenna over a wide

range of frequencies in the HF frequency region. A larger bandwidth, however, implies

that more undesired signals are received into the system. This does not cause problems

for a passive circuit. However, NICs consists of active devices such as BJTs, FETS and

Op-amps and these active devices introduce non-linear behaviour to the circuit. The

non-linearity of the circuit will create new frequencies due to the interaction between

the input signals. These signals modulate each other and could significantly increase the

noise floor of the system. The noise floor, if raised too high, would reduce the signal to

noise ratio significantly. A widely used figure of merit for the non-linear performance of

an active circuit is a circuit’s third order intercept point (IIP3). A two tone test was

simulated in order to analyse the Intermodulation Distortion (IMD) of the NIC circuit.

The two tone test was used in order to build a numerical model describing the non-

linear behaviour of the NIC. Two tones with an input voltage of 3 mV were used. The

first tone consists of frequencies 3, 5, 10, 15 and 20 MHz, while the second tone

consists of 3.01, 5.01, 10.01, 15.01 and 20.01 MHz. These two tones were used in

combination with each other. It is to be noted that the frequencies differ by 0.01 MHz

such that the frequency components could be distinguished. These values are

representative of typical values of broadcast channels in the HF frequency range. These

simulations were performed by using the harmonic balance analysis provided by the

ADS software simulation tool (Figure 55 shows the ADS simulation setup). The

harmonic balance analysis only required three orders of harmonics in order to achieve

similar results, with a maximum deviation of less than 0.8 %, with a seven order

analysis. Thus the three order analysis was deemed to be sufficient. Figure 56 shows an

example spectrum output a three order analysis is performed on an two tone test with at

15.17 MHz and 15.72 MHz.

Non-linear Analysis

Page 88

Figure 55 : NIC two tone harmonic balance analysis

Vin

Vout

M2

VA

R

VA

R2

freq1=

15.1

7

ord

er=

3

freq2=

15.7

2

Eqn

Var

R68

R=R

sta

b O

hm

R R41

R=

R1 O

hm

V_DC

SRC

20

Vdc=

Vb V

R R42

R=R

2 O

hm

BJT3

Model=

MR

F949

C C36

C=0.1

uF

S1P

Ante

nna2

1Ref

V_nTone

SR

C1

V[2

]=polar(

0.0

0255,0

) V

V[1

]=polar(

0.0

0625,0

) V

Fre

q[2

]=freq2 M

Hz

Fre

q[1

]=freq1 M

Hz

R R39

R=R

e O

hm

L L30

R=

Rbot

L=Lbot uH

C C66

C=

0.0

01 u

F

R R69

R=

Rsta

b O

hm

C C63

C=

5 u

F

L L43

R=

L=

1 u

H

VAR

VAR

48

Rm

id=

6.5

Cm

id=

0.0

86235

Lto

p=200

Lbot=

470

Rbot=

2.6

Rto

p=6.5

Cbot=

0.1

124

Cb=

1

Cto

p=0.0

86235

Lm

id=470

Eqn

Var

VA

R

VA

R61

Rsta

b=1

Eq

nVa

r

VA

R

VA

R51

VD

C=

20

Vb=20

Re=100

R2=4200

R1=59800

Rc=2900

Eq

nVa

r

BJT

_M

odel

MR

F949

BJT

4L L31

R=

L=

Lbot

uH

R117

R=R

buf kO

hm

VAR

VAR

62

Rbuf=

1000.0

Eqn

Va

r

C108

C=0.1

uF

Term

Term

1

Z=

50 O

hm

Num

=1

C C101

C=0.1

uF

Harm

onic

Bala

nce

HB1

Oth

er=

Ord

er[2]=

ord

er

Ord

er[1]=

ord

er

Fre

q[2

]=freq2 M

Hz

Fre

q[1

]=freq1 M

Hz

MaxO

rder=

3HA

RM

ON

IC B

ALA

NC

E

R R76

R=5 O

hm

L L47

R=

L=5 n

H

L L39

R=

L=

Lto

p u

H

R R37

R=R

c O

hm

V_DC

SRC

18

Vdc=V

DC

L L56

R=

L=10 u

H

C C77

C=

0.1

055 n

F

R R75

R=95 O

hm

C C106

C=

1.0

nF

C C105

C=1.0

nF

R R40

R=

Re O

hm

R R118

R=R

buf kO

hm

V_D

C

SR

C34

Vdc=

7

R R115

R=

665 O

hm

R R44

R=

R1 O

hm

V_D

C

SRC

21

Vdc=

Vb V

R R43

R=R

2 O

hm

C C33

C=27 p

F

R R38

R=R

c O

hm

V_D

C

SR

C19

Vdc=

VD

C

L L38

R=

L=

Lto

p u

H

Chapter 6

Page 89

5 10 15 20 25 30 35 40 450 50

-160

-140

-120

-100

-80

-60

-40

-180

-20

freq, MHz

dBm

(Vout)

m3m4

m5

m3freq=dBm(Vout)=-33.853

15.17MHzm4freq=dBm(Vout)=-42.025

15.72MHz

m5freq=dBm(Vout)=-135.337

14.62MHz

Figure 56 : Vout spectrum arising from input frequencies of 15.17 MHz and 15.72 MHz

The results of the two tone simulation were used to create a model that characterised the

nonlinear behaviour of the NIC based active antenna.

The theory of numerical analysis is as follows. For a two-tone test, the voltage V

measured at the output of the NIC can be described by the following expression.

twwVVatwwVVatwwVVa

twwVVatwVatwVatwwVVa

twwVVatwVatwVatwVatwVaV

)2cos()2cos()2cos(

)2cos()3cos()3cos()cos(

)cos(2cos2coscoscos

12

2

211212

2

2111212

2

110

212

2

192

3

281

3

1721216

212152

2

241

2

13222111

−+++−+

++++−+

+++++=

(6.1)

V1 and V2 are the amplitude of the two signals at the input to the NIC and w1 and w2 are

their frequencies respectively.

Non-linear Analysis

Page 90

By using the results of the ADS simulations, the data for the spectra of each

combination of input frequencies was calculated. By applying a least squares quadratic

fit to this data, the coefficients an (n>2) can be found for a frequency dependent model

of the form:

2

26

2

1521423121 wbwbwwbwbwbban +++++=

(6.2)

Coefficients a1 and a2 are different from the other coefficients as they have voltage

dependence of the form:

)(2

1 2

2

2

1

2

1

0

11 VVa ++= αα

(6.3)

)(2

1 2

2

2

1

2

2

0

22 VVa ++= αα

(6.4)

A MATLAB program was written to apply the least squares fit to all these coefficients

according to Equations 6.2, 6.3 and 6.4. The results of the MATLAB computations are

tabulated in Tables 8 and 9. In addition, surface plots were drawn to graphically

describe the variation of coefficients with frequency. It is to be noted that the black dots

shown in Figures 58 to 60 represents the coefficients of the respective frequency

components given in Equation 6.1, while 57 refers to Equation 6.3.

Table 8: Least squares quadratic fit for first 6 coefficients (c.f. Equation 6.1; The relationship

between coefficients an and bn is described by Equation 6.2)

a1 a2 a3 a4 a5 a6

2

1α 0

1α 2

2α 0

2α 2w1 2w2 w1+w2 w2-w1

b1 -7.24E-

01 -7.24E-

01 -

8.29E+00 -6.41E-

01 -2.91E-01 -2.91E-01 -5.56E-01

-4.31E-01

b2 2.41E-

01 -1.92E-

16 2.64E+00 2.14E-01 9.02E-02 5.33E-06 7.06E-02 5.24E-02

b3 -1.07E-

16 2.41E-01 -1.86E-15

-1.09E-16

-4.49E-17 9.02E-02 7.06E-02 5.24E-02

b4 3.19E-

18 3.30E-18 4.23E-17 3.48E-18 1.25E-18 -2.26E-08 2.20E-03 7.85E-04

b5 -8.05E-

03 4.51E-18 -1.41E-01

-6.64E-03

-3.15E-03 -1.58E-07 -3.13E-03 -1.98E-

03

b6 2.85E-

18 -8.05E-

03 5.47E-17 2.66E-18 1.24E-18 -3.15E-03 -3.13E-03

-1.98E-03

Chapter 6

Page 91

Table 9: Least squares quadratic fit for next 6 coefficients (c.f. Equation 6.1; The relationship

between coefficients an and bn is described by Equation 6.2)

This model was then validated by comparing its modelled IMD results with the ADS

simulated results (as shown in Table 10). It can be seen that the model and simulation

are sufficiently close, in most cases, to provide a model that is representative of the

intermodulation introduced by device non-linearity. It is to be noted that the quadratic

fit used to model the w2-w1 coefficients (Figure 58b) show some discrepancies between

simulated and curve fitted results. Hence a higher order polynomial could be used to

curve fit these coefficients. However, as this frequency component can be filtered out in

typical HF applications, these discrepancies should not pose any practical problems.

Table 10: MRF949’s IMD modelled and simulated performance when the 15.17MHz signal at

0.00652V interacts with the 15.72MHz signal at 0.00255V).

Freq 2w1 2w2 w1+w2 w2-w1 2w1+w2 2w1-w2 2w2+w1 2w2-w1

Modelled Mag(V)

1.50E-

05

2.27E-

06

1.09E-

05

7.16E-

06

5.77E-

08

6.73E-

08

2.24E-

08

2.67E-

08

ADS Mag(V)

1.32E-

05

2.00E-

06

1.03E-

05

1.03E-

05

5.36E-

08

5.41E-

08

2.09E-

08

2.11E-

08

a7 a8 a9 a10 a11 a12

3w1 3w2 2w1+w2 2w1-w2 2w2+w1 2w2-w1

b1 -1.77E-01 -1.77E-01 -5.14E-01 -5.66E-01 -5.14E-01 -5.68E-01

b2 5.49E-02 1.57E-05 7.39E-02 6.81E-02 5.65E-02 8.03E-02

b3 4.30E-06 5.48E-02 5.65E-02 8.10E-02 7.39E-02 6.93E-02

b4 8.85E-09 -3.24E-06 1.69E-03 2.53E-03 1.69E-03 2.53E-03

b5 -2.01E-03 -1.03E-06 -3.25E-03 -3.20E-03 -2.51E-03 -3.95E-03

b6 -1.65E-07 -2.01E-03 -2.51E-03 -3.99E-03 -3.25E-03 -3.25E-03

Non-linear Analysis

Page 92

(a)

510

1520

5

10

15

20

0

0.2

0.4

0.6

0.8

1

w1

αααα21

w2

Coef

Coef

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

(b)

5

10

15

20

5

10

15

20

0

0.2

0.4

0.6

0.8

1

w1

αααα01

w2

Coef

Coef

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

Figure 57 : Surface plots for MATLAB’s least squares quadratic fit to the coefficients of (a)2

1α and

(b) 0

1α (as described in Equation 6.3).

Chapter 6

Page 93

(a)

5

10

15

20 5

10

15

20

0

0.1

0.2

0.3

w2

2w2

w1

Coef

Coef

0

0.05

0.1

0.15

0.2

0.25

0.3

0.35

(b)

5

10

15

20

5

10

15

20

0

0.2

0.4

0.6

w1

w2-w1

w2

Coef

Coef

-0.1

-0.05

0

0.05

0.1

0.15

0.2

0.25

0.3

0.35

0.4

Figure 58 : Surface plots for MATLAB’s least squares quadratic fit to the coefficients of (a) 2w2

(i.e. a4) and (b) w2-w1 (i.e. a6) (as described in Equation 6.1).

Non-linear Analysis

Page 94

(a)

5

10

15

20

5

10

15

20

0

0.2

0.4

0.6

w1

w1+w2

w2

Coef

Coef

-0.1

0

0.1

0.2

0.3

0.4

0.5

0.6

(b)

5

10

15

20

5

10

15

20

0

0.05

0.1

0.15

w1

3w1

w2

Coef

Coef

-0.02

0

0.02

0.04

0.06

0.08

0.1

0.12

0.14

0.16

0.18

Figure 59 : Surface plots for MATLAB’s least squares quadratic fit to the coefficients of (a) w2+w1

(i.e. a5) and (b) 3w1 (i.e. a7) (as described in Equation 6.1).

Chapter 6

Page 95

(a)

5

10

15

20

5

10

15

20

-0.1

0

0.1

0.2

0.3

0.4

0.5

w1

2w1+w2

w2

Coef

Coef

-0.1

0

0.1

0.2

0.3

0.4

0.5

(b)

5

10

15

20

5

10

15

20

-0.2

0

0.2

0.4

0.6

0.8

w1

2w1-w2

w2

Coef

Coef

-0.2

-0.1

0

0.1

0.2

0.3

0.4

0.5

0.6

Figure 60 : Surface plots for MATLAB’s least squares quadratic fit to the coefficients of (a)

2w1+w2 (i.e. a9) and (b) 2w1-w2 (i.e. a10) (as described in Equation 6.1).

Non-linear Analysis

Page 96

6.3 Broadcast Stations

In the preceding section, we have developed a numerical model describing the non-

linear effects and the Intermodulation distortion of the NIC circuit. The model from

Tables 8 and 9 could be utilised to estimate the intermodulation products received from

broadcast stations. The level of possible input signals can be derived from the World

Radio TV Handbook [43] and a number of internet sources [44, 45]. Some typical, but

relevant, broadcast stations from Australia and internationally is detailed in Table 11.

The voltage induced at the receiving antenna was calculated and is shown in Table 11.

Table 11: Typical shortwave broadcast stations’ signals, as received in Adelaide, Australia.

Station Frequency (kHz) Distance

(km)

EIRP

(kW)

Voltage (V) at

receiving

antenna

Radio Australia

5995, 7150, 9580,

11660, 13605,

15170

2300km

300 0.00652

National ABC

2310, 4835 1300km 50 0.00471

2485, 5025 2400km 50 0.00255

2325, 4910 1800km 50 0.0034

Radio New Zealand

International

6170, 7440, 9765,

11725, 13660,

15720

3400km 100 0.00255

Trans World Radio

Pacific 9870, 11580 5361km 100 0.00162

KWHR World Harvest

Radio (Hawaii) 6120, 9930 9174km 100 0.00094

Far East Broadcasting

Company (Northern

Mariana Islands)

9670, 11650,

15380 5590 100 0.00155

National Broadcasting

Commission of Papua

New Guinea

4890, 9675 2970 100 0.00292

Voice of America

5995, 7405, 9840,

11580, 13775,

15120

16778 500 0.00115

Radio Thailand 4830, 7245, 9655,

15370 6937 500 0.00279

Chapter 6

Page 97

Voice of America (Relay

station – Thailand)

7110, 9770,

11785, 15265 6943 500 0.00279

Radio Singapore

International (RSI) 9530 5418 250 0.00253

BBC Far Eastern Relay

station (Singapore) 3915, 5975 5424 250 0.00252

The voltage induced at the antenna (column 5 in Table 11) was calculated as follows. It

is to be noted that the distance calculations were made for a path from Adelaide (which

has the geographical coordinates 34°55’S 138°35’E) to the respective transmitting base

stations. We will assume a receiver with a 2m monopole antenna (typical of short wave

reception).

The Electric Field Strength received is given by

RE

EIRP30=

(6.5)

where

E : field strength (V/m)

EIRP : Effective Isotropic Radiated Power (W)

R : Distance (m)

The voltage induced at an antenna is given by

effhEV .= (6.6)

where effh is the effective height of the antenna.

Assuming that the 2 meter short monopole antenna is perfectly aligned with the electric

field for a maximum voltage condition (worse case)

EV = (6.7)

Since

lheff2

1=

(6.8)

where l = physical length of the antenna (assuming that the antenna is short).

Thus the voltage induced, at the receiving antenna, by the broadcast stations can be

calculated from Equation (6.5) and has been listed in Table 11. With these values, and

Non-linear Analysis

Page 98

the numerical model produced in section 6.2, an estimate of the IMD products can be

obtained and is shown in the following section.

6.4 Theoretical or Expected IMD Noise Levels

Intermodulation between signals received can cause major problems by generating

artificial signals that interfere with desired weak signals. In the preceding section,

typical broadcast signals were calculated to assist in predicting some typical IMD noise

to be expected in the real world environment. Amongst frequencies created due to non-

linearity, the 2w1-w2 and 2w2-w1 components are the most significant concern. This is

because such IMD components are sometimes extremely difficult to filter out due to

their proximity, in frequency, to the desired signal frequency.

A wide range of typical broadcast signals were given in section 6.3 and Table 11.

From these signals, a matrix was tabulated to discover the worse case combination, such

that the strongest 2w1-w2 or 2w2-w1 component that is realised. This value is then

compared to other sources of noise, such as the environmental noise and internal noise

in chapter 5.

From Table 11 the signals broadcasted by Radio Australia, National ABC, Radio New

Zealand International and National Broadcasting Commission of Papua New Guinea

will be considered due to their signal strength and frequency. Since Radio Australia’s

HF signals are the largest in magnitude, it will be one of the two signals which could

give the worse case IMD combination.

The signals broadcasted by Radio Australia are received with a voltage of 6.52 mV on

frequencies 9.58, 11.66, 13.6 and 15.17 MHz. These are labelled as signal (a), (b), (c)

and (d) respectively. Similarly, the signal by National ABC will be labelled as signal

(e). Radio New Zealand International broadcasts at 9.77 MHz is labelled by (f), 11.73

MHz by (g), 13.66 MHz by (h) and 15.72 MHz by (i). The signal from the broadcast

station at Papua New Guinea is labelled as signal (j). A matrix, using these notations, is

shown in Table 12 along with the highest calculated level of 2w1-w2 or 2w2-w1

component. This is necessary to discover the worse case combination and the IMD

behaviour of the NIC.

Chapter 6

Page 99

Table 12: Highest 2w1-w2 or 2w2-w1 components due to the different two tone combinations. (The

highest value was bolded)

Highest 2w1-w2

or 2w2-w1 (dBm) (a) (b) (c) (d)

(e) -137.60 -136.59 -136.63 -137.35

(f) -136.43 -135.47 -135.07 -135.04

(g) -135.70 -134.65 -134.14 -134.00

(h) -135.57 -134.37 -133.73 -133.50

(i) -136.03 -134.59 -133.79 -133.43

(j) -135.30 -134.34 -133.95 -133.94

From Table 12, we can see that there is a tendency for the IMD to become worse as

frequency increases. This, however, is not always true as can be seen in row (e), i.e. the

combinations involving National ABC signal. The highest IMD signal was the 2w1-w2

component caused by the combination of signal (i) and (d), i.e. the 15.17 MHz and

15.72 MHz signals. In a crowded broadcast spectrum, this is hard to remove with

filtering, as the IMD is at 14.62 MHz. This would be closer if the two input signals were

nearer in frequency. This IMD level is -133.43 dBm, or 67.34 nV. This, however, is just

an estimate value. The simulated value (obtained through ADS) is 54.1 nV (as also

shown in Figure 56 and Table 10). In the next section, a comparison will be made

between some typical IMD levels with the external noise that was discussed in section

5.3.

6.5 Comparison with External Noise

As discussed in section 5.3, the external noise of the NIC in the HF frequency range

varies with frequency. Thus the frequency range of the IMD components is an

important consideration in comparing the IMD with the external noise. (Man-made

noise was obtained from Figures 52 and Figure 53.) Only the signal interactions from

Radio Australia and Radio New Zealand International are considered here as they

produce the highest levels of IMD.

Non-linear Analysis

Page 100

Table 13: Comparison between IMD levels with environmental noise in rural areas and cities.

IMD Frequency (MHz)

(2w1-w2 component) IMD Voltage (nV) Rural Noise (nV) City Noise (nV)

14.62 54.1 1839.4 5463.7

11.59 58.54 2683.5 8216.3

5.82 18.3 85.1 523.4

From Table 13, we see that environmental noise is significantly higher across the entire

frequency range for both rural and city areas. This difference increases with frequency

and this implies that the IMD effects are lesser of a concern at high frequencies.

Therefore, for applications in the frequency range above 10 MHz, IMD’s effect is

manageable as the environmental noise is the limiting factor for the NIC matching

circuit’s noise performance. Thus overall, the device is noise limited according to its

context of application.

In addition, improvements in transistor technology could further improve the non-linear

performance of the NIC. The transistor used in this thesis is MRF949. It is published in

MRF949’s datasheet that its IP3 level is at +29 dBm at 1 GHz with a collector current

of 20 mA. This explains the good non-linear performance for the NIC circuit. Another

low noise and highly linear BJT, namely BFP460, was used to check for incremental

improvement. The simulation results of both transistors’ Intermodulation products are

listed in Table 14 as a means of comparison.

Table 14: Transistor IMD performance comparison. The 2w1-w2 component represents the most

significant IMD problem (as bolded).

Freq 2w1 2w2 w1+w2 w2-w1 2w1+w2 2w1-w2 2w2+w1 2w2-w1

MRF949 Mag(V)

1.32E-05 2.00E-06 1.03E-05 1.03E-05 5.36E-08 5.41E-08 2.09E-08 2.11E-08

BFP460 Mag(V)

1.30E-05 1.99E-06 1.02E-05 1.01E-05 5.22E-08 5.27E-08 2.04E-08 2.06E-08

From Table 14, we see that there is some reduction in IMD noise level. This is a

positive result and implies that as transistors improve in their non-linear performance,

Chapter 6

Page 101

IMD will be less of an issue even at lower frequencies. However, some caution should

be taken in the choice of the transistor and the NIC’s context of application.

6.6 Chapter summary

In this chapter, a non-linear analysis was performed on the NIC circuit. This has not

been done in prior work, but it is necessary because NICs utilise active devices to

achieve positive feedback to negate impedance. A numerical model was produced to

model the non-linear behaviour of the NIC, which was then used to predict the

Intermodulation Distortion products produced due to the input of typical broadcast

signals. It was found that the device, at the HF range, is externally noise limited as the

IMD’s 2w1-w2 and 2w2-w1 components are at a level at least 4 times lower than the

environmental noise. It was also found that by choosing a transistor with a better non-

linear performance, the IMD level can be reduced. This implies that improvements in

transistor technology could extend the scope of application for future NIC circuits to be

used at lower frequencies.

Non-linear Analysis

Page 102

Page 103

Chapter 7

Conclusion

HIS chapter draws together the conclusions from the work described in this

thesis and provides recommendations for further research. It summarises all

the factors that are important in the design of an NIC matching network for

HF receive antenna systems. In addition, a summary of the original contributions

produced from this research is given.

Conclusion

Page 104

7 Conclusion

7.1 Results and Conclusions

The concept of Negative Impedance Converters (NIC), since its inception over half a

century ago, has attracted the attention of scientists and engineers. Such circuits have

the potential to cancel impedance and hence overcome certain limitations with passive

circuits. In the case of antennas, the ability to cancel impedance over a wide range of

frequency can overcome the limitations of passive matching. This research aims to

analyse the feasibility of NICs as matching networks for HF receiver antenna systems,

in particular, to be able to provide broadband matching for small (length <<

wavelength) antenna.

Chapter 1 contains a literature review on the efforts to reduce the size of antennas and,

in particular, the use of NICs. In chapter 2, we focus on the definition of Negative

Impedance Converters and carry out a linear analysis in order to understand their

operation. Through simulation, it is shown that an NIC is able to achieve an effective

match over the frequency range 8 – 12 MHz for a 2 meter monopole. This is achieved

by negating a single capacitor in order to cancel the capacitive reactance of the 2 meter

monopole. By replacing the capacitor with a network of elements, the bandwidth was

improved to 11 MHz. However, due to the parallel resonance of the network, this

modification had implications for the instability of the NIC circuit.

As NICs are known to be only conditionally stable, this is an issue that has to be

carefully analysed. Chapter 3 analysed stability by means of two methods, namely a

reflection coefficient analysis and a transient analysis. By applying these methods to the

circuit, it was found that the circuit oscillates due to low frequency instability. Steps

were then taken to stabilise the circuit and, in particular, the loading of the NIC had to

be carefully chosen. In addition, it was found that the DC bias of the transistors needs to

be designed, such that the voltage at the base is relatively low (1/10th or smaller) as

compared with the supply voltage. Finally, a band-stop filter and a notch filter were

introduced to remove frequencies at which the instability occurred. This solution,

however, has the drawback that it causes deterioration in the NIC’s bandwidth.

Chapter 7

Page 105

It was also found, in chapter 3, that the matching of the NIC circuit to the 50 Ohms of

the receiver could be significantly improved by introducing a source follower buffer

amplifier at the output of the NIC. Such an approach leverages the fact that an NIC is

open circuit stable. The use of a buffer is similar to the methods used in traditional

active antennas. In this case, however, the NIC significantly improves performance as

the reactance of the monopole is cancelled, which increases output voltage.

The objective of this thesis had been to understand the practical issues of using NICs as

antenna matching elements. Therefore, it is important to understand the effects of device

variations upon the performance of the circuit. Chapter 4 explores the impact of device

variation, temperature changes and supply voltage variation upon the performance of

the NIC circuit. It was found that the NIC performance is not heavily affected by these

variations. Variations in the filter values, however, have a significant effect on the

performance of the NIC. Consequently, careful selection of filter values is necessary

for the NIC to perform as simulated. A sensitivity analysis was performed and this

confirmed the conclusions made in chapter 4.

In any antenna system, noise can pose a problem if the level is higher than that of the

signals to be received. Chapter 5 explores the effects of NIC circuit noise and external

environmental noise. The results obtained in this chapter lead to the conclusion that

noise performance is limited mainly by the external environmental noise and not by

internal noise. Figure 54 confirms the conclusion by comparing the internal noise of the

circuit with the voltage at the receiver caused by external sources (man-made noise as

measured from rural areas), across the band 3 to 20MHz.

Another possible source of ‘noise’ is the artificial signals produced by the

Intermodulation Distortion (IMD) of the signals that enter the antenna system. This is

the due to the presence of active devices within the NIC and the large bandwidth. In

chapter 6, a non-linear analysis was performed on the NIC circuit. As a result, a

numerical model was produced which could then be used to predict the Intermodulation

Distortion products due to the input of typical broadcast signals. Among the IMD

components, typically the 2w1-w2 and 2w2-w1 components are the ones that cause the

Conclusion

Page 106

most problems as they can be hard to filter out without removing the desired signals.

However, the IMD levels of these components (given a set of typical broadcast stations’

signals as received in Adelaide), were found to be at least 4 times lower than the

environmental noise. Therefore, the effect of IMD does not change the conclusion that

the NIC in this research is externally noise limited. Indeed, it was also found that by

choosing a transistor with a better non-linear performance, the IMD level can be further

reduced.

The worked performed in this research could be improved in a number of ways. For

instance, other methods of predicting stability, namely Middlebrook’s technique [30]

and Rollet’s proviso [31, 32], could be explored. Such an approach yields a better

understanding of where in the circuit the instability arise and hence provides some

insight into how the instability might be eliminated. It is clear that the use of filtering

within the NIC is not an ideal solution and some improved techniques for reducing

instability are required if NIC based matching is to be viable.

This thesis has demonstrated that, in a short antenna, an NIC can provide effective

antenna matching over a large range of frequencies by eliminating the capacitive

reactance of the antenna. The limitations of the NIC, however, mean that it is probably

best employed as part of an active antenna and not the total device. Explicitly, it is best

combined with a traditional active antenna such as a source follower buffer amplifier.

Further, we have demonstrated that possible concerns, such as internal noise and non-

linearity, are not an issue for the target application, i.e. a short antenna for HF

communications reception.

The major contribution of this work has been the analysis of the application of NICs to

HF communication reception. This includes the following:

1) The interaction of the environment with the non-linearity in the NIC circuit.

2) A comparison between the external and internal noise effects

3) The stability of the NICs when operated as matching circuits for these

frequencies.

Chapter 7

Page 107

HF antennas can be very large and impractical. It is hoped that the work of this thesis

has provided some progress towards HF antennas of a manageable size. In particular,

such antennas would be useful for HF radios for domestic purposes where antenna size

is a major concern.

Conclusion

Page 108

Page 109

Appendix A

Software Implementation

A Matlab program was written in order to create a numerical model for a non-linear

analysis of the NIC circuit, as given in chapter 6. If this model is to be reproduced, this

program is to be used concurrently with ADS to obtain data. Then, the data is to be

processed according to Equation 6.1, 6.3 and 6.4. Matlab 7.10.0 (R2010a) was used to

implement this program.

% Surface model of the voltage independent coefficient of (2w1+w2) term.

% BJT used = MRF949, 2 meter monopole antenna

% Points chosen = 3, 5, 10, 15, 20 MHz

close all;

%% Instructions:

% Manually load the excel file (OrderedList)

% which consists of columns data for the different signal combinations

% File>Importdata>ChooseFile>Sheet1>Next>

% Then choose CreateVectorsFromEachColumnUsingColumnNames

y=x2w1pw2;

% Add the alphabet 'x' to the labels which start with a number

% p - represents 'plus'

% m - represents 'minus'

% Other examples:

% y=x2w1; % 2w1's coefficient

% Declaring the frequency points which relates to the data

x2=[3; 5; 10; 15; 20; 3; 5; 10; 15; 20; 3; 5; 10; 15; 20; 3; 5; 10; 15; 20; 3; 5; 10; 15; 20];

Appendix

Page 110

x1=[3; 3; 3; 3; 3; 5; 5; 5; 5; 5; 10; 10; 10; 10; 10; 15; 15; 15; 15; 15; 20; 20; 20; 20; 20];

x=[x1 x2];

% A surface plot using quadratic fit is implemented in the following:

stats = regstats(y,x,'quadratic','beta');

b = stats.beta; % Model coefficients

xx1 = linspace(min(x1),max(x1),32);

xx2 = linspace(min(x2),max(x2),32);

yy=linspace(min(y), max(y), 32);

[X1,X2] = meshgrid(xx1,xx2);

Y = b(1) + b(2)*X1 + b(3)*X2 + b(4)*X1.*X2 + b(5)*X1.^2 + b(6)*X2.^2;

% a= b(1) + b(2)*X11 + b(3)*X22 + b(4)*X11.*X22 + b(5)*X11.^2 + b(6)*X22.^2

% Plotting the surface plot

hmodel = scatter3(X1(:),X2(:), Y(:), 5, Y(:), 'filled');

hold on

hdata = scatter3(x1,x2,y,'ko','filled');

axis tight

xlabel('w1');

ylabel('w2');

zlabel('Coef');

hbar = colorbar;

ylabel(hbar, 'Coef');

title('{\bf Coefficient of (2w1+w2) }')

Appendix

Page 111

Appendix B

SPICE MODELS

Bipolar Junction Transistors

1) MRF949

Table 15: MRF949 Die Gummel Poon Parameters

Name Value Name Value Name Value IS 4.598E-16 IRB 8.00E-05 TF 1.00E-11

BF 175 RBM 3 XTF 50

NF 0.9904 RE 0.45 VTF 1.2

VAF 22 RC 6 ITF 0.32

IKF 0.08 XTB 0 PTF 32

ISE 1.548E-14 EG 1.11 TR 1.00E-09

NE 1.703 XTI 3 FC 0.9

BR 76.1 CJE 8.70E-13

NR 0.9952 VJE 0.905

VAR 2.1 MJE 0.389

IKR 0.02059 CJC 3.60E-13

ISC 3.395E-16 VJC 0.4907

NC 1.13 MJC 0.2198

RB 8 XCJC 0.43

2) BFP460 .OPTION TNOM=25, GMIN= 1.00e-12 *BFP460 C B E

.SUBCKT BFP460 1 2 3

CBEPAR 22 33 1.875E-013

CBCPAR 22 11 1.48E-013

CCEPAR 11 33 8.007E-016

LB 22 2 9.312E-010

LE 33 3 3.981E-010

LC 11 1 4.664E-010

CBEPCK 2 3 1.154E-016

CBCPCK 2 1 1.617E-014

CCEPCK 1 3 2.749E-015

Q1 11 22 33 4 M_BFP460

.MODEL M_BFP460 NPN(

+ IS = 1.221E-016

+ BF = 187.3

Appendix

Page 112

+ NF = 1.005

+ VAF = 37.95

+ IKF = 0.5364

+ ISE = 6.757E-014

+ NE = 2.312

+ BR = 14.19

+ NR = 1.004

+ VAR = 2.455

+ IKR = 0.0866

+ ISC = 1.335E-015

+ NC = 1.5

+ RB = 5.708

+ IRB = 0

+ RBM = 1.968

+ RE = 0.2919

+ RC = 1.067

+ XTB = -0.001

+ EG = 1.11

+ XTI = 5

+ CJE = 3.967E-013

+ VJE = 0.4605

+ MJE = 0.4485

+ TF = 4.702E-012

+ XTF = 18.02

+ VTF = 3.248

+ ITF = 0.8641

+ PTF = 0.1

+ CJC = 2.777E-013

+ VJC = 0.6477

+ MJC = 0.2943

+ XCJC = 0.7031

+ TR = 2.703E-006

+ CJS = 3.01E-013

+ MJS = 0.08335

+ VJS = 0.1506

+ FC = 0.5

+ KF = 0

+ AF = 1)

***************************************************************

.ENDS BFP460

Field Effect Transistors

1) 2N6660

*2N6660 MODEL

*

.MODEL 2N6660 NMOS (LEVEL=3 RS=0.36 NSUB=1.0E15

+DELTA=0.1 KAPPA=0.0506 TPG=1 CGDO=6.343E-10

+RD=0.43 VTO=1.600 VMAX=1.0E7 ETA=0.0223089

+NFS=6.6E10 TOX=1.0E-7 LD=1.698E-9 UO=862.425

+XJ=6.4666E-7 THETA=1.0E-5 CGSO=9.09E-9 L=2.5E-6

+W=5.0E-3)

.ENDS

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Practical Issues of Using Negative Impedance Circuits as ... · Practical Issues of Using Negative Impedance Circuits as an Antenna Matching Element by Fu Tian Wong B.E. (Electrical