Intertwined inductive frequency selective surface:An application for satellite communicationsJuan Andres Vasquez-Peralvo1, Jose Manuel Fernandez-Gonzalez1, Jonathan M. Rigelsford2,

1Grupo de Radiacion, Depto. de Senales, Sistemas y Radiocomunicaciones, Universidad Politecnica de Madrid,Madrid, Spain, {jvasquez,jmfdez}@gr.ssr.upm.es

2Department of Electronics and Electrical Engineering, University of Sheffield, Sheffield, United Kingdom,j.m.rigelsford@sheffield.ac.uk

Abstract—An intertwined tri-band Inductive Frequency Se-lective Surface (FSS) configured as Cassegrain sub-reflector forEarth to Satellite communication is presented. The sub-reflectoris designed to provide linear polarization independency and max-imum transparency to electromagnetic waves in K and Ka bandat frequencies 16.4-20.4 GHz and 28.2-32.5 GHz respectively, andprovide maximum reflectivity to electromagnetic waves in K bandat frequencies 23.6-25.4 GHz. The sub-reflector is designed usingthe Jerusalem cross element along with an intertwined shape.The intertwine shape will reduce the second resonant frequencyas well as given more angular stability and maximum bandwidth.The transmission and reflection parameters are shown in allfrequencies of interest. Finally, the full structure will be simulatedas a flat sub-reflector and placed at the front of horn antennasworking at the centre of the frequency bands to compare theradiation pattern agains the classical Cassegrain and primefocus configurations. The simulation are carried out using CSTMicrowave Studio.

Index Terms—Frequency Selective Surfaces, Inductive FSS,Dichroic, Cassegrain, Intertwined.

I. INTRODUCTION

Frequency Selective Surface (FSS) are periodic resonantelements separated from each other at a known distance,arranged in one or two dimensional array, acting as microwavefilters at certain frequencies. Depending whether the resonantelements are cut off from a metallic sheet or metallic resonantelements printed over a substrate, the surface will act as bandpass filter (Inductive FSS) or band stop filter (CapacitiveFSS) respectively [1]. Mathematical and applications insightsof FSS has been researched since 1960, which gives awide range of applications like electromagnetic filters, HighImpedance Surfaces (HIS), Artificial Magnetic Conductors(AMC), radomes, Electromagnetic Band Gaps (EBG) [2]and absorbers just to mention a few. Nowadays, due to highperformance workstations and improved electromagneticsimulation software, the applications of these structures areon continuous research, facing design challenges like stabilityat different angles of incidence, polarization independence,bandwidth enhancement, multi-band operation, grating lobereduction and cross-polarization isolation. [3]

Inductive FSS have two noticeable advantages over theCapacitive FSS. The first advantage is the mechanical stability

Fig. 1. Parabolic antenna with a Gregorian dichroic sub-reflector.

due to be self supported, meaning, that the FSS does notrequire any substrate where to stand. The second advantage isderived from the first and being that the resonant frequenciesare not affected due to the absence of a substrate. The additionof a substrate in the FSS structure induces losses and shiftsresonants frequency downward approximately by f0/

√εr,

were f0 is the FSS design frequency, and εr is the permittivityof the dielectric. To compensate this frequency shift the FSSelements size should be reduced, therefore making it difficultto manufacture when working at high frequencies [4].One inductive FSS application is the dichroic sub-reflector forCassegrain antennas. A dichroic sub-reflector is built usingan FSS structure which is transparent to electromagneticwaves at certain frequencies, but at the same time, reflectselectromagnetic waves at other frequencies [1]. A ray analysisof a Cassegrain antenna using an inductive FSS dichroic assub-reflector is shown in Fig. 1

Many contributions regarding dichroic subreflectors can befound on [5]–[15]. Most of those works haven’t analyzedthe effects of the FSS over the feed horns radiation patterns

and compared them with the traditional Cassegrain and primefocus configurations. In addition, the previous works haven’tused inductive intertwined shapes along with resonant ele-ments.

Therefore, this paper presents a design of an intertwinedinductive FSS working as a dichroic subreflector for aCassegrain antenna configuration. The FSS is comprised ofa Jerusalem Cross surrounded by an intertwined shape. Thesubreflector will work as band pass filter at 16.4− 20.4 GHzand 28.2 − 32.5 GHz, and as band stop filter at 23.6 − 25.4GHz. Those frequencies are used for earth to satellite com-munication in Europe [16]. The radiation pattern simulationsof the feed horn along with the FSS will be shown andcompared with the classical feed configurations of prime focusand Cassegrain.

II. DESIGN AND SIMULATION

A. Unit Cell Design and simulationAccording to Munk in his book [1] there are two important

characteristics to have in mind when designing a multibandFSS that provides high angular stability and bandwidth. Thefirst is the shape of the resonant element and the second isthe inter-element spacing. The most suitable resonant elementthat has those two characteristics is the Jerusalem cross formulti-band operation, surrounded by an intertwined shapefor better angular stability and bandwidth enhancement. Theunit cell of this resonant element is shown in Fig. 2, and itsnumerical dimensions in Table I. The thickness of the unitcell is 0.2 mm and the material is steel-1008 to enhancemechanical stability.

Fig. 2. Intertwined Unit Cell.

TABLE IDIMENSIONS OF THE UNIT CELL

Parameter DimensionsA 1 [mm]B 0.3 [mm]C 0.2 [mm]D 0.3 [mm]E 2.25 [mm]F 0.3 [mm]

The unit cell shows a transparent behavior in K and Kaband at frequencies 16.4-20.4 GHz and 28.2-32.5 GHz respec-tively, and maximum reflectivity to electromagnetic waves inK band at frequencies 23.6-25.4 GHz. The bandwidths arewide enough to provide communication in multiple frequencyallocations. The unit cell S-parameters for TE(0,0) mode areshown in Fig.3. The TM(0,0) mode will not be analyzed dueto the symmetry of the unit cell.

Fig. 3. Reflection and transmission of the inductive FSS.

B. FSS and Horn antenna design and simulations

To calculate the subreflector and horn antenna dimensions,a cassegrain antenna was designed and tweaked in orderto make the subreflector as flat as possible. This allows tosimulate it as a flat structure with minimal errors. Anotherimportant parameter while designing the Cassegrain antenna isthe distance d1 and d2 between the FSS and the horn antennas.Those distances should be large enough to place the FSS inthe near field region and not in the reactive field region of thehorn antennas. The design process is not included here but itwill be explained during the paper presentation.

The FSS subreflector with a diameter of 68.9mm and hornantennas working at 18.6 GHz, 24.58 GHz and 30.2 GHz weresimulated and radiations patterns were acquired. For the first

and third frequencies the FSS was placed at a distance d1 =29.9mm away from the horn antenna. For the third frequencythe FSS will be placed at a distance d2 = 34.67. To comparethe radiation patterns with the classical Cassegrain and primefocus configurations at the first and third frequencies, the FSSwere removed and the radiation pattern of the horn antennaswere acquired. For the second frequency the FSS was removeand instead a flat ground plane was placed at a distance d2.The radiation patterns can be seen in Fig.4, Fig.5 and Fig.6.

Fig. 4. Radiation pattern at 18.6 GHz cut at phi=90. FSS transparent toElectromagnetic Waves

Fig. 5. Radiation pattern at 24.6 GHz cut at phi=90. FSS working as groundplane

The results at 18.6 GHz and 30.2 GHz, when the FSSis transparent to electromagnetic waves show good agree-ment with the results of the horn antenna alone. The cross-polarization levels remain very low, therefore will not cause

Fig. 6. Radiation pattern at 30.2 GHz cut at phi=90. FSS transparent toElectromagnetic Waves

any cross-polarization problems. For the case at 24.6 GHz,when the FSS works as ground plane, the results shows goodagreement reflecting the electromagnetic waves and placingthe main beam at 180 degrees as expected. The cross polar-ization levels are very low especially in the main beam. Thelosses in all cases are low being the maximum of 0.3 dBi.

III. CONCLUSION

An intertwined inductive dichroic subreflector for earth tosatellite communication was designed, simulated and analyzed.The intertwine shape allows to increase the bandwidth andangular stability because the inter-element space is reduced.The radiation patterns at the three frequencies of interest wereacquired and they show good agreement against the classicalCassegrain configuration with low levels of cross-polarization.

ACKNOWLEDGMENT

Simulations done in this work have been performed us-ing CST Microwave Studio Suite 2018 under a cooperationagreement between Computer Simulation Technology (CST)and Technical University of Madrid. Authors would like toacknowledge the Spanish Government, Ministry of Economy,National Program of Research, Development and Innovationfor the support of this publication in the projects FUTURE-RADIO “Radio systems and technologies for high capac-ity terrestrial and satellite communications in an hypercon-nected world“ (project number TEC2017-85529-C3-1-R) andMadrid Region Government for the project S2013/ICE-3000(SPADERADAR-CM).

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