Tri-Band Coaxial Antenna Feed for Satellite Terminal · 2012. 8. 3. · the C and Ku bands...

Tri-Band Coaxial Antenna Feed for Satellite Terminal

Ku-Band Orthomode Transducer, X-Band Coaxial Waveguide Transition and Polarizer Study

Nicolas Gagnon, Gilbert A. Morin and Éric Choinière

The work described in the document was partially sponsored by the Department of National Defence under Prject 15cx.

Defence R&D Canada √ Ottawa TECHNICAL MEMORANDUM

DRDC Ottawa TM 2006-053

Communications Research Centre Canada CRC REPORT

CRC-RP-2006-001 January 2006

Tri-Band Coaxial Antenna Feed for Satellite Terminal Ku-Band Orthomode Transducer, X-Band Coaxial Waveguide Transition and Polarizer Study

Nicolas Gagnon Communications Research Centre Canada

Gilbert A. Morin Defence R&D Canada – Ottawa

Éric Choinière Defence R&D Canada – Ottawa

The work described in the document was partially sponsored by the Department of National Defence under Project 15cx.

Defence R&D Canada – Ottawa Technical Memorandum DRDC Ottawa TM 2006-053

Communications Research Centre Canada CRC Report CRC-RP-2006-001 January 2006

iDRDC Ottawa TM 2006-053 CRC-RP-2006-001

Abstract This document describes the contribution of the Advanced Antenna Technology group (RAATlab) to the design of tri-band antenna terminals for the Canadian Forces. As part of this project, waveguide components in the C, X and Ku bands were studied and designed. The components described in this report are an orthomode transducer (OMT) for the Ku band and a dual-rectangular waveguide to coaxial waveguide transition for the X band. Additionally, a polarizer in square waveguide geometry has been studied and design. Although the tri-band antenna requires coaxial waveguide polarizers, the work performed on the square waveguide polarizer serves as a preliminary investigation into the potentially realizable performance of such polarizers and some of the results obtained could be transposed for the design of the required circular and coaxial polarizers. Résumé

Ce document décrit la contribution du groupe de Technologie des antennes de pointe (RAATlab) à la conception d’antennes tri-bande pour les Forces canadiennes. Dans le cadre de ce projet, l’étude et la conception d’éléments de guide d’ondes en bandes C, X et Ku ont été effectuées. Les éléments en question sont un coupleur orthomode (ou OMT) pour la bande Ku et une transition de guides d’ondes bi-rectangulaire à coaxial pour la bande X. De plus, un polariseur en guide d’ondes carré a été étudié et conçu. Puisque l’antenne tri-bande nécessite des polariseurs en guides d’ondes coaxiaux, le polariseur en guide d’ondes carré actuel n’est pas adapté à l’antenne tri-bande. Néanmoins, le travail effectué sur le polariseur en guide d’ondes carré peut éventuellement être utilisé comme point de départ dans la conception de polariseurs en guide d’ondes circulaire et coaxial.

ii DRDC Ottawa TM 2006-053 CRC-RP-2006-001

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iiiDRDC Ottawa TM 2006-053 CRC-RP-2006-001

Executive Summary The Canadian Forces have shown interest in acquiring tri-band antenna terminals for satellite communications. The antenna uses the waveguide technology to provide coverage in the C and Ku bands supported by Anik F2 and X band for military use. The antenna concept consists of concentric, axially-aligned waveguide horns, each covering a band of interest. As part of this project, waveguide components were studied and designed by the Advanced Antenna Technology group (RAATlab). The components are an orthomode transducer (OMT) for the Ku band and a dual-rectangular waveguide to single-coaxial waveguide transition for the X band. Additionally, a study of a polarizer in a square waveguide was conducted.

In the Ku and X bands, the transmit (Tx) and receive (Rx) signals are supported by the same waveguide and horn in their respective frequency band. The orthomode transducer (OMT) and the dual-rectangular waveguide to single-coaxial waveguide transition are used to isolate the transmit and receive channels from one another by propagating them in an orthogonal polarization manner. For satellite communications, circular polarization is required. In order to achieve such a polarization, polarizers must be designed. A polarizer in a square waveguide using the ridge waveguide approach was studied and design. The results of this study will form the basis of designs for the other waveguide polarizers intended to be used in the tri-band antenna. For all waveguide components, simulation results show that the required specifications were achieved or nearly achieved. In the future, these components would have to be fabricated and tested. In all cases, the fabrication might be highly challenging due to the mechanical complexity of the structures and the high level of tight fabrication tolerances required. Additionally, the C-band transitions and polarizers require a separate design for each frequency band (possibly based on the study of the ridge waveguide polarizer in square waveguide). Gagnon, N., Morin, G. A., Choinière, E., 2006. Tri-Band Coaxial Antenna Feed for Satellite Terminal: Ku-Band Orthomode Transducer, X-Band Coaxial Waveguide Transition and Polarizer Study. DRDC Ottawa TM 2006-053. Defence R&D Canada – Ottawa.

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Sommaire Les Forces canadiennes se sont montrées intéressées à acquérir des antennes tri-bande pour des communications par satellites. L’antenne utilise la technologie des guides d’ondes pour fournir une couverture en bandes C et Ku supporté par le satellite Anik F2 anisi qu’en bande X pour des applications militaires. Le concept de l’antenne consiste en plusieurs cornets concentriques partageant le même axe, chaque cornet offrant une couverture dans une des bandes de fréquence supportées par l’antenne tri-bande. Dans le cadre de ce projet, l’étude et la conception d’éléments de guide d’ondes ont été effectuées par le groupe de Technologie des antennes de pointe (RAATlab). Les éléments en question sont un coupleur orthomode (ou OMT) pour la bande Ku et une transition de guides d’ondes bi-rectangulaire à coaxial pour la bande X. De plus, un polariseur pour un guide d’ondes carré a été étudié. Dans la bande Ku et la bande X, les signaux transmis (Tx) et reçu (Rx) sont supportés par le même guide d’ondes et le même cornet dans leur bande respective. Le coupleur orthomode (OMT) et la transition de guides d’ondes bi-rectangulaire à coaxial servent à isoler le signal transmis et le signal reçu en les propageant de telle sorte que leurs polarisations soient orthogonales.

Pour les communications par satellites, une polarisation circulaire est requise. Pour obtenir une telle polarisation, des polariseurs doivent être conçus. Un polariseur en guide d’ondes carré utilisant une approche de type guide d’ondes cloisonné (ridge waveguide) a été étudié et conçu. Les résultats du travail effectué sur le polariseur en guide d’ondes carré peuvent éventuellement être utilisés comme point de départ dans la conception de polariseurs pour des guides d’ondes servant à l’antenne tri-bande.

Pour tous les éléments de guide d’ondes, les résultats de simulations démontrent que les spécifications requises sont atteintes ou presque atteintes. Dans l’avenir, ces éléments devront être fabriqués et mesurés. Dans tous les cas, la fabrication pourrait être un défi de taille en raison de la complexité des structures et des tolérances de fabrication serrées. De plus, les transitions en bande C ainsi que les polariseurs doivent être conçus séparément pour chacune des bandes.

Gagnon, N., Morin, G. A., Choinière, E., 2006. Tri-Band Coaxial Antenna Feed for Satellite Terminal: Ku-Band Orthomode Transducer, X-Band Coaxial Waveguide Transition and Polarizer Study. DRDC Ottawa TM 2006-053. R & D pour la défense Canada – Ottawa.

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Table of Contents Abstract ............................................................................................................................................ i

Résumé............................................................................................................................................. i

Executive Summary ....................................................................................................................... iii

Sommaire ....................................................................................................................................... iv

Table of Contents............................................................................................................................ v

List of Figures .............................................................................................................................. viii

List of Tables ................................................................................................................................. ix

Acknowledgements......................................................................................................................... x

1 Introduction.................................................................................................................................. 1

1.1 Background .......................................................................................................................... 1

1.2 RAATLab Contribution ....................................................................................................... 2

2 Ku-Band Orthomode Transducer................................................................................................. 3

2.1 Introduction .......................................................................................................................... 3

2.2 Definition ............................................................................................................................. 3

2.3 Theory .................................................................................................................................. 3

2.4 Specifications ....................................................................................................................... 5

2.5 Design and results ................................................................................................................ 5

2.5.1 Orthomode transducer design....................................................................................... 6

2.5.1.1 Common port size ................................................................................................. 6

2.5.1.2 Branching region................................................................................................... 8

2.5.1.3 Branching port ...................................................................................................... 8

2.5.1.4 Tuning process ...................................................................................................... 9

2.5.2 Orthomode transducer results....................................................................................... 9

2.5.3 Orthomode transducer results discussion ................................................................... 12

2.5.4 Circular waveguide to square waveguide transition design ....................................... 13

2.5.5 Orthomode transducer and circular waveguide to square waveguide transition design

............................................................................................................................................. 14

2.5.6 Orthomode transducer and circular waveguide to square waveguide transition results

............................................................................................................................................. 15

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2.5.7 Orthomode transducer and circular waveguide to square waveguide transition results

discussion............................................................................................................................. 17

2.6 Discussion .......................................................................................................................... 18

3 X-Band Dual-Rectangular Waveguide to Single-Coaxial Waveguide Transition .................... 19

3.1 Introduction ........................................................................................................................ 19

3.2 Definition ........................................................................................................................... 19

3.3 Theory ................................................................................................................................ 20

3.4 Specifications ..................................................................................................................... 21

3.5 Design and results .............................................................................................................. 23

3.5.1 Coaxial waveguide symmetry .................................................................................... 23

3.5.2 Rectangular waveguide size reduction ....................................................................... 24

3.5.3 Rectangular waveguides location ............................................................................... 25

3.5.4 Shorting wings............................................................................................................ 26

3.5.5 Quarter-wave transformers ......................................................................................... 27

3.5.6 Optimization process .................................................................................................. 27

3.5.7 Results ........................................................................................................................ 27

3.5.8 Results discussion....................................................................................................... 29

3.6 Discussion .......................................................................................................................... 30

4 Polarizer Study........................................................................................................................... 31

4.1 Introduction ........................................................................................................................ 31

4.2 Definition ........................................................................................................................... 31

4.3 Theory ................................................................................................................................ 31

4.3.1 Polarization................................................................................................................. 31

4.3.2 Technology overview ................................................................................................. 34

4.3.3 Ridge waveguide ........................................................................................................ 35

4.4 Specifications ..................................................................................................................... 37

4.5 Design and results .............................................................................................................. 38

4.5.1 Step ridge waveguide.................................................................................................. 38

4.5.2 Initial case................................................................................................................... 38

4.5.3 Parameter tuning......................................................................................................... 39

4.5.4 Results ........................................................................................................................ 40

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4.5.5 Results discussion....................................................................................................... 48

4.6 Discussion .......................................................................................................................... 49

5 Conclusions................................................................................................................................ 51

References..................................................................................................................................... 53

Appendix A: Layout of the Ku-band Orthomode Transducer (branching section only).............. 55

Appendix B: Layout of the Ku-band Orthomode Transducer (including circular waveguide to

square waveguide transition) ........................................................................................................ 59

Appendix C: Layout of the X-band dual-rectangular waveguide to single-coaxial waveguide

transition ....................................................................................................................................... 63

Appendix D: Layout of the C-band square-waveguide polarizer ................................................. 67

Appendix E: Quarter-wave transformer design in Agilent Advance Design System (ADS™) ... 71

viii DRDC Ottawa TM 2006-053 CRC-RP-2006-001

List of Figures Figure 1.1. Conceptual representation of the tri-band antenna (from [1])...................................... 1

Figure 2.1. Schematic representation of an OMT........................................................................... 4

Figure 2.2. Physical representation of an OMT (branching section only)...................................... 4

Figure 2.3. Circular waveguide to square waveguide transition with common port square

waveguide dimension details. ......................................................................................................... 7

Figure 2.4.Side view of the branching region of the OMT (without branching port). ................... 8

Figure 2.5.a. S-parameter results of the OMT for return loss and coupling, from -50 dB to 5 dB.

....................................................................................................................................................... 10

Figure 2.5.b. S-parameter results of the OMT for isolation, from -170 dB to -50 dB.................. 11

Figure 2.6. Physical representation of the circular waveguide to square waveguide transition. .. 13

Figure 2.7. Side view of the full OMT with section names and dimensions. ............................... 14

Figure 2.8. S-parameter results of the full OMT. ......................................................................... 16

Figure 2.9. Representation of the full OMT. ................................................................................ 17

Figure 3.1. Schematic representation of the dual-rectangular waveguide to single-coaxial

waveguide transition. .................................................................................................................... 20

Figure 3.2. Physical representation of the dual-rectangular waveguide to single-coaxial

waveguide transition. .................................................................................................................... 21

Figure 3.3. Representation of the TEM mode in a coaxial waveguide (continuous lines for E-

field; dashed lines for H-field). ..................................................................................................... 23

Figure 3.4. Coaxial waveguide fed by rectangular waveguide with a. original size rectangular

waveguide and b. reduced size rectangular waveguide. ............................................................... 24

Figure 3.5. Three-dimensional view of the dual-rectangular waveguide to single-coaxial

waveguide transition with waveguide port location details. ......................................................... 26

Figure 3.6.a. S-parameter results of the dual-rectangular to single coaxial waveguide transition

for return loss and coupling, from -50 dB to 5 dB........................................................................ 28

Figure 3.6.b. S-parameter results of the dual-rectangular to single coaxial waveguide transition

for isolation, from -60 dB to -30 dB. ............................................................................................ 29

Figure 4.1. Electric field orientation for feeding the ridge-waveguide polarizer. ........................ 32

Figure 4.2. Contour plot of cross-polarization levels. .................................................................. 34

Figure 4.3. Square (double-)ridge waveguide cross-section representation. ................................ 35

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Figure 4.4. Electric field representation of the first two modes in a double-ridge waveguide..... 36

Figure 4.5. Side view of the square waveguide polarizer showing ridge sections. ...................... 39

Figure 4.6.a. S-parameter results of the square-waveguide polarizer for return loss and coupling,

from -80 dB to 10 dB (zeros indicated by *). ............................................................................... 41

Figure 4.6.b. S-parameter results of the square-waveguide polarizer for isolation, from -150 dB

to -70 dB. ...................................................................................................................................... 42

Figure 4.7.a. Phase difference results from 4 GHz to 10 GHz; — EMPIRE, × HFSS................. 43

Figure 4.7.b. Phase difference results from 5.8 GHz to 6.6 GHz; — EMPIRE, × HFSS............. 44

Figure 4.8. Magnitude ratio as a function of frequency; — EMPIRE, × HFSS. .......................... 45

Figure 4.9. Axial ratio as a function of frequency; — EMPIRE, × HFSS. .................................. 46

Figure 4.10. Cross-polarization level as a function of frequency; — EMPIRE, × HFSS. ........... 47

Figure 4.11. Side view of the square waveguide polarizer with some dimensions. ..................... 48

Figure E.1. ADS™ screen capture of the X-band Tx quarter-wave transformer. ........................ 72

Figure E.2. ADS™ screen capture of the X-band Rx quarter-wave transformer. ........................ 72

List of Tables Table 1.1. Frequency bands to be supported by the tri-band antenna............................................ 2

Table 2.1. Dimensions and specifications of the Ku-band OMT. ................................................. 6

Table 3.1. Dimensions and specifications of the X-band double-rectangular waveguide to single-

coaxial waveguide transition......................................................................................................... 22

Table 4.1. Dimensions, specifications and guidelines of the C-band square waveguide polarizer.

....................................................................................................................................................... 37

Table 4.2. Effect of increasing the dimensions of the ridge waveguide polarizer........................ 40

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Acknowledgements Nicolas Gagnon would like to thank the following people who provided valuable

assistance for this project:

• Aldo Petosa for his scientific assistance throughout this work;

• David Lee for his technical assistance, especially for generating the mechanical drawings

of the waveguide components;

• Reza Chaharmir for his helpful assistance in simulating some structures presented in this

work and;

• Apisak Ittipiboon for his scientific assistance, particularly for the polarizer study.

1DRDC Ottawa TM 2006-053 CRC-RP-2006-001

1 Introduction

1.1 Background The Canadian Forces have shown interest in acquiring tri-band antenna terminals providing

coverage in the C, X and Ku bands [1]. The antenna is to be made of a conical feed horn for the

higher frequency band and coaxial feed horns for the other bands, as shown in Figure 1.1 [1].

Similarly, the horns are fed by a circular waveguide for the higher band and coaxial waveguides

for the other bands. Each feed horn is used to transmit and receive, except at C band: the C-

band coverage is performed using two antennas, one to transmit (Tx) and one to receive (Rx).

This is done because of the wide separation between the Tx and Rx bands in the C band. Table

1.1 summarizes the frequency bands to be covered by each antenna. For more information, refer

to [1].

Figure 1.1. Conceptual representation of the tri-band antenna (from [1]).

feed port(1 of 4 per wg)

polarizerOMT

C (Tx)C (Rx)

X Ku

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Table 1.1. Frequency bands to be supported by the tri-band antenna.

Antenna / frequency band Application Tx band Rx band

C-band Rx Anik F2 ⎯ 3.7-4.2 GHz

C-band Tx Anik F2 5.925-6.425 GHz ⎯

X-band Military 7.9-8.4 GHz 7.25-7.75 GHz

Ku-band Anik F2 14.0-14.5 GHz 11.7-12.2 GHz

1.2 RAATLab Contribution As part of this project, the Advanced Antenna Technology group (RAATlab) was asked to

investigate various waveguide components to be used for the tri-band antenna described in

section 1.1. Two components were designed:

• an orthomode transducer (OMT) for the conical horn antenna at Ku band (covered in

Chapter 2);

• a dual-rectangular waveguide to single-coaxial waveguide transition for the coaxial

antenna at X band (covered in Chapter 3).

These two components were designed for both transmit and receive modes in their own bands.

Furthermore, a study was also conducted on the design of waveguide polarizers to be used

for the C and X frequency bands. The study included the design of a polarizer in a square

waveguide (covered in Chapter 4), the results of which would form the basis of designs for the

circular and coaxial waveguides.


2 Ku-Band Orthomode Transducer

2.1 Introduction In order to transmit and receive through the same antenna in a given band, the transmitted

(Tx) and received (Rx) signals must not interfere with each other. In this particular application,

the Tx and Rx frequency bands are different, however the horn antenna and waveguide

components are designed to support and cover both the Tx and Rx bands. Therefore, a means

must be found to isolate the various Tx and Rx signals from one another. This can be achieved if

the two signals are orthogonally polarized. One of the key components to separate these

orthogonally polarized signals is an orthomode transducer.

2.2 Definition An orthomode transducer (OMT), also known as a polarization diplexer, an orthomode tee

or a dual-mode transducer, is a device used to separate or combine orthogonally-polarized

signals in dual-polarized antennas [2-4]. It is generally a pure waveguide component; however a

coaxial port may be used. It is often used for frequency reuse, which allows doubling the system

capacity since the two orthogonal, isolated channels can coexist in the same frequency band.

The OMT is an important element of an antenna feed system, especially for satellite

communications.

2.3 Theory The operation of an OMT is schematically described in Figure 2.1 and a physical

representation is shown in Figure 2.2. An OMT is composed of four electrical ports, but only

three physical ports. The longitudinal port, referred to as port 1, is located at one of the

rectangular waveguides; it carries one of the signal channels. In the current design, it will be

used as the Tx input. The branching port, referred to as port 2, is located on the other rectangular

waveguide, perpendicular to the longitudinal port. It carries the other signal channel which, in

this case, is the Rx signal. The last physical port, called the common port, must simultaneously

support the two orthogonal modes. The vertically-polarized port, i.e. port 4 supporting the TE10

mode, couples directly to the longitudinal port (port 1); the horizontally-polarized port, i.e. port 3


supporting TE01, couples to the branching port (port 2). For signals operating in the same band,

the cross-section of the common port will have physical symmetry, usually square or circular.

Figure 2.1. Schematic representation of an OMT.

Figure 2.2. Physical representation of an OMT (branching section only).

4-Port OMT

Longitudinal port Rectangular waveguide TE10 - Electrical port 1

Branching portRectangular waveguideTE10 - Electrical port 2

Common port Square or circular

waveguide

TE10 - Electrical port 4

TE01 - Electrical port 3


From the above description of the OMT, the scattering matrix of an ideal OMT would be

given as follow:

⎥⎥⎥⎥⎥

⎦

⎤

⎢⎢⎢⎢⎢

⎣

⎡

=

000000000

000

1

2

2

1

φ

φ

φ

φ

j

j

j

j

ee

ee

S (2.1)

In other words, the coupling between the branching and longitudinal ports should be zero; the

coupling between the longitudinal (branching) port and the horizontal (vertical) polarization at

the common port should be zero; the coupling between the longitudinal (branching) port and the

vertical (horizontal) polarization at the common port should have a magnitude of one and a phase

term and; the return loss should be perfect for all ports, i.e. the reflection coefficient should be

zero for each port.

2.4 Specifications For this particular application, the output of the OMT must feed into a circular feed horn

and so a circular-to-square waveguide transition is required between the common port of the

OMT and the input of the circular horn. Table 2.1 gives a summary of the specifications of the

OMT and transition.

2.5 Design and results The OMT is designed following two separate steps. First, the OMT itself, including the

branching region, is designed with standard, commercially-available, waveguide dimensions at

the longitudinal and branching ports and a square waveguide at the common port. Secondly, a

transition between the square waveguide and the required circular waveguide is designed and

connected to the initial OMT design. This allows for the undesired higher-order modes that may

propagate in the circular-to-square waveguide transition to be cut off by the square waveguide

section. In all cases, simulations are conducted using the finite-difference time-domain simulator

EMPIRE™ from IMST.


Table 2.1. Dimensions and specifications of the Ku-band OMT.

Channel Tx Rx

Frequency (GHz) 14-14.5 11.7-12.2

Port number 1 2

Port type Longitudinal Branching

Standard waveguide type WR 62 WR 62

Rectangular

waveguide port

Size (mm) 15.8 × 7.9 15.8 × 7.9

Port number 4 3

E-field orientation Vertical Horizontal

Mode TE10 TE01

Square waveguide (mm) 13.7 × 13.7

Common port

(square/circular

waveguide)

Circular waveguide (mm) Ø 20

Return loss1 (dB) 25 20

Isolation (dB) 30

Branching region length (mm) 50

Total length (mm) 105

2.5.1 Orthomode transducer design

2.5.1.1 Common port size

It is usually a natural choice to have the width of the common port equal to the width of the

rectangular waveguide at the longitudinal port. This simplifies the design as it allows for a

constant width in the branching region and one less parameter to account for. In this case, the

standard-size rectangular waveguide has a width of 15.8 mm and the band to be covered is from

11.7 GHz to 14.5 GHz. If a square waveguide of size 15.8 mm × 15.8 mm is used, the first

higher-order modes to occur, i.e. the TE11 and TM11 modes, both have a cutoff frequency of 13.4

GHz. Since the Tx band is from 14 GHz to 14.5 GHz, it is preferred to choose a smaller

1 In this report, the following definition of the return loss (RL) is used: RL = -20log|Γ| [dB], where Γ = Sxx is the

reflection coefficient.


waveguide size to make sure that the cutoff of the first higher-order modes is above 14.5 GHz.

Therefore, a square waveguide of dimensions 14.6 mm × 14.6 mm or less would be necessary.

To facilitate the transition between the square waveguide and the circular waveguide, it is

preferred to choose a square waveguide with dimensions smaller than that of the circular

waveguide. The radius of the circular waveguide being 10 mm means that the square waveguide

should be less than 14.1 mm × 14.1 mm, as shown in Figure 2.3.a. A slightly smaller square

waveguide size of 13.7 mm × 13.7 mm, shown in Figures 2.3.b and 2.3.c, was finally chosen in

order to allow for a higher margin at the upper band. With such a waveguide size, the cutoff of

the two degenerate fundamental modes TE10 and TE01 is 10.94 GHz and the first higher-order

modes cutoff frequency is 15.47 GHz.

a b c

Figure 2.3. Circular waveguide to square waveguide transition with common port square

waveguide dimension details.

a. face view showing maximum square waveguide size; b. actual face view; c. actual side view.


2.5.1.2 Branching region

The branching region of the OMT is the waveguide section located between the

longitudinal port and the common port on which the branching port is connected. In the

branching region, the dimensions of the waveguide cross section vary as a function of the

distance. For this reason, it is also called the taper region. A smooth variation is generally

preferred since it allows for good coupling between the longitudinal port and the vertically-

polarized fundamental mode at the common port, as well as a good return loss at the same ports.

After choosing the dimensions of the common port, the taper in the branching region was

designed. The vertical variation was accomplished using a natural spline. A side view of the

branching region with the spline taper is shown in Figure 2.4. For simplicity, the horizontal

variation was chosen to be a linear taper. With no branching port and without any effort in

tuning the spline profile, the return loss at the longitudinal is better than 25 dB.

Figure 2.4.Side view of the branching region of the OMT (without branching port).

2.5.1.3 Branching port

The location of the branching port is varied in order to minimize its influence on the

longitudinal port and the vertically-polarized fundamental mode at the common port. At the

same time, a good return loss for the branching port and the horizontally-polarized common port,

as well as a good coupling performance between these two ports must be obtained. A few

simulations were conducted and showed that the best location resulted in a return loss at the

longitudinal port of 11 dB and a return loss at the branching port of 8 dB in their respective

bands. It was concluded that the branching port could not simply be added to the structure but


rather needed to be connected in such a way to minimize the impact on the longitudinal port and

to tune the branching port.

As suggested in [2], the branching port is generally constructed as an inductive iris, which

results in a smaller rectangular aperture and, consequently, a better match at the longitudinal

port. In this case, an inductive-capacitive iris was used as it allowed for a better matching at the

branching port. The thickness of the iris is chosen to be 500 μm, which is believed to be the

smallest practical thickness to fabricate. Irises with different dimensions were simulated in order

to maximize the performance of the OMT.

2.5.1.4 Tuning process

After an initial reasonable configuration was chosen for the iris, a tuning process was

initiated in order to further improve the performance of the OMT. The following parameters

were tuned:

• the iris dimensions (except for the thickness);

• the branching port location;

• the tapering profile of the branching region, i.e. the spline function.

The tapering profile was generated using a natural spline function with five points: two at the

longitudinal port to ensure a null slope; two at the common port, again to ensure a null slope and;

one at the centre of the branching region. Therefore, the spline function was made relatively

simple with only one parameter to tune, which was the vertical position of the centre point.

2.5.2 Orthomode transducer results This section presents the simulation results obtained with IMST EMPIRE™. In

order to validate these results, additional simulations were also conducted in Ansoft

HFSS™. The results are presented in Figure 2.5. A representation of the OMT was

previously shown in Figure 2.2. The layout of the OMT is shown in Appendix A.


S11 S41 S22 S32 S23 S33 S14 S44

EMPIRE ⎯ ⎯ ⎯ ⎯ ⎯ ⎯ ⎯ ⎯

HFSS × × × × + + + +

Figure 2.5.a. S-parameter results of the OMT for return loss and coupling, from -50 dB to 5 dB.


S21 S31 S12 S42 S13 S43 S24 S34

EMPIRE ⎯ ⎯ ⎯ ⎯ ⎯ ⎯ ⎯ ⎯

HFSS × × + + + + × ×

Figure 2.5.b. S-parameter results of the OMT for isolation, from -170 dB to -50 dB.


2.5.3 Orthomode transducer results discussion In Figure 2.5, it is observed that the agreement between EMPIRE™ and HFSS™ is very

good, especially in Figure 2.5.a for the return loss and coupling results. For the isolation shown

in Figure 2.5.b, there is a discrepancy between the results from the two simulators: the

EMPIRE™ S-parameter results are better than -115 dB while the HFSS™ results are between

-70 dB and -60 dB. The first thing to note is that the meshing of the structure simulated in

EMPIRE™ has been symmetrically defined along the vertical axis whereas the meshing

automatically generated by HFSS™ is not. A comparison of EMPIRE™ simulations revealed a

major difference in the low-value results such as the isolation whether a symmetrical meshing or

a non-symmetrical meshing is defined. Nevertheless, the results from either simulator are better

than -60 dB, which is very acceptable for this application. Therefore, the decision was taken not

to be concerned about such a discrepancy.

From Figure 2.5.a, it can be seen that the return loss for port 2 and port 3 operating in the

Rx band from 11.7 GHz to 12.2 GHz is better than 19.2 dB. In the same band, the coupling

between port 2 and port 3 is almost perfect, with a worst case value of -0.055 dB. The isolation

with the other fundamental modes is better than 60 dB and the coupling to the higher-order

modes is -35 dB or less, except for the TE21 mode at the common port, which is -19.5 dB. In the

Tx band, from 14 GHz to 14.5 GHz, the return loss for port 1 and port 4 is better than 27.5 dB

and the coupling is -0.01 dB or better. The isolation is still better than 60 dB for the other

fundamental modes and better than 32 dB for the higher-order modes.


2.5.4 Circular waveguide to square waveguide transition design A smooth transition between the common port square waveguide and the circular

waveguide connecting to the horn was designed. It was decided to use a smooth transition in

order to obtain a wider band operation. It was found that the performance of the transition gets

better as the length was increased, which was also noticed for the branching region of the OMT.

However, since we were limited by the length of the full structure (i.e. branching region and

transition), the circular waveguide to square waveguide transition was kept as short as possible.

Figure 2.3.b and 2.3.c previously showed a front and side view of the circular waveguide to

square waveguide transition. Figure 2.6 shows a three-dimensional representation of the circular

waveguide to square waveguide transition.

Figure 2.6. Physical representation of the circular waveguide to square waveguide transition.


2.5.5 Orthomode transducer and circular waveguide to square waveguide transition

design The previously-designed orthomode transducer and the circular waveguide to square

waveguide transition are connected together in order to form a complete OMT with rectangular

waveguide ports and circular waveguide common port. The maximum total length of the

structure was specified to be 105 mm. This includes a 5mm-long rectangular-waveguide section

at the input of the longitudinal port and a 5mm-long circular-waveguide section at the input of

the circular-waveguide common port. Since it was determined that the branching section had a

length of 50 mm, this means the transition section could be no longer than 45 mm. Figure 2.7

gives the details of those dimensions.

Figure 2.7. Side view of the full OMT with section names and dimensions.


Instead of designing a circular waveguide to square waveguide transition with a length of

45 mm, the addition of a square waveguide section between the branching section and the

circular waveguide to square waveguide section was investigated. It was found that adding a

short section of square waveguide actually improved the performance compared to simply

having a circular waveguide to square waveguide transition. This is because some of the higher-

order modes are coupling well in the circular waveguide to square waveguide transition. These

modes are the TM11 mode in the square waveguide and the TM01 mode in the circular

waveguide. Their respective cutoff frequencies are 15.5 GHz and 11.6 GHz. The TM01 mode

can propagate in the operational band (11.7 GHz to 14.5 GHz), then coupling to the TM11 mode

in the square to circular waveguide transition. Consequently, near the square waveguide port in

the transition, the TM11 mode is not fully attenuated; adding a square waveguide section has the

effect of cutting it off, thus increasing the isolation with the higher-order modes. The length of

the square-waveguide section is 15 mm and the length of the circular waveguide to square

waveguide transition is 30 mm, as shown in Figure 2.7. Figure 2.6, presented in the previous

section, shows a physical representation of the circular waveguide to square waveguide

transition.


results This section presents the simulations of the complete orthomode transducer obtained in

EMPIRE™. The so-called complete OMT is composed as follows: a rectangular waveguide

section of length of 5 mm; the branching region (i.e. OMT itself), having a length of 50 mm; a

square-waveguide section of length equal to 15 mm; a 30 mm-long circular waveguide to square

waveguide transition and; a circular-waveguide section of length of 5 mm. For more detail on

the waveguide sections and dimensions, refer to Figure 2.7 in the previous section. The S-

parameter results are shown in Figure 2.8. Figure 2.9 shows a representation of the full structure.

Appendix B presents the layout of the complete OMT.


S11 S44 S21 S12 S31 S13 S41 S14 S22 S33 S32 S23 S42 S24 S43 S34

⎯ ⎯ ⎯ ⎯ ⎯ ⎯ ⎯ ⎯

Figure 2.8. S-parameter results of the full OMT.


Figure 2.9. Representation of the full OMT.


results discussion In Figure 2.8, the reflection coefficient of the longitudinal port (port 1) and the reflection

coefficient of the vertically-polarized common port (port 4) are -27 dB or better in the Tx band,

i.e. from 14 GHz to 14.5 GHz. The reflection coefficient of the branching port (port 2) and the

reflection coefficient of the horizontally-polarized common port (port 3) are -20.7 dB or better in

the Rx band, i.e. from 11.7 GHz to 12.2 GHz. The isolation between the fundamental modes is

29.7 dB or better. The coupling between the longitudinal port and the vertically-polarized

common port is better than -0.01 dB in the Tx band; the coupling between the branching port and

the horizontally-polarized common port is better than -0.04 dB. The isolation with the higher-

order modes (not shown) is better than 26 dB. These results assume a null reflection coefficient

at the input of the common port, i.e. a well-matched antenna at the common port.

In theory, since all the fundamental modes of the ports are well-matched, well-coupled to

the respective ports and isolated from the higher-order modes, the isolation between the ports

should be the same. However, it is seen that the isolation varies between about 30 dB to about

110 dB. This behaviour is similar to what was described in section 2.5.3 on the HFSS™

simulations, i.e. the results where the isolation is not the best are probably the cases where the


symmetry is the worse. In the case of the isolation between the two rectangular waveguide ports,

which both have a good symmetry, the isolation is better than 90 dB.

2.6 Discussion The results presented in the previous section meet the specifications provided. However, if

these specifications are to be changed, a couple of modifications can be made to achieve the new

requirements.

If the electromagnetic requirements are modified but the physical parameters are

unconstrained, the structure can always be made longer in length. The critical parameters are the

length of the branching section and the length of the circular waveguide to square waveguide

transition. Increasing the length of the circular waveguide to square waveguide transition allows

obtaining a slightly better match of a few decibels – especially in the Rx band – without having

to redesign the whole structure. If much better performance needs to be achieved, then

redesigning is probably necessary. To improve the return loss specifications by 5 dB or more, it

is suggested to increase the length of the branching section. This should improve the return loss

at both branching and longitudinal ports. If the longitudinal port is meeting the specifications (or

close) and the branching port is not, then irises can be added in the branching waveguide section;

in fact, having more than one iris should improve the matching performance of the branching

port. Furthermore, if there is interaction between the branching port and the longitudinal port,

improving the match at the branching port could also improve the match at the longitudinal port.


3 X-Band Dual-Rectangular Waveguide to Single-Coaxial

Waveguide Transition

3.1 Introduction At the highest frequency band, the conventional orthomode transducer was used as an

interface between the standard-size rectangular waveguides and the circular waveguide feeding

the conical feed horn. Since the waveguides and radiating horns have a common axis (as shown

in Figure 1.1), coaxial waveguides and coaxial horn antennas are used for the other frequency

bands, i.e. the X band and C band.

At C band, due to the high frequency separation between transmit (Tx) and receive (Rx)

channels, two antennas are used, i.e. one antenna per channel. This will allow for a relatively

simple transition between the rectangular waveguide and the coaxial waveguide. However, at X

band, a single antenna will be used for both Tx and Rx. This will make the transition more

complicated as two well-matched, well-isolated ports – rather than a single well-matched port –

must be designed.

This chapter presents the design of a dual-rectangular waveguide to single-coaxial

waveguide transition at X band. It is believed that, after designing such a component, the design

of single-rectangular waveguide to single-coaxial waveguide transitions for the C-Tx and C-Rx

bands will be much simpler to achieve.

3.2 Definition The dual-rectangular waveguide to single-coaxial waveguide transition described in this

chapter is actually a coaxial waveguide orthomode transducer. The behaviour is the same as the

OMT described in Chapter 2, i.e. two isolated rectangular waveguide ports couple with two

isolated orthogonal electrical ports at the common port. The only difference is as follow:

• because of the way a coaxial waveguide is made, there is no longitudinal port since

adapting a rectangular waveguide to a coaxial waveguide longitudinally would be really

difficult to achieve;

• the longitudinal port is replaced by an additional branching port, thus there are two


branching ports orthogonal to each other;

• the common port supports the two orthogonal fundamental modes as in a conventional

OMT, however it is coaxial instead of being square or circular;

• the branching region has no taper profile.

3.3 Theory The operation of the dual-rectangular waveguide to single-coaxial waveguide transition is

schematically described in Figure 3.1. It works essentially the same way as the orthomode

transducer (refer to section 2.3). The fundamental mode in a coaxial waveguide is the TE11

mode, which is degenerate. Figure 3.2 shows a physical representation of the dual-rectangular

waveguide to single-coaxial waveguide transition.

Figure 3.1. Schematic representation of the dual-rectangular waveguide to single-coaxial

waveguide transition.

Dual-rectangular waveguide to

Single-coaxial waveguide

Branching port along horizontal axis (x) Rectangular waveguide TE10 - Electrical port 1

Branching port along vertical axis (y)

Rectangular waveguide TE10 - Electrical port 2

Common port Coaxial waveguide

TE11y - Electrical port 4

TE11x - Electrical port 3


Figure 3.2. Physical representation of the dual-rectangular waveguide to single-coaxial

waveguide transition.

3.4 Specifications The dual-rectangular waveguide to single coaxial waveguide transition connects with the

coaxial waveguide, which then connects to the coaxial feed horn. Table 3.1 provides the

specifications of the device. The coaxial waveguide must be fed by a single rectangular

waveguide for each frequency band: the traditional feed design, which consists of feeding each

channel with two rectangular waveguides placed on opposite side of the coaxial waveguide with

a phase difference of 180 degrees, must be avoided as it makes the structure too bulky.


Table 3.1. Dimensions and specifications of the X-band double-rectangular waveguide to single-

coaxial waveguide transition.

Channel Tx Rx

Frequency (GHz) 7.9-8.4 7.25-7.75

Port number 1 2

Port type Branching Branching

Port orientation Horizontal Vertical

Port location Near waveguide short

circuit

Away from waveguide

short circuit

Standard waveguide type WR 112 WR 112

Rectangular

waveguide port

Size (mm) 28.5 × 12.6 28.5 × 12.6

Port number 4 3

E-field orientation Vertical Horizontal

Mode TE11y TE11x

Inner radius (mm) 7.1

Common port

(coaxial

waveguide)

Outer radius (mm) 10.5

Return loss (dB) 20 20

Isolation (dB) 35

Approximate total length (mm) 75


3.5 Design and results

3.5.1 Coaxial waveguide symmetry Because the transverse electromagnetic (TEM) mode may be excited inside coaxial

waveguides, care must be taken in the design. Coaxial waveguides are problematic in that there

is no simple means to get rid of the TEM mode since it has no cutoff frequency. The TEM mode

is characterized by electrical field lines going from one conductor (inner or outer conductor) to

the other, as shown in Figure 3.3. In free-space, the field lines of the TEM mode will generate a

pattern with a boresight null, which is undesirable for this particular antenna application. If two

orthogonal planes of symmetry are used inside the coaxial waveguide, it is possible to suppress

the TEM mode.

Figure 3.3. Representation of the TEM mode in a coaxial waveguide (continuous lines for E-

field; dashed lines for H-field).


3.5.2 Rectangular waveguide size reduction The rectangular waveguides used are relatively large compared to the coaxial waveguide,

as shown in Figure 3.4.a: the smallest dimension of the rectangular waveguide is 12.6 mm

whereas the coaxial waveguide diameter of the outer conductor is 21 mm. This results in

matching and isolation problems. In order to solve this problem, it is required to reduce the

smallest dimension of the rectangular waveguide at the interface with the coaxial waveguide, as

shown in Figure 3.4.b. A quarter-wave transformer is inserted to convert the resultant

impedance to that of the standard waveguide dimension.

Figure 3.4. Coaxial waveguide fed by rectangular waveguide with a. original size rectangular

waveguide and b. reduced size rectangular waveguide.


3.5.3 Rectangular waveguides location In order to properly feed the coaxial waveguide, the rectangular waveguides must be

placed about a quarter wavelength (or odd multiples of a quarter wavelength) from the

waveguide end (i.e. short circuit). It is better to place the rectangular waveguide as close as

possible to the short circuit, i.e. a quarter wavelength away since it will result in a better

broadband match and a larger bandwidth.

However, having the two orthogonal rectangular waveguides placed a quarter wavelength

away from the short circuit causes high interaction between the two ports, which is undesired as

it results in poor isolation. To avoid this problem, one of the two rectangular waveguides must

be placed further away from the coaxial waveguide short circuit. This will unfortunately reduce

the bandwidth of this port. In order to keep a resonable bandwidth, the rectangular waveguide

was placed at a location three quarters of a wavelength away from the short circuit.

It was observed that the isolation is better when the separation between the two

rectangular waveguides is increased. This distance must not be too large since, as mentioned

above, it will limit the bandwidth. In order to put the two rectangular waveguide ports at one

quarter of a wavelength and three quarters of a wavelength from the short circuit while

improving the isolation, the Tx port was chosen to be closest to the short circuit. Since the

wavelength of the Rx band (from 7.25 GHz to 7.75 GHz, corresponding to a guided wavelength

inside the coaxial waveguide between 55.1 mm and 63.7 mm) is longer than the wavelength of

the Tx band (from 7.9 GHz to 8.4 GHz, corresponding to a guided wavelength inside the coaxial

waveguide between 47.3 mm and 53.0 mm), the Rx port is then located further away from the

short circuit than the Tx port would be and similarly, the Tx port is closer to the short circuit than

the Rx port would be. This results in a larger separation between the two ports and,

consequently, in a better isolation. Figure 3.5 provides more detail on this subject.


Figure 3.5. Three-dimensional view of the dual-rectangular waveguide to single-coaxial

waveguide transition with waveguide port location details.

3.5.4 Shorting wings Because of the size of the longest dimension of the rectangular waveguide, it is not

possible to directly put the Tx waveguide port – the port located near the short circuit – at a

distance of a quarter wavelength. In order to fix the problem, the coaxial waveguide short circuit

must virtually be moved. This was accomplished using shorting wings.

Shorting wings were shown earlier in Figure 3.2; they are also shown in Figure 3.5. They

consist in thin metal plates parallel to the Tx port opening. Since they have two planes of

symmetry, they will not excite the TEM mode. They are used to virtually move the location of

the short circuit inside the coaxial waveguide for the Tx port only: since the electrical field lines

are parallel to the shorting wings, the short circuit is seen as being moved. The Rx port, which is

orthogonal with respect to the Tx port, is not significantly affected by the shorting wings. The


match at the Tx port is then obtained by changing the length of the shorting wings with only a

small effect on the match at the Rx port.

3.5.5 Quarter-wave transformers IMST EMPIRE™ simulations were conducted in attempts to improve the isolation

without matching the ports. After a resonable case for the isolation was obtained, the input

impedance of the two rectangular waveguide ports was exported from EMPIRE™ and imported

in Agilent Advance Design System (ADS™). In ADS™, a quarter-wave transformer was

designed using ideal rectangular waveguide components for each of the port. The dimensions

obtained were then transposed into EMPIRE™ to electromagnetically simulate the complete

matched structure. For more detail, refer to Appendix E.

3.5.6 Optimization process Once the quarter-wave transformers were attached to the previously unmatched structure

in EMPIRE™, an optimization process was initiated in order to improve the performance of the

dual-rectangular waveguide to single-coaxial waveguide transition. The following parameters

were optimized:

• the length of each section of the quarter-wave transformers;

• the waveguide shortest dimension (height) for each section of the quarter-wave

transformers (the longest dimension – the width – was kept constant) and;

• the length of the shorting wings.

The location of both ports was kept constant. Furthermore, including two additional parameters

in the optimization process would have resulted in a fairly complicated problem to optimize.

3.5.7 Results This section presents the simulation results obtained with EMPIRE™. Some parameters

were also simulated using Ansoft HFSS™ in order to validate the results obtained in EMPIRE™.

The results are shown in Figure 3.6. The dual-rectangular waveguide to single-coaxial

waveguide transition was presented in Figures 3.2 and 3.5. The layout is shown in Appendix C.


S11 S44 S41 S14 S22 S33 S32 S23

EMPIRE ⎯ ⎯ ⎯ ⎯

HFSS × N/A × N/A

Figure 3.6.a. S-parameter results of the dual-rectangular to single coaxial waveguide transition

for return loss and coupling, from -50 dB to 5 dB.


S21 S12 S31 S13 STEM1 S42 S24 STEM2 S43 S34 STEM3 STEM4

EMPIRE ⎯ ⎯ ⎯ ⎯ ⎯ ⎯ ⎯ ⎯

HFSS × N/A × N/A × N/A N/A N/A

Figure 3.6.b. S-parameter results of the dual-rectangular to single coaxial waveguide transition

for isolation, from -60 dB to -30 dB.

3.5.8 Results discussion In Figure 3.6, the agreement between EMPIRE™ and HFSS™ is good, however some

difference can be noticed. The return loss results are slightly different depending on which

software was used. The isolation agreement is good for S21 (and S12), But it is slightly different

for the isolation with the TEM mode.

The way the meshing is performed in EMPIRE™ and HFSS™ could explain why the

agreement is not as good as expected. In EMPIRE™, the discretization is manually performed in


x, y and z independently and can be non-uniform; the meshed structure is made of rectangles and

squares (hexahedrons). In HFSS™, the discretization is automatically performed using some

convergence criteria and physical constraints; the meshed structure is made of tetrahedrons.

When comparing the discretization of the two simulators, it looks quite different, particularly

because EMPIRE™ and HFSS™ do not fit a curved shape the same way. Since the current

structure is mostly circular, this seems to have an impact on the results. Furthermore, the

HFSS™ discretization inside the coaxial waveguide is non-symmetrical and the restrictions on

the convergence criteria had to be reduced in order to limit the memory usage. Consequently,

the results would probably be closer in agreement if symmetry was applied in HFSS™ and if

more memory was available; nevertheless the agreement is good.

In Figure 3.6.a, the return loss for port 2 and port 3 is better than about 15 dB in the Rx

band (7.25 GHz to 7.75 GHz). The return loss for port 1 and port 4 is better than about 17 dB in

the Tx band (7.9 GHz to 8.4 GHz). The coupling between port 2 and port 3 is better than -0.2 dB

in the Rx band whereas the coupling between port 1 and port 4 is better than -0.1 dB in the Tx

band. Figure 3.6.b shows that the isolation is better than 34 dB. Since the TEM mode is not

excited, good far-field radiation will be possible if this transition is used.

3.6 Discussion The optimization of the dual-rectangular waveguide to single-coaxial waveguide

transition was interrupted in order to move ahead in the project. At the time the design was

stopped, the specifications were not quite met: the return loss was not meeting the 20 dB

requirements and the isolation was slightly less than required, i.e. 34 dB instead of 35 dB.

However, it is believed that slight modifications to the actual design could allow meeting the

requirements.

The first thing to mention is that the optimization process described in section 3.5.6 was

not fully completed. A resonable solution (the one presented in this report) has been obtained,

but a finer tuning could have allowed meeting the specifications or at least getting closer to

meeting the specifications. If this was not enough, the quarter-wave transformers could have

been modified to add one or two additional sections. In ADS™, the addition of sections in the

quarter-wave transformer has shown an improvement in the return loss performance.


4 Polarizer Study

4.1 Introduction The circular waveguide at Ku band and the coaxial waveguides at C band and X band are

all characterized by a linear polarization, i.e. the electric field does not change orientation.

However, the tri-band satellite terminal antenna requires that the linear polarization has a

controllable orientation in all bands as well as the capability to convert to circular polarization in

the C band and X band [1]. In order to achieve such polarization agility, polarizers must be

designed.

4.2 Definition In its most general definition, a polarizer is a device that allows for converting one kind

of polarization (i.e. linear, elliptical or circular) into another. For most applications, a polarizer

is used to convert a linear polarization into another linear polarization with different orientation,

a linear polarization into a circular polarization or a circular polarization into a linear

polarization. Since the polarization can be modified by changing the phase of the orthogonal

electric field components, the principle of operation of a polarizer consists in producing a phase

delay between the field components by inserting some kind of structure inside the waveguide.

4.3 Theory

4.3.1 Polarization A circular polarizated field can be achieved by adding two spatially-orthogonal linearly

polarization fields having equal magnitudes and a phase difference of 90 degrees. Thus, to

convert a linear polarization into a circular polarization, the polarizer must first decompose the

field into two spatially-orthogonal components having equal magnitudes and then introduce a

90-degree phase shift between the two linear field components without affecting their

magnitudes. In the specific case of the tri-band antenna, there is a single rectangular waveguide

port per channel (i.e. transmit – Tx – or receive – Rx). In order for the polarizer to successfully


transform the polarization, the components of the electric field must be properly separated. To

do so, the linear electric field must be 45-degree incident on the polarizer, as shown in Figure

4.1. This implies having the rectangular waveguide port feeding the waveguide at 45 degrees

with respect to the polarizer. In Figure 4.1, the decomposition of the electric field into x- and y-

components is shown; the x-component of the electric field, perpendicular to the ridges, will not

be significantly affected by the ridges whereas the y-component, parallel to the ridges, will

undergo a phase delay. The polarizer then has to be designed so that the phase delay is 90

degrees over a broad frequency range.

Figure 4.1. Electric field orientation for feeding the ridge-waveguide polarizer.

A phase shift of 90 degrees between the two electric field components does not necessarily

guarantee a good operation of the polarizer. As mentioned above, a magnitude ratio of one

between the two field components is also required as well as a good return loss. If the magnitude

ratio is not equal to one, an elliptical polarization will be obtained even if the phase shift is 90

degrees.

A polarization is usually quantified in terms of axial ratio or cross-polarization, defined as

[5]

)2cos(2

)2cos(2log10

224422

224422

θ

θ

yxyxyx

yxyxyx

EEEEEE

EEEEEEAR

++−+

++++= (4.1)

E

Ex

Ey


110

110log2020

20

+

−= AR

AR

X (4.2)

where AR is the axial ratio (in dB), Ex is the magnitude of the x-component of the electric field,

Ey is the magnitude of the y-component of the electric field, θ is the phase difference between the

x- and y- components of the electric field and X is the cross-polarization level (in dB). A perfect

circular polarization is obtained when Ex is equal to Ey and the phase difference is equal to 90

degrees, in which case the axial ratio is equal to 0 dB and the cross-polarization level is equal to

-∞ dB. Figure 4.2 presents a contour plot of cross-polarization levels as a function of the angle

error, φ, and the magnitude ratio, R, which are defined as

φ = 90º−θ (4.3)

⎪⎪⎩

⎪⎪⎨

⎧

≤

≥=

yxx

y

yxy

x

EEEE

EEEE

R if

if (4.4)


Figure 4.2. Contour plot of cross-polarization levels.

4.3.2 Technology overview Waveguide polarizers have been studied for more than 50 years. There are different

kinds of waveguide polarizers, among which a few are mentioned here. The corrugated

waveguide polarizer [6-9] consists of inserting corrugations on two opposite walls of a

waveguide while keeping the two other walls untouched. The corrugations can be considered as

irises: in one plane, the electric field is parallel to the corrugations, which act as inductive irises

and produce a phase advance; in the other plane, the electric field is perpendicular to the

corrugations, which act as capacitive irises and produce a phase delay [9]. The stepped septum

waveguide polarizer [10-13] consists of having two isolated, half-size waveguides (normally

rectangular or semi-circular) merging to form a full-size waveguide (normally square or

circular). The septum-loaded section is used to transform the two polarizations and produce the

desired phase shift. The ridge waveguide polarizer [14] consists of inserting thin ridges in one


polarization to delay the phase; the other polarization is unaffected if the ridges are thin enough.

Other types of waveguide polarizers are described in [15-16].

For this application, it was decided to study a ridge waveguide polarizer for the following

reasons:

• the working principle for the ridge waveguide polarizer is easy to understand and

thus constitutes a good start for a polarizer study;

• the all-metal nature of the ridge waveguide polarizer makes it potentially easier to

fabricate than polarizer structures with dielectric materials;

• the ridge structure is simple to fabricate compared to other structures such as

corrugations, which require a lengthy fabrication process and higher tolerances.

4.3.3 Ridge waveguide The ridge waveguide is a well-know technology which has been studied for about 60

years. Many papers [17-19] and books [20] have been written on the subject. A representation

of the cross-section of a ridge waveguide is shown in Figure 4.3. In this section, only a general

overview of ridge waveguides is given.

Figure 4.3. Square (double-)ridge waveguide cross-section representation.


Ridge waveguides are often used to enlarge the operating bandwidth: a bandwidth

enhancement is obtained because the fundamental mode cutoff frequency is reduced by a larger

amount than that of the higher-order modes [2]. Not only is the cutoff frequency changed, but

the characteristic impedance and the guided wavelength are also changed. Considering the two

orthogonal modes propagating, the horizontally-polarized mode, shown in Figure 4.4.a, is not

much affected by the ridges; on the other end, the vertically-polarized mode, shown in Figure

4.4.b, is significantly affected by the ridges. If the ridges were infinitely thin, the horizontally-

polarized mode would theoretically be identical to the TE01 mode in a normal rectangular

waveguide. Indeed, the cutoff frequency is virtually unaffected for thin ridges. To keep the

return loss to an acceptable level, thin ridges are required. The vertically-polarized mode is

characterized by a lower cutoff frequency. As the ridge height is increased, the gap between the

two ridges is reduced, the fields are more concentrated in this region and the field distribution

resembles more that of a dual-conductor line, such as a bifilar. The consequence is a lower

cutoff frequency, which is expected since structures like the dual-conductor lines have no cutoff

frequency.

a b

Figure 4.4. Electric field representation of the first two modes in a double-ridge waveguide

a. horizontally-polarized; b. vertically-polarized.


4.4 Specifications Unlike Chapter 2 and Chapter 3, which described the design of waveguide components to

be used in the tri-band antenna, this chapter is intended to provide more of a study than a design.

For this reason, a simpler version of a polarizer – which consists of a square waveguide polarizer

– is designed. The effect of changing some parameters will be discussed and a design is then

carried out to determine whether some specifications and guidelines could be achieved.

The studied polarizer is to be designed around the frequency band of the C-Tx band,

which is from 5.925 GHz to 6.425 GHz. A square waveguide of dimensions 35 mm × 35 mm

with a cutoff frequency of 4.28 GHz was chosen for that purpose. Table 4.1 presents the

specifications and guidelines for the polarizer.

Table 4.1. Dimensions, specifications and guidelines of the C-band square waveguide polarizer.

Frequency (GHz) around 5.925-6.425 GHz

Ridge orientation Vertical

Port number 1 2

E-field orientation Horizontal Vertical

Mode TE01 TE10

Input port

Waveguide size (mm) 35 × 35 35 × 35

Port number 3 4

E-field orientation Horizontal Vertical

Mode TE01 TE10

Output port

Waveguide size (mm) 35 × 35 35 × 35

Return loss (dB) 35 35

Cross-polarization level (dB) -35

Total length As short as possible

Bandwidth As large as possible


4.5 Design and results In order to study the polarizer, two orthogonal polarizations are studied, i.e. the

polarization along x and the polarization along y. The two degenerate modes at the input and

output of the waveguide are used as ports, in a similar way as was used for the common port of

the orthomode transducer in Chapter 1.

4.5.1 Step ridge waveguide The geometry used for the polarizer is a double-ridge waveguide with step sections.

Introducing ridges significantly changes the characteristic impedance and guided wavelength of

the vertically-polarized mode. The changed guided wavelength results in a different phase

compared to the horizontally-polarized orthogonal mode, which is virtually unaffected by the

ridge as long as it is kept thin.

If a single step section is used (N = 1), a mismatch is introduced because of the different

impedance in the ridge section. A match can be obtained if the ridge section has an electrical

length of half a guided wavelength, but in this case there is only one zero – i.e. one case of deep

match – and the bandwidth is quite small.

Additional sections can be used in order to improve the bandwidth. If two sections are

used (N = 2) – which corresponds to adding one section before the central section and one

section after – three zeros are obtained if the additional sections – also called the matching

sections – have an electrical length of a quarter of a guided wavelength. This approach is

actually the same as that of a quarter-wave transformer. The bandwidth and return loss level can

be tuned by changing the impedance of the matching section (which is accomplished by

changing the height of the ridges), however these two parameters are dependent of each other

(e.g., the bandwidth can only be increased if the return loss level is reduced).

We chose a value of N = 2 since it provides a better match than a single section and is

simpler to tune compared to cases with a higher number of sections.

4.5.2 Initial case A few values of central ridge height, corresponding to given impedances, along with

proper matching sections, were simulated. The polarizer structure is shown in Figure 4.5.


Depending on the height of the ridge, a given phase shift is obtained. However, this phase shift

may not be the desired phase shift, i.e. 90 degrees. Two parameters have a considerable effect

on the phase shift: the length of the central section ridge and the height of the central section

ridge. However, one cannot simply change the length or height of the central section ridge to

obtain the proper phase shift: by doing so, the matching section dimensions also need to be

retuned in order to maintain a good return loss. Furthermore, attempts to obtain a phase shift

only by varying one of the two parameters results in shifted return loss band and phase shift

band. The return loss bandwidth and phase shift bandwidth must be aligned by varying more

than one parameter at a time. For this reason, finding a suitable initial case is a long process.

Figure 4.5. Side view of the square waveguide polarizer showing ridge sections.

4.5.3 Parameter tuning After a proper initial case is chosen, the return loss, phase shift and bandwidth can be

tuned to obtain a better performance. In all cases, the ridge width is kept small to a value of

1 mm. This leaves the following four parameters to be tuned:

• the height of the central section ridge;

• the length of the central section ridge;

• the height of the matching section ridge and;

• the length of the matching section ridge.


The effect of the each of these parameters on the location of the zeros, return loss and phase shift

is presented in Table 4.2. In the cases studied, the second and third zeros were located in the

operation band whereas the first zero was located lower in frequency. This obviously had the

effect of reducing the bandwidth of the polarizer. A discussion on this topic is presented in

section 4.6.

Table 4.2. Effect of increasing the dimensions of the ridge waveguide polarizer.

Height of central

section ridge

Length of central

section ridge

Height of

matching section

ridge

Length of

matching section

ridge

First zero

location

Slightly

increased

Slightly

decreased

Decreased No significant

impact

Second zero

location

Increased Increased Decreased Decreased

Third zero

location

Decreased Decreased Increased No significant

impact

Return loss Level increased;

Bandwidth

decreased

Level increased;

Bandwidth

decreased

Level decreased;

Bandwidth

increased

Level decreased;

Bandwidth

increased

Absolute phase

shift

Significantly

increased

Increased Increased Slightly

increased

4.5.4 Results The simulated results obtained in IMST Empire™ for the square-waveguide polarizer are

presented in this section. In order to validate the simulation results from EMPIRE™, the

structure was also simulated in Ansoft HFSS™. Figure 4.6 presents the S-parameter results,

from which it is seen that the return loss bandwidth for the vertically-polarized ports (assuming

34 dB of return loss with the EMPIRE™ results) covers the band from 5.94 GHz to 6.57 GHz.

Figure 4.7 shows the phase difference results. The magnitude ratio is shown in Figure 4.8.

Finally, the axial ratio is shown in Figure 4.9 and the cross-polarization level is presented in


Figure 4.10. Appendix D presents the layout of the polarizer. A side view with some

dimensions is shown in Figure 4.11.

S11 S33 S31 S13 S22 S44 S42 S24

EMPIRE ⎯ ⎯ ⎯ ⎯

HFSS × × × ×

Figure 4.6.a. S-parameter results of the square-waveguide polarizer for return loss and coupling,

from -80 dB to 10 dB (zeros indicated by *).


S21 S12 S41 S14 S32 S23 S43 S34

EMPIRE ⎯ ⎯ ⎯ N/A

HFSS × × × ×

Figure 4.6.b. S-parameter results of the square-waveguide polarizer for isolation, from -150 dB

to -70 dB.


Figure 4.7.a. Phase difference results from 4 GHz to 10 GHz; — EMPIRE, × HFSS.


Figure 4.7.b. Phase difference results from 5.8 GHz to 6.6 GHz; — EMPIRE, × HFSS.


Figure 4.8. Magnitude ratio as a function of frequency; — EMPIRE, × HFSS.


Figure 4.9. Axial ratio as a function of frequency; — EMPIRE, × HFSS.


Figure 4.10. Cross-polarization level as a function of frequency; — EMPIRE, × HFSS.


Figure 4.11. Side view of the square waveguide polarizer with some dimensions.

4.5.5 Results discussion In Figure 4.6, the agreement between EMPIRE™ and HFSS™ is good. The return loss

and coupling results agree very well; the isolation results are slightly different, but since the

levels are below -70 dB this could be caused by numerical noise. In fact, the EMPIRE™ results,

for which a symmetrical meshing was generated, have better isolation than the HFSS™ ones, for

which the meshing was automatically generated and therefore not symmetrical. Figure 4.7

shows that the phase difference is only slightly different between EMPIRE™ and HFSS™, the

worst case difference in the C-Tx band being less than 0.5 degrees. In order to obtain such a

good agreement between the two simulators, the meshing had to be very dense, especially in

critical regions, i.e. around the ridges. The problem with HFSS™ is that the mesh cannot be set

manually; therefore it is refined not only in the ridge region but everywhere inside the waveguide

even if it is not necessary. The consequence is a high memory usage and long simulation time.

Consequently, the meshing was coarsened in order to obtain results in a reasonable time. The

HFSS™ results are acceptable, but could probably be improved, which explains the slight

discrepancy with the EMPIRE™ results. Consequently, even if the agreement is close, the

EMPIRE™ results are analyzed instead of the HFSS™ ones since the confidence in the

EMPIRE™ results is better because of the denser mesh in the ridge region.

In Figure 4.6, it can be seen that the return loss of the horizontally-polarized ports is

easily meeting the 35 dB requirements from about 5.7 GHz and above, including the band of

interest, i.e. from 5.925 GHz to 6.425 GHz. The vertically-polarized ports almost meet the

35 dB requirements in the same band; a slight tuning of the parameters would actually allow


achieving the required specifications. A 34 dB return loss bandwidth covering the band from

5.94 GHz to 6.57 GHz will therefore be considered. The bandwidth is 630 MHz or 10 %. The

phase results, presented in Figure 4.7, show a good performance in this band with an angle error

of less than a degree. The magnitude ratio, presented in Figure 4.8, is very good with less than

0.05 % difference between the two orthogonal magnitudes in the return loss band. The axial

ratio and cross-polarization levels, both computed using the phase difference and the magnitude

ratio, are presented in Figure 4.9 and Figure 4.10, respectively. From Figure 4.10, it is shown

that the cross-polarization level is better than the requirements, achieving a worst case value of

-42 dB.

4.6 Discussion The design of this square-waveguide polarizer looks promising. The cross-polarization

level is better than the requirements; the return loss and frequency band can easily be tuned to

meet the requirements. The bandwidth is excellent at 10 % and the device is relatively compact,

with a total ridge length of about 60 mm.

Keeping the same number of sections, the bandwidth might also be improved, since there

is a third zero present but it is not in the desired frequency band. Modifications of the polarizer

structure should allow obtaining all three zeros in the same frequency band in order to extend the

bandwidth. With this third zero, the bandwidth might significantly be improved, perhaps even

doubled. However, what is not known at this point is whether the phase difference will have a

similar bandwidth if three zeros are in the same frequency region.

Another way to improve the bandwidth would be by inserting additional ridge sections.

However, the problem with using more than two sections is the complexity of the model to be

optimized and the longer device length. A circuit model of the polarizer should then be made to

allow for reasonable development time.

The sensitivity of the structures to small variations is also a critical aspect to address.

When running the current simulations, it was found that tiny variations in length and height of

the ridges were significantly changing the results. For example, changing the height of the

central section by a few tens of microns results in a return loss variation of a few decibels (dB)

and a phase variation of the transmission coefficient of a few tenths of degrees for the vertical

polarization. This could be a potential problem when the structure is fabricated: if tight


tolerances cannot be achieved in the fabrication process, then the performance of the device will

degrade significantly.

Finally, since this structure could not be used in the actual tri-band antenna terminal

because of its geometry, the final polarizers will be built either in a circular waveguide for the

Ku band or in coaxial waveguides for the other bands. Designing a similar polarizer in a circular

waveguide seems relatively easy at this point because of the field distribution of the degenerate

fundamental modes, which is similar to those of a square waveguide. However, it is not

guaranteed that such a ridge polarizer could be easily designed and offer good performances in

coaxial waveguide.


5 Conclusions

This report has described the design of an orthomode transducer at Ku band, the design of

a dual-rectangular waveguide to coaxial waveguide transition at X band, and the study and

design of a square waveguide polarizer at C band. The simulation results of the orthomode

transducer meet the specifications. The simulation results of the dual-rectangular waveguide to

coaxial waveguide transition do not meet the specifications at this point, however slightly tuning

the structure or adding one section in the quarter-wave transformers would most likely allow to

meet the specifications. The polarizer presented good simulation results and can also slightly be

tuned if necessary.

In the future, more work would have to be done for the continuation of the project,

including the fabrication and measurement of the components described previously. Even if the

simulation results are good for these components, their fabrication might be highly challenging

due to the mechanical complexity of the structures and the high level of tolerances required. For

these reasons, the fabrication will have to be performed precisely – which may require a time and

cost consuming process – otherwise the components might not meet the specifications.

Furthermore, more components need to be designed, including single-rectangular

waveguide to coaxial waveguide transitions at C band (for both Tx and Rx). The design of these

transitions should not be a problem because they are actually simpler versions of the X-band

dual-rectangular waveguide to coaxial waveguide transition described in this report.

Additionally, polarizers for the X and C bands need to be designed using the ridge approach

described in this report or another approach. However, since these other bands operate in coaxial

waveguides, the ridge waveguide approach may not be applicable. If this is the case, a new

polarizer approach will be required.


References

[1] Éric Choinière, “Tri-Band Coaxial Antenna Feed for Satellite Terminal: Sizing of

Waveguide Input Section,” unpublished working document, Defence Research and

Development Canada, Ottawa, Ontario, Dec. 2004.

[2] J. Uher, J. Bornemann and U. Rosenberg, Waveguide Components for Antenna Feed

Systems: Theory and CAD, Artech House, Boston, MA, 1993.

[3] H. Schlegel and W. D. Fowler, “The Ortho-Mode Transducer Offers a Key to Polarization

Diversity in EW Systems,” Microwave System News, pp. 65-70, Sept. 1984.

[4] A. M. Bøifot, “Classification of Ortho-Mode Transducers,” European Transactions on

Telecommunications and Related Technologies, vol. 2, no. 5, pp. 503-510, Sept.-Oct. 1991.

[5] D. M. Pozar and S. Targonski, “Axial Ratio of Circularly Polarized Antennas with

Amplitude and Phase Errors,” IEEE Antennas Propagat. Mag., vol. 32, no. 5, pp. 45-46,

Oct. 1990.

[6] A. J. Simmons, “Phase Shift by Periodic Loading of Waveguide and its Application to

Broad-Band Circular Polarization,” IRE Trans. Microwave Theory Tech., vol. 3, no. 6, pp.

18-21, Dec. 1955.

[7] F. Arndt, U. Tucholke and T. Wriedt, “Broadband Dual-Depth E-Plane Corrugated Square

Waveguide Polariser,” Electronics Letters, vol. 20, pp. 458-459, May 1984.

[8] U. Tucholke, F. Arndt and T. Wriedt, “Field Theory Design of Square Waveguide Iris

Polarizers,” IEEE Trans. Microwave Theory Tech., vol. MTT-34, no. 1, pp. 156-160, Jan.

1986.

[9] K. K. Chan and H. Ekstrom, “Dual Band/Wide Band Waveguide Polarizer,” in Asia-

Pacific Microwave Conf., Dec. 3-6, 2000, pp. 66–69.

[10] M. H. Chen and G. N. Tsandoulas, “A Wide-Band Square-Waveguide Array Polarizer,”

IEEE Trans. Antennas Propagat., vol. AP-31, pp. 389-391, May 1973.

[11] T. Ege and P. McAndrew, “Analysis of Stepped Septum Polarizers,” Electronics Letters,

vol. 21, no. 24, pp. 1166-1168, Nov. 1985.

[12] R. Behe and P. Brachat, “Compact Duplexer-Polarizer with Semicircular Waveguide,”

IEEE Trans. Antennas Propagat., vol. 39, no. 8, pp. 1222-1224, Aug. 1991.

[13] J. Bornemann and V. A. Labay, “Ridge Waveguide Polarizer with Finite and Stepped-


Thickness Septum,” IEEE Trans. Microwave Theory Tech., vol. 43, no. 8, pp. 1782-1787,

Aug. 1995.

[14] J. Bornemann, S. Amari, J. Uher and R. Vahldieck, “Analysis and Design of Circular

Ridged Waveguide Components,” IEEE Trans. Microwave Theory Tech., vol. 47, no. 3,

pp. 330-335, Mar. 1999.

[15] P. J. Meier and S. Arnow, “Wide-Band Polarizer in Circular Waveguide Loaded with

Dielectric Discs,” IEEE Trans. Microwave Theory Tech., vol. MTT-13, no. 6, pp. 763-767,

Nov. 1965.

[16] E. Lier and T. Schaug-Pettersen, “A Novel Type of Waveguide Polarizer with Large

Cross-Polar Bandwidth,” IEEE Trans. Microwave Theory Tech., vol. 36, no. 11, pp. 1531-

1534, Nov. 1988.

[17] S. B. Cohn, “Properties of Ridge Wave Guide,” Proceedings of the IRE, vol. 35, pp. 783-

788, Aug. 1947.

[18] S. Hopfer, “The Design of Ridged Waveguides,” IRE Trans. Microwave Theory Tech., vol.

3, no. 5, pp. 20-29, Oct. 1955.

[19] W. J. R. Hoefer and M. N. Burton, “Closed-Form Expressions for the Parameters of Finned

and Ridged Waveguides,” IEEE Trans. Microwave Theory Tech., vol. MTT-30, no. 12, pp.

2190-2194, Dec. 1982.

[20] J. Helszajn, Ridge Waveguides and Passive Microwave Components, IEE, London, UK,

2000.


Appendix A: Layout of the Ku-band Orthomode Transducer

(branching section only)

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Appendix B: Layout of the Ku-band Orthomode Transducer

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Appendix C: Layout of the X-band dual-rectangular waveguide

to single-coaxial waveguide transition

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Appendix D: Layout of the C-band square-waveguide polarizer

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Appendix E: Quarter-wave transformer design in Agilent

Advance Design System (ADS™)


Figure E.1. ADS™ screen capture of the X-band Tx quarter-wave transformer.

Figure E.2. ADS™ screen capture of the X-band Rx quarter-wave transformer.

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1. ORIGINATOR (the name and address of the organization preparing the document. Organizations for whom the document was prepared, e.g. Establishment sponsoring a contractor’s report, or tasking agency, are entered in section 8.)

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Tri-Band Coaxial Antenna Feed for Satellite Terminal: Ku-Band Orthomode Transducer, X-Band Coaxial Waveguide

Transition and Polarizer Study (U)

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Gagnon, Nicolas; Morin, Gilbert, A.; Choinière, Éric

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January 2006

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This document describes the contribution of the Advanced Antenna Technology group (RAATlab) to the design of tri-band antenna terminals for the Canadian Forces. As part of this project, waveguide components in the C, X and Ku bands were studied and designed. The components described in this report are an orthomode transducer (OMT) for the Ku band and a dual-rectangular waveguide to coaxial waveguide transition for the X band. Additionally, a polarizer in square waveguide geometry has been studied and designed. Although the tri-band antenna requires circular and coaxial waveguide polarizers, the work performed on the square waveguide polarizer serves as a preliminary investigation into the potential realizable performance of such polarizers and some of the results obtained could be transposed for the design of the required circular and coaxial polarizers.

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Waveguide, Antenna, Satellite, Terminal, Orthomode Trasnducer, Polarizer

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