Design and Feasibility Study of an Orthomode Transducer for the FAST Experiment

Thesis submitted to The University of Manchester for the Degree of Masters of Astrophysics Jodrell Bank Centre for Astronomy.

September 2012

Louis Smith School of Physics and Astronomy 2 Design and Feasibility Study of an Orthomode Transducer for the FAST Experiment Contents

List of Figures 7

List of Tables 9 Abstract ...... 11 Declaration ...... 12 Copyright Statement ...... 13 Dedication ...... 14

1 Introduction 17 1.1 Overview ...... 17 1.2 Design Requirements ...... 18 1.3 Basic Theory ...... 19 1.3.1 Maxwell’s Equations ...... 19 1.3.2 Electromagnetic Spectrum ...... 19 1.3.3 Plane Waves and Polarization ...... 21 1.3.4 Linear Polarization ...... 21 1.3.5 Circular Polarization ...... 22 1.3.6 Isolation ...... 23 1.3.7 Cross Polarization ...... 23 1.3.8 Return Loss ...... 24 1.4 Waveguides ...... 24 1.4.1 Boundary Conditions ...... 27 1.4.2 Coordinate Systems and Dominant Modes ...... 28

Louis Smith 3 CONTENTS

1.4.3 Cut-oﬀ Frequency (Fc)...... 30 1.4.4 Operating Bandwidth ...... 31 1.4.5 Binomial Rule ...... 32 1.4.6 Reﬂection and Scattering Parameters ...... 32 1.5 Computational Electromagnetism ...... 33

I Research and Development 39

2 Current state of OMT Research 41 2.1 Overview ...... 41 2.2 OMT Typologies ...... 44 2.3 Planar OMTs ...... 44 2.4 Waveguide OMTs ...... 48 2.4.1 B∅ifot Classification, Class I ...... 50 2.4.2 B∅ifot Classification, Class II ...... 51 2.4.3 B∅ifot Classification, Class III ...... 56 2.5 Finline ...... 63

3 Detailed Development of a Turnstile Junction, appropriate for the FAST Experi- ment 67 3.1 The Turnstile Junction Waveguide OMT ...... 67 3.1.1 The Turnstile Splitting Junction ...... 68 3.1.2 Compact 90 degree Twist ...... 71 3.1.3 H and E plane Bends ...... 74 3.1.4 Y Junction Tapered Power Combiner ...... 76

II Design and Results 79

4 Simulated Disign and Results 81 4.1 Overview ...... 81 4.2 H-Plane Bend with E-Plane Stepped Impedance Transformer ...... 82 4.3 Turnstile Junction ...... 86

4 Design and Feasibility Study of an Orthomode Transducer for the FAST Experiment CONTENTS

4.4 Compact Ninety Degree Twist ...... 89 4.5 Y Junction Tapered Power Combiner ...... 92 4.6 Simulated FAST OMT Design ...... 95

5 Conclusions and Future Work 103 5.1 Conclusion ...... 103

III Appendices 105

Louis Smith 5 CONTENTS

6 Design and Feasibility Study of an Orthomode Transducer for the FAST Experiment List of Figures

1 Artist impression of the FAST project in situ ...... 15

1.1 Electromagnetic Spectrum, with the visible section having been expanded. . . . 20 1.2 Cross section of a rectangular waveguide ...... 25 1.3 Waveguide flashlight analogy...... 26 1.4 Magnetic fields propagating through a waveguide ...... 28 1.5 Propagation of EM field along waveguide at various frequencies ...... 29 1.6 2D Grid pattern examples for the FDTD method ...... 36 1.7 Grid pattern 2D and 3D examples for the FEM ...... 37

2.1 Schematic view of an OMT as a four-port device ...... 43 2.2 Reference diagram of a microstrip waveguide component...... 46 2.3 Reference diagram of a basic microstrip OMT, where the microstrip is connected to the circular waveguide via the microstrips dielectric material...... 47 2.4 A. High performance Class III waveguide based OMT with B. showing the incoming waves are coupled out within the inbuilt Turnstile Junction...... 49 2.5 Class I OMT device...... 50 2.6 Reference diagram of a class II OMT...... 53 2.7 Reverse coupling class II structure showing both input and output modes . . . . 56 2.8 Reference diagram of a class three turnstile junction...... 57 2.9 Metallic scattering element it situ ...... 59 2.10 Reference sketch of a coaxial cable...... 60 2.11 Reference sketch of a basic coaxial cable orthomode transducer...... 61 2.12 Systematic diagram of a coaxial cable turnstile junction OMT...... 62

Louis Smith 7 LIST OF FIGURES

2.13 Schematic view of the ﬁnline OMT...... 64 2.14 A Finline OMT sketch with the resistive card illustrated at the base of the output port...... 65

3.1 Turnstile Junction splitting a dually polarised TE11 mode...... 69 3.2 Detailed view of a designed scattering element...... 70 3.3 General conﬁguration of the multi-section bow-tie steps twist...... 73 3.4 Rectangular waveguide twist...... 74 3.5 Rectangular waveguide bends...... 75 3.6 Standardised simulated layout of a Y junction combining section as shown this consists if two incoming polarisations...... 77

4.1 Design concept of E-plane transformer with bend ...... 82 4.2 Simulated 90 degree H-bend with an E-plane transition...... 83 4.3 Return loss vs frequency graph for the reduced height H-bend transition. . . . . 85 4.4 FAST simulated OMT Turnstile Junction...... 86 4.5 Simulated return loss characteristics for the independent Turnstile Junction. . . 88 4.6 Simulated Compact 90 degree twist...... 89 4.7 Simulated return loss characteristics for the separate compact 90 degree twist. . 91 4.8 Simulated Y junctions...... 92 4.9 Simulated return loss characteristics for the personalised Y junction...... 94 4.10 Simulated Planar waveguide based OMT for the FAST experiment...... 96 4.11 FAST planar OMT systematic diagram...... 97

4.12 FAST OMT Simulated return losses for the ﬁrst port S11...... 99

4.13 FAST OMT Simulated Isolation measurements for the second ports S 21. . . . . 100 4.14 FAST OMT Simulated Cross Polarisation measurements for the second ports

S 21...... 101

8 Design and Feasibility Study of an Orthomode Transducer for the FAST Experiment List of Tables

1.1 OMT Requirements according to the FAST documentation ...... 19

5.1 OMT Requirements vs simulated results according to the FAST documentation 104

Louis Smith 9 LIST OF TABLES

10 Design and Feasibility Study of an Orthomode Transducer for the FAST Experiment The University of Manchester

An Orthomode Transducer (OMT) is a waveguide structure capable of discriminating two independent signals of an orthogonal dominant mode incident upon its common port and to the output port in its fundamental single mode form, therefore enabling the wave to be separated in a passive manner. It is essential that this function is achieved whilst maintaining excellent matching between all electrical ports and a high cross polarisation discrimination and isolation to maintain the required independent signals.

The purpose of this thesis is to produce a feasibility study into the production of an Orthomode Transducer for the FAST experiment; china’s contribution to the SKA, a global cosmological collaboration which will operate with approximately a 34 percent bandwidth across the L-band (0.95-1.45Ghz). With this in mind, a class three planar turnstile based OMT was investigated, designed and then simulated using Ansofts HFSS 13, a commercially available package.

The method presented in the final design was formed through the use of a H-plane bend with an integrated reduced height transition, a compact ninety degree twist, turnstile junction and a Y junction recombining section all individually simulated during the course of this project. This resulted in a highly, compact of total volume of 212mm3 uniquely planar low loss component; average return losses -28dB, isolation of -49dB and cross polarization of -55dB. All having been recorded across the chosen scaled W-band of 75-115GHz, with a view for this simulated design to be manufactured and analysed using the University of Manchester’s VNA operating at this frequency. These measurements represent a sufficient improvement on both the specified thresholds stated in the FAST literature as well as other waveguide designs of similar size.

September 2012.

Louis Smith 11 Declaration

I do hereby declare that no portion of the work referred to in this thesis has been submitted in support of an application for another degree or qualiﬁcation of this or any other university or other institute of learning.

12 Design and Feasibility Study of an Orthomode Transducer for the FAST Experiment Copyright Statement

(i) Copyright in text of this thesis rests with the Author. Copies (by any process) either in full, or of extracts, may be made only in accordance with instructions given by the Author and lodged in the John Rylands University Library of Manchester. Details may be obtained from the Librarian. This page must form part of any such copies made. Further copies (by any process) of copies made in accordance with such instructions may not be made without the permission (in writing) of the Author.

(ii) The ownership of any intellectual property rights which may be described in this thesis is vested in The University of Manchester, subject to any prior agreement to the contrary, and may not be made available for use by third parties without the written permission of the University, which will prescribe the terms and conditions of any such agreement.

(iii) Further information on the conditions under which disclosures and exploitation may take place is available from the Head of School of Physics and Astronomy.

Louis Smith 13 Dedication

To me, my family, friends and supervisor without whom none of this would have been possible

14 Design and Feasibility Study of an Orthomode Transducer for the FAST Experiment Figure 1: Artist impression of the FAST project in situ

Louis Smith 15 16 Design and Feasibility Study of an Orthomode Transducer for the FAST Experiment 1

Introduction

1.1 Overview

An Orthomode Transducer (OMT) is a passive device which has the task of separating orthogonal polarizations. It thus allows the use of two frequency channels simultaneously, enhancing a systems capacity, whilst improving its versatility by permitting the structure to operate over an improved bandwidth.

The intention of this masters thesis is to research, design and simulate the performance of an Orthomode Transducer (OMT) operating with approximately a 34 percent bandwidth centred at 1.45 GHz (the L-frequency band) using current waveguide technology. This concluding design shall then be produced using a suitable production method and have its performance compared to that of its computational cousin, enabling a comparison to be made (beyond the scope of this thesis). This ﬁnal design is required to provide excellent electrical matching be- twixt all ports together with suitably high isolation, cross polarization and return losses with all values speciﬁed for the wider application of the Five-hundred meter Aperture Spherical radio Telescope (FAST), an astrophysical experiment which once built will be the largest single dish radio telescope in the world[1].

Cosmology is the science of investigating the universe at its largest scales, to understand its structural origins and evolution. In this vain FAST represents Chinas contribution to the inter-

Louis Smith 17 1: INTRODUCTION national endeavour to build the Square Kilometre Array (SKA) is enabling copious experimental investigations to be performed, at a combined cost of over 700 billion yuan. These investigations will include but not be limited to; a spectroscopic survey of neutral hydrogen in the Milky Way and other galaxies, detection of faint pulsars, conduct a visual examination for the ﬁrst shining stars or hearing the possible signals from other civilizations all of which are being recorded for the ﬁrst time or in greater detail than presently possible.[1]

There is an on-going requirement for antenna systems to operate across increasing bandwidths in almost all applications from defence to as in this case radio astronomy. For this reason OMTs with dual-polarization operation are key components in modern systems such as FAST.

While reviewing the literary sources, it was noted that an OMT (a passive device which acts as means of separating or combines two orthogonal linearly polarized signals within the same frequency band) can be referred to by various nom de plumes, including but not limited to, polarization diplexers[2], dual-mode transducers[4], orthomode junctions[4], or orthomode tees[5]. During this thesis I shall refer to this device as an orthomode transducer[6], due to its preva- lence.

1.2 Design Requirements

Although the electrical and mechanical requisites of a design in respect to a microwave passive assembly depend on the specific application, the common figure-of-merits of a dual-polarized system are commonly low reflection losses measured through the use of a return loss measurement, high polarization purity related to an isolation and cross polarization value, compactness and reconfigurability[6]. The specified electrical specifications for this OMT are illustrated in table 1 where the terms referred to shall be defined in more detail in sections 1.3.6, 1.3.7 and 1.3.8:

18 Design and Feasibility Study of an Orthomode Transducer for the FAST Experiment 1.3: BASIC THEORY

Table 1.1: OMT Requirements according to the FAST documentation[1]

1.3 Basic Theory

Some basic terminologies and concepts associated with the design and manufacture of a passive device such, as an OMT, are relevant to this assignment; the expressions described in this section shall be used throughout.

1.3.1 Maxwell’s Equations

Electromagnetic phenomena are all phenomena involving electric and magnetic fields propagating through a vacuum or a dielectric medium. These physical phenomena were mathemat- ically unified and described by Maxwell at the end of the 19th century then presented in their modern rigorous form in 1887 by Heaviside, whose efforts to solve them resulted in the introduction of vector notation provided its application to guided waves and transmission lines. Maxwells equations have been proven at all frequencies and in any transmission system irre- spective of complexity, therefore these equations are universally used in some form during the modelling of any electromagnetic wave.

1.3.2 Electromagnetic Spectrum

The electromagnetic spectrum as introduced in figure 1.1 is a classification system for the varying frequency bands therefore providing a useful method of separating the spectrum into its associated energies, thus enabling the effects of EM radiation at various wavelength band to be distinct. An initial natural division of the spectrum occurs at a point over which can be observed through use of the human eye referred to as visible light (750-390nm spectrum) after which sub-optical and super-optical respectively refer to lower and higher frequencies. As energy is directly proportional to frequency through Planck’s constant, the upper part of the

Louis Smith 19 1: INTRODUCTION super-optical radiation band can be referred to as the ionising radiation; an area comprising the far Ultraviolet to Gamma radiation bands.

In the optical bands, waves have lengths generally far smaller than the objects they interact with and do not carry great quantities of energy. Therefore Maxwells equations can be simpliﬁed leading to the classical geometric optical rules.

Figure 1.1: Electromagnetic Spectrum, with the visible section having been expanded. As seen the EM spectrum can be split into numerous distinct bands

At extremely low frequencies (long radio wave bands) analogue dimensional considerations lead to a lumped element description, usual in circuit theory. In this case the wavelengths are far greater than the characteristic dimensions of the circuit components and cables. An exten- sive part of the sub-optical spectrum is the radio wave band, which conventionally goes from 3 KHz to 300GHz (or wavelengths from 100Km to 1mm). The lower part of this radio ﬁeld is widely exploited for data transmission and communication, resulting in use of the distinct frequencies being restricted and regulated by international agreements; with the upper echelon from 30GHz to 300GHz, being known as EFE (Extremely High Frequencies) or the millimetric band with wavelengths from 1cm to 1mm.

During this thesis I will be interested in operating within the Ultra High Frequency band.

20 Design and Feasibility Study of an Orthomode Transducer for the FAST Experiment 1.3: BASIC THEORY

Therefore, a microwave component shall be a prerequisite of the final design. In microwave engineering it is usual to handle transmission line components and instruments with dimensions similar to those in which they transmit. A lumped description similar to the standard circuit theory is often not valid in these fields since the phase of a voltage or current may result in a significant change in the physical characteristics of the device. Therefore one must often approach a microwave problem with Maxwells equations and their solutions, as such, mathematical complexity must be expected.

1.3.3 Plane Waves and Polarization

A general plane wave has non-zero components in a plane orthogonal to the direction of propagation. When a time harmonic E or H-plane wave is propagated in the positive z-direction within free space the ﬁeld can be described by either equation 1.1 or equation 1.2.

−→ −→ − jkz −→ −→ − jkz E = E te = [E x x + E yy]e (1.1)

−→ −→ −→ − jkz −→ −→ − jkz H = zE = zxE te = [E x x + E yy]e (1.2)

The polarization of a wave is determined by the characteristics of the E-ﬁeld. It can be described in terms of a desired co-polar component Eco which is parallel with the unit vector co and an undesired cross-polar component Exp, which is laterally aligned to the cross-polar unit vector xp and is orthogonal to co. Both co and xp are orthogonal to the direction of propagation z as well as each other. Thus the total ﬁeld can be expressed as equation 1.3.

− jkz E = [Eco + Exp xp]e (1.3)

Using a scalar multiplication of the E ﬁeld with the co and xp, the respective co-polar and cross-polar components of the E-ﬁeld (Et) can be calculated by the application of equation 1.4.

Eco = Etco Eco = Et xp (1.4)

1.3.4 Linear Polarization

If the start of the E-ﬁeld vector oscillates in a straight line within the X-Y plane running perpendicular to the transmission of the wave; with the z-axis propagating in a linear polarization

Louis Smith 21 1: INTRODUCTION it can be seen that the two field projections have a zero phase difference. While if the field is y-directed, it can be defined as linearly polarised as expressed in equations, 1.5, 1.6 and 1.7.

ucob = y xp = x (1.5)

Eco = Ety = Ey (1.6)

Exp = Et x = Ex (1.7)

An arbitrary linear polarization can be expressed in the co or cross polar unit vectors given in equations 1.8 and 1.9: co = cos(θx) + sin(θy) (1.8)

xp = sin(θx) + cos(θy) (1.9) where, θ = π/2 represents the y-polarization and θ = 0 representing the x-polarization value.

1.3.5 Circular Polarization

A circularly polarized E-ﬁeld vector can be thought of as a circularly polarized wave propagating along a circular helix in the direction of propagation. Such polarization will be either right (RHC) or left hand (LHC) circularly polarized relating to whether its rotation is clockwise or counter clockwise. RHC polarization can be expressed by the unit vector expressed in equation 1.10. x − jy co = √ (1.10) 2 It can therefore be observed that the y-component processes a phase factor − j π -j= e 2 compared to the x-component, resulting in the y-component being delayed by a quarter of a period, giving an RHC polarized plane wave as described in equation 1.11.

The body of research over which this FAST experiment has been designed to operate and by association the OMT described during this thesis, operates using a linear rather than circular model of polarization, therefore, from now on I shall only be concerned with a linearly polarized system.

22 Design and Feasibility Study of an Orthomode Transducer for the FAST Experiment 1.3: BASIC THEORY

1.3.6 Isolation

The observed isolation between the two ports of an OMT represents one of the main criteria for deﬁning its performance. The isolation of a device is a unit of measurement deﬁned in negative dBs. Determined in the primary arm as the ratio between the dominant mode in the main arm to the leakage to a secondary side arm, or vice-versa an isolation measurement represents the undesired signal level on adjacent ports of a device. Therefore, the greater the isolation value the lower interference experience from one signal on one port is present at the other.

If a received signal contains considerably less power than the transmitted signal it can be seen that there is inadequate isolation between the output ports. Isolation greater than -35dB is consequently usually required in the case of a dually polarized passive device such as an OMT, where the two orthogonal polarizations being transmitted are required to be incoherent hence excellent separation (or isolation) is essential.

1.3.7 Cross Polarization

Cross Polarization (sometimes referred to as X-pol) has been described in detail in [39] and [40] and is a measurement of polarization orthogonal to those being discussed. These were expertly defined by Luduig’s three definitions of which the 3rd is the most useful in this instance; that the reference and cross polarization are deemed to be what one measured when antenna pattern are taken in the usual manner[40]. For instance, in this case the field is defined as horizontally polarized, therefore the cross polarized version of this wave would be vertically polarized.

This term arises due to imperfections which may arise within an antenna systems polarization resulting in two radiation patterns being presented: the co-pol (or desired polarisation component) and the cross polarization component. Therefore, it can be seen that the lower the cross polarization value, the higher the purity of the vacating wave.

The cross polarization is speciﬁed for an antenna system as a power level in dB’s. Cross polarization greater than negative inﬁnity indicates a level of polarization below optimum.

Louis Smith 23 1: INTRODUCTION

1.3.8 Return Loss

The third key measurement of an OMTs performance is the return loss; the input reﬂections from an electrical port of the microwave device. A return loss below -15dB is necessary in most common microwave designs[7]. However, a return loss below -20dB over most of the operating band width is desirable. An average return loss -25dB is speciﬁed for this OMT design.

1.4 Waveguides

As hollow metal pipes waveguides in essence take the form of either a circular or a rectangular cross section, although a rectangular orientation is the most common conﬁguration. Figure 1.2 shows an end view of a rectangular waveguide, where the b dimension is the wider and a the narrower sides. These labels are considered the standard form of notation for waveguide dimensions[7] and will be used in the following discussion.

The signal within a waveguide propagates as an electromagnetic wave, not as a current, as the current in motion down the line gives rise to electric and magnetic fields both of which behave as an electromagnetic field. The propagation of an EM field is influenced and modified by the introduction of boundary conditions interacting with a non vacuum environment. The possibility of using conductive materials to transfer electromagnetic waves with low losses through a desired path is the basis of waveguide transmission. A simplistic non-mathematical approach to waveguide solutions will now briefly be introduced.

As previously stated, this OMT is required to operate within the microwave spectrum, covering frequency range of between 0.4-300GHz, or a free space wavelength range of 75cm to 1mm. A traditional transmission line based system is applicable at frequencies from dc to 50-60GHz[7], however beyond 5GHz only short runs are practical due to increased attenuation.

As an electromagnetic wave travels through the waveguide an oscillator can be assumed, driv- ing an electrical fluctuation at high frequency across the conducting walls of the waveguide. As such, at one instance the oscillator will cause a surplus of electrons on the top face of the structure and a deficiency on the bottom, facilitating a potential difference to be produced. This

24 Design and Feasibility Study of an Orthomode Transducer for the FAST Experiment 1.4: WAVEGUIDES motivates an electrical current to ﬂow down the guide and thus the formation of a magnetic ﬁeld which will endeavour to circle around the created current.

Due to the presence of the waveguides metallic wall these fields cannot completely enclose the current but combine, resulting in as the polarity slowly reverses the wave to travel down the guide. A flux therefore occurs in the field facilitating the walls themselves to generate a current further along the waveguide by induction, perpetuating the production of the electromagnetic vectors further along the waveguide. As such, at any point along the guides internal wall one would observe the electrons first cluster at the top then the bottom of the guide in a smooth manner, this feature enables a waveguide system to be a highly efficient method to expedite the radiation across the required space.

Figure 1.2: Cross section of a rectangular waveguide

There are three types of losses in conventional transmission lines: ohmic, dielectric and radiation. The first of these, caused by currents flowing causing a resistance in the conductor making up the transmission lines thus skin effects are formed; which themselves increase with escalat- ing frequencies. Losses such as these tend to increase across the microwave region. Dielectric losses are caused by the electric field acting on the molecules of the insulator and thereby causing heating through molecular agitation. Radiation losses represent a loss of energy as an electromagnetic wave propagates away from the surface of the transmission line conductor.

Losses on long runs of coaxial transmission line (the type most commonly used) give design-

Louis Smith 25 1: INTRODUCTION ers cause for concern even at the low 0.4 to 5 GHz region due to increased losses. Power handling capability also decreases at higher frequencies therefore, within higher microwave bands where long runs make coaxial losses unacceptable or where high power levels would overheat the coaxial line, waveguides are preferable, for this design.

Figure 1.3: Waveguide ﬂashlight analogy: in free space the beam spreads according to the inverse square law.[7]

Waveguides are an imperative component within most modern OMT systems due to their field focusing facilities. When an electromagnetic wave is propagated along a confining conducting surface it is forced to obey Maxwells equations, while applying certain boundary conditions at all points on the conducting walls. This device can be nicely illustrated with the flashlight analogy in figure.1.3 where the flashlight serves as a RF source. In figure 1.3.a, this source is radiated into free space and spreads out as a function of distance, with the intensity per unit area at the destination (a wall) falling off as a function of distance D according to the inverse square law.

26 Design and Feasibility Study of an Orthomode Transducer for the FAST Experiment 1.4: WAVEGUIDES

As shown in figure.1.3.b, compared to a freely propagating diffused beam over the same distance D, a waveguide confines the propagating waves inside a pipe, so intensifying the final beam. While not perfect, this light pipe analogy with its mirrored walls neatly summarises simply the operation of microwave waveguide. Thus, it can be considered that a waveguide is analogous to an RF pipe.

The internal walls of a microwave waveguide are not, however, mirrored surfaces as in an optical analogy (ﬁbre-optical technology), but rather electrical conductors. Most waveguides are made of aluminium, brass or copper, with eﬀorts occasionally taken to reduce the ohmic losses through the use of electroplating, a process requiring the internal surfaces to be plated with a highly conductive material such as gold or silver, due to their lower resistivity in comparison to other metallic substances[8].

1.4.1 Boundary Conditions

A TEM wave will not propagate in a perfect rectangular waveguide conductor by virtue of certain boundary conditions[7] whilst the ﬁeld in a waveguide propagates through air or an inert dielectric gas in a manner similar to free-space propagation. This phenomenon of being bound by the walls of the waveguide, implies certain conditions which must be met in order for the wave to progress, the conditions are as follows:

1. The electric ﬁeld must be orthogonal to the conductor.

2. The magnetic ﬁeld must not be orthogonal to the surface of the waveguide.

A TEM modes boundary conditions do not meet these requirements as its magnetic ﬁeld does not propagate parallel to the surface of the conductor; so does not occur in a rectangular waveguide. In order to satisfy these boundary conditions, two diﬀerent types of propagation modes are allowed:

1. Transverse Electric mode (TE mode)

2. Transverse Magnetic mode (TM mode)

Louis Smith 27 1: INTRODUCTION

Therefore, a transverse electric ﬁeld results in the E-ﬁeld propagating perpendicular to the con- duction wall. This requirement is met by the use of a correctly coupled scheme at the input end of the waveguide.

The second of these boundary condition requirements; stating that the magnetic field (H) must not be orthogonal to the conductor surface, is fulfilled by applying a predefined constraint that the E-field must consistently be placed at right angles to said field as illustrated in figure 1.4. The planes formed by this magnetic field are parallel to both the direction of propagation and the wide dimension surface.

Figure 1.4: Magnetic ﬁelds propagating through a waveguide [7]

1.4.2 Coordinate Systems and Dominant Modes

The angle of incidence within the waveguide wall increases as the frequency drops with the angle rising towards 90 degrees the cut-off frequency is approached, as can be seen in figure 1.5. Below the cut-off frequency, at an angle of 90 degrees, the wave bounces back and forth between the walls, resulting in the stagnation of the propagating wave.

The a and b dimensions of the waveguide correspond to the X-Y axis of a Cartesian system (ﬁgure 1.2), while the Z axis is the direction of propagation. In describing the various modes of propagation, the use a shorthand notation:

28 Design and Feasibility Study of an Orthomode Transducer for the FAST Experiment 1.4: WAVEGUIDES

Figure 1.5: Propagation of EM ﬁeld along waveguide at various frequencies[9]

T xm,n

Where: X = E for a transverse electric mode and M for a transverse magnetic mode. m = Number of half-wavelengths along the X-axis (the a dimension). n = Number of half-wavelengths along the Y-axis (the b dimension).

The TE01 mode is known as the dominant mode for rectangular waveguides and is the most

Louis Smith 29 1: INTRODUCTION

suitable mode for low-attenuation propagation in the Z axis. The nomenclature TE01 indicates that there is one half-wavelength in the a dimension and zero half-wavelengths in the b dimension.

1.4.3 Cut-oﬀ Frequency (Fc)

As the radiated wave propagates away from the input radiator, it resolves into two components neither of which are parallel to the axis of propagation, or orthogonal to the walls. The component along the waveguide axis is rapidly attenuated due to the waveguide boundary conditions. This has been shown in ﬁgure 1.5, where for the sake of simplicity; only one component has been shown. The propagation of a signal across a decreasing frequency (from A to C) in a waveguide depends in part to the applied signal. As illustrated, the angle of incidence made by a plane wave to the waveguide wall is a function of frequency. As this frequency drops, the angle of incidence increases toward 90 degrees.

The propagation of a wave depends on the angle of incidence and its associated reﬂection propagation. Indeed, both phase and group velocities are a function of the angle of incidence, so much so that as the frequency drops to a point where the angle of incidence is 90 degrees, the group velocity is zero and the concept of a phase velocity is meaningless. A general mode equation based on the system in equation 1.11 can be formed.

1 m n = ( )2 + ( )2 (1.11) 2 λc 2a 2b Where:

λc = The longest wavelength that will propagate, the cut-off waveguide. a,b = The waveguide dimensions m,n = The integers that define the number of half-wavelengths that will fit in the a and b dimensions respectively.

Therefore it can be seen from an extension of equation 1.11, that the longest TE-mode that can propagate in a dominant (TE10) mode is given by equation 1.12.

λc = 2a (1.12)

30 Design and Feasibility Study of an Orthomode Transducer for the FAST Experiment 1.4: WAVEGUIDES

For which an expression for the cut-oﬀ frequency can be written:

c F = (1.13) c 2a

Where:

Fc = Lowest frequency that will propagate in hertz, the cut-oﬀ frequency. c = Speed of light (3x108 m/s) a = Wide waveguide dimensions.

1.4.4 Operating Bandwidth

The operating bandwidth of a waveguide and by association its corresponding OMT, is deﬁned between the cut-oﬀ frequency of the fundamental modes in the circular/ rectangular waveguides

(TE11 and TE10 respectively) and the cut-oﬀ frequency of the higher order modes propagating within these structures.

It can be shown that the fundamental mode in a rectangular waveguide is the TE01 mode, provided a > b with the bandwidth of a single-order mode for a rectangular waveguide being dependent on the value of b. If a > 2b, the ﬁrst higher-order mode is the TE20 with a cut-oﬀ ratio fC,20 = 2 fC,10 propagating otherwise. In the case of b

(TE01) frequency is given by equation 1.14.

a f = f (1.14) C,20 b C,10

In practice almost all the standard waveguides have dimensions equal to a=2b[7] resulting in the maximum bandwidth for the minimal ohmic costs, this configuration has been widely used for previous OMT applications. In the case of the main port having an a = b configuration it is customary for both orthogonal field configurations to propagate with the same properties, constituting a very attractive structure for this application.

To design a broadband component, it is seen as necessary to produce transitions, such that, only even higher order modes are present, due to the relative ease by which they can be compensated. A waveguide device is deﬁned as symmetrical if the diﬀerent transitions cause the

Louis Smith 31 1: INTRODUCTION dominant mode to generate only symmetrical (even-order) higher modes, while deﬁned as non- symmetrical if the dominant mode, in addition, produces odd-symmetrical higher order modes.

1.4.5 Binomial Rule

The binomial rule is generally recognised as a basis for reducing the reflection in certain waveguide components operating over a substantial bandwidth. If several small bumps of the same kind are spaced at quarter-wave intervals, their resultant reflection at frequencies near the frequency of interest is (nearly minimized) by proportioning their individual reflections in the ratio of a set of binominal coefficients. This rule provides a simplistic starting point for many designs, even though most apply a flexible approach to its application resulting in the best results in both providing exceptional return losses with conventionally substantial bandwidth. In applying the binominal rule, it is noted again that the reflection at each face is roughly proportional to the square of the angle of a twist. Therefore, the angles at the respective faces are made proportional to the square roots of a set of binomial coefficients. For a three face example for instance, the binominal coefficients are 1 : 2 : 1, therefore, the square of the angles are √ so proportioned and the angles are proportioned to 1 : (2) : 1. Giving the three angles as 26.4+37.2+26.4 = 90 degrees.

1.4.6 Reﬂection and Scattering Parameters

A significant parameter to describe the propagation through a transmission line is the reflection parameter Γ(z). The generalised solution of the wave equations describes a wave travelling in both a positive and negative z-direction, with the latter having the physical interpretation of the reflected wave component. Reflection can also occur in a microwave network if an impedance discontinuity is present, due to for instance a local discontinuity being present.

Since in general the point of interest is the efficiency of power transmitted from the input to the output sections, defined as ports in black box description of any network with n ports can be formed. In this case allowing for simplicity ai and b j to be respectively the incoming power at the ith port and the outgoing power at the jth port, we can relate transmission T and the reflection

32 Design and Feasibility Study of an Orthomode Transducer for the FAST Experiment 1.5: COMPUTATIONAL ELECTROMAGNETISM

Γ to the transfer function matrix of the device, (or a scattering matrix S as shown below).

The S-parameters of a network can then be calculated considering the single port excitation and matching conditions on the non involved ports. Lossless networks satisfy the conservation of total power, equation 1.16.

If a network is passive (as in the case of an OMT) and made up of reciprocal materials, it will show a symmetric scattering matrix. The deﬁnition of scattering parameters comes, as seen, from an analogy between waveguides and transmission lines, but can be generally used to describe a n-port network of any desired complexity. Recent computational methods widely used in microwave engineering rely on the use of S-parameters to equate the simulated results into useful data.

1.5 Computational Electromagnetism

Computer Aided Design (CAD) is predominantly used for the detailed engineering of 3D models as a step towards the production of physical components. They therefore enable the con- ceptual design and layout of a product to be created through the construction of numerous standardised shapes or freehand vector drawings which are then allocated material speciﬁcations within a frequency band or bands depending on method. As such, the strength of this method is in its dynamic analysis of assemblies in respect to the manufacturing methods under-which are applied. CAD has become an especially important technique in the ﬁeld of reducing product costs and a greatly shortened design cycle, facilitated by the layout and development of the component to be produced on screen, then printed or shared and saved for future editing.

Computational electromagnetism (CEM) comprises a wide variety of numerical algorithms all

Louis Smith 33 1: INTRODUCTION

finding an approximate solution to the exact Maxwells equations over cells of finite dimensions so the exact domain is divided, enabling a solution to be formulated, rather than solving exactly the approximate equations given by the transmission line approximate. These methods can be classified with respect to the form of hyperbolic Maxwells equations, they are based on either differential or integral forms.

There are several methods, by which computational electromagnetism can be achieved. Many of these approaches exhibit distinct features and advantages. Among these methods, there are four of particular importance, all of which have been successfully used in the design of passive components; the Method of Moments (MOM), Mode Matching method (MM), Finite- Diﬀerence Time Domain method (FDTD) and ﬁnally the Finite-Element Method (FEM).

The most popular integral equation solver is the Method of Moments (MOM): requiring the calculation of only the boundary values rather that the characteristics throughout the space, therefore it is more efficient in terms of computational resources for problems with a small surface area to volume ratio. Conceptually, MoM works by constructing a mesh of elements over the modelled surface, however, for many problems this method is significantly less efficient than corresponding volume-discretization methods, since boundary element formulations typically give rise to fully populated matrices. This means that the storage requirements and computational time grow according to the square of the unknowns. FEKO is a popular software solver for radio frequency problems using the MoM solvers.

The mode matching method (MM) is a frequency-domain iterative integral method, based on the notion that the ﬁeld is expanded into analytical ﬁeld eigen-functions under a region of analysis leading, when boundary conditions are imposed to an algebraically linear system. In order to solve this problem, an inversion of a set of matrices formed at each boundary is required.

Eigenmodes[7] are found by solving Maxwells equations relying on the decomposition of the electromagnetic ﬁelds into a basis set of local eigenmodes that exists in the cross-section of the device. This necessitates the devices to be represented as a stack of layers where each layer is uniform in the z-direction. Curved devices modelled with layers use a staircase approximation.

34 Design and Feasibility Study of an Orthomode Transducer for the FAST Experiment 1.5: COMPUTATIONAL ELECTROMAGNETISM

It can be seen from the mathematical formation that the algorithm is inherently bi-directional using a scattering matrix technique to join the varying sections of the waveguide or modes non-uniform structures.

In a typical waveguide, there are few guided modes (which propagate without coupling along the waveguide) and an infinite number of radiation modes. This method is only suitable with two or more separate regions. The µ -wave wizard software uses this MM technique. It has been shown that the time scale and memory requirements square as a factor of the unknowns. Consequently this method is limited in terms of the size of the cross-section for three dimensional problems. A main limitation of this method is that, it is restricted to linear problems and is inefficient in modelling structures requiring numerous modes. The Mode Matching method is generally seen as a more efficient method of CAD than FDTD as it does not require discretization along the direction of propagation resulting in errors.

A differential equation solver is the most frequent method to solve Computational EM problems. Many commercial and university-developed tools using FDTD algorithms were developed during the early 1990s. FDTD belongs to a class of computational design tools known as grid-based differential time-domain numerical methods. These take advantage of Maxwells equations which are modified into a central difference equation, discretised then implemented into software.

This involves the equations being organised into a matrix form which are then solved in a cyclic manner (i.e. the electric ﬁeld is solved at a given time, followed by the magnetic at the next instance and so on). Since this method operates in the time-domain, solutions can operate over a wide frequency range with a single solution run, provided that the intermediate time domains steps are small enough to satisfy the Nyquist Shannon sampling theorem for the desired frequency.

In order to ensure that these domains are of suitable accuracy, the elementary cells or meshes are small in relation to the minimum wavelength of the signal these meshes take can only take regular forms as illustrated in ﬁgure 1.6. The time-elementary step which approximates the

Louis Smith 35 1: INTRODUCTION diﬀerential part of the derivative (with respect to time in the Maxwell equations) must satisfy certain restraints i.e. that the ratio between the elementary cell dimensions and the light velocity must be smaller than one. This leads directly to a solution with no need for matrix inversion. The main disadvantage of this method is its time consuming nature and high computational demand, as well as its order of magnitude inaccuracy in comparison to the MoM

Figure 1.6: 2D Grid pattern examples for the FDTD method

36 Design and Feasibility Study of an Orthomode Transducer for the FAST Experiment 1.5: COMPUTATIONAL ELECTROMAGNETISM

FEM is a frequency-domain method, similar to FDTD. The finite difference method is also based on a discretisation of the domain, but it gives more flexibility than the previous methods in choosing the element cells of the defining mesh. This may take the form of different shapes within a single domain (resulting in better results being obtained with curved surfaces), as well as not requiring the properties of the defined materials to be defined outside of the frequency band of interest see figure 1.7.

Figure 1.7: Grid pattern 2D and 3D examples for the FEM

The Finite Element Method (FEM) is a widely used technique to find an approximate solution of the partial differential and integral equations. Involving the exact rendering of the equations into their weak integral form, using a weighted shape function as a solution base, FEM provided a mathematical method such that the functions fit the order of the derivatives present thus enabling the equations to be solved in a smooth nature. The domain in questions volume is divided into geometrically simple elements whose definitions must be made with care, since they define the accuracy and stability of the entire method.

This ﬂexibility in discretization is obtained at the expense of a more complex electromagnetic formulation. When boundary conditions are imposed, the EM problem becomes an algebraic linear system of equations which can be solved using conventional methods, to which very eﬃ- cient solvers can be applied. Both HFSS and CST Microwave Studio are based on this method.

The FEM was ﬁrst proposed to solve elastic problems, but has been applied well to solve various phenomena, including electromagnetic ones. HFSS is a software which exploits the versatility of the FEM to solve problems involving various electromagnetic problems, FEM however is more expensive in terms of CPU loads as the computational costs grow with the square of the number of total elements; therefore FEM solver algorithm optimisation has be-

Louis Smith 37 1: INTRODUCTION come one of the principle aims of software developers.

When the problem is simple, it is routine to use a mode matching method, due to rapidity of analysis. However, due to the improved accuracy and computational capacity of modern com- puters, this project uses a program based on the FEM method of analysis due to its perceived flexibility and aptitude to overcome EM complications which are foreseen to occur within the design of a relatively complex shape such as an OMT. OMTs are typically designed and optimised using a commercial finite-element analysis software package such as Ansofts HFSS or CST Microwave Studio, both industry standard simulation tools for 3D full-wave electromagnetic field simulation. During this thesis I will use Ansofts HFSS 13 released in 2011 to define the electromagnetic design which will be presented in the following chapters.

This choice is based on two considerations:

1. The availability of the licensing agreements

2. The proven accuracy of FEM in comparison to other deﬁned methods

Due to the inherent diﬃculty associated with the design of a highly symmetric system such as those associated with the OMT. The use of CAD programs has become commonplace with numerous examples being forthcoming such as those in the references which all employ Ansofts HFSS while demonstrate the use of the CST Microwave studio designs. It can also be seen that the results obtained by the diﬀerent FEM programs provide comparable overall results.

38 Design and Feasibility Study of an Orthomode Transducer for the FAST Experiment Part I

Research and Development

Louis Smith 39 40 Design and Feasibility Study of an Orthomode Transducer for the FAST Experiment 2

Current state of OMT Research

2.1 Overview

In almost all applications, from radio astronomy to defence, an increase in demand for capacity in satellite communication systems has brought about the need to operate over ever-increasing bandwidths. Almost all wavelengths, including the millimetre bands, demand precise characterisation of the amplitude, spectrum and polarization of the electromagnetic radiation is essential. To further enhance capacity and versatility of an antenna system, dual-polarization operation is often required, or in some cases, mandatory[10].

The conventional method of separating orthogonal polarizations for submillimeter receivers is a grid of freestanding laterally standing wires, in which parallel and perpendicular E-field polarizations are reflected and transmitted respectively, depending on the initial grid composition. This configuration necessitates the precise alignment of the associated feedhorns, thus careful considerations are required to reduce vibrational damping.

Orthomode transducers are passive devices, which allow, through geometrical design, the trans- duction of a generic dually polarized EM wave in two orthogonally polarized signals or vise- versa. An OMT collocates in the radiometric chain between the feed horns and the receiving system and must be designed to adapt both to the circular section of the antenna and to the electric properties of the cabling, this system has numerous merits and demerits over a conven-

Louis Smith 41 2: CURRENT STATE OF OMT RESEARCH tional wiregrid; these include: Merits:

1. The use of an OMT can facilitate a receiver system to be simplistic and compact, removing the need for an unwieldy wire grid conﬁguration.

2. There are no requirements for calibrations to take place between grids recording their respective polarizations.

3. Problems associated to the limited lifetimes of the wiregrid conﬁguration can be overcome.

4. In order to ﬁt into existing dewars, a component must be compact; hence there is a strong preference for the use of a waveguide based design rather than a much bulkier alternative. Demerits:

1. Fabrication and assembly of an OMT structure can prove problematic especially at higher frequencies, as its small dimensions and tight tolerances pose a signiﬁcant challenge with only few broadband OMT designs having been demonstrated to work suitably at higher frequencies (above 100GHz).

2. An OMT must be formed with a suitable structure, since its performance has a signiﬁ- cant impact on the entire antenna feed system, therefore the design of a high performance OMT requires the use of computer aided design software.

3. The joule losses of a waveguide must be included in the design aspects, in comparison to an ideal wire grid conﬁguration which processes almost no losses.

Due to the apparent strengths of an OMT’s design in comparison to current alternatives these components are conventionally favoured (usually symmetric in nature) over traditional quasi- optical wire grids for focal plane imaging arrays. From a system perspective, the key demerits having been shown to be alleviated if mechanical robustness is made paramount and production using a highly conductive electroforming ﬁnish (such as gold-plating) or alternative to reduce the associated joule losses.[10]

42 Design and Feasibility Study of an Orthomode Transducer for the FAST Experiment 2.1: OVERVIEW

From an electromagnetic prospective, OMTs are a four port devices, with two ports assigned to the same physical duct (Port.1 and Port.2 in ﬁgure 2.1) while the two remaining vestibules corresponding to the principle output modes. This passive device works as a polarization diplexer; while transmitting, it combines the two orthogonally polarized separate signals into a singular output channel, thus enabling information to be transmitted over the same frequency band while isolation is maintained between the two outgoing signals.

In the case of receiving, the transducer separates the incoming dually-polarized signals into its two output channels, each carrying the information associated with a singular polarization states. These polarization states have been known to be either linear or circular; however in the circular state this component is more properly termed a polariser, therefore form this point on I shall only be concerned with a linearly polarized source, during this work.

Figure 2.1: Schematic view of an OMT as a four-port device

As inferred in chapter one, the electric quantities within an OMT can not be uniquely deﬁned, since they vary signiﬁcantly through its length. Thus, the most common approach to verifying its performance is to consider the component as a black box and produce a transfer functions matrix, between all possible combinations of the input-output pairs.

th If a generic amplitude is called ai of an incoming signal at the i port, and b j is that of an outgoing signal at the jth port, a matrix of correlation between inputs and outputs can be created, forming a scattering matrix S, which in the case of an OMT is four-by-four conﬁguration.

Louis Smith 43 2: CURRENT STATE OF OMT RESEARCH

The diagonal parameters S ii represents the reflection coefficients on the four ports; the 2 square of their module |S ii| defining a Power Loss (PLi) due to the electrical mismatch of port i, while its mathematical reciprocal is the Return Loss (RLi). An ideal OMT should exhibit a power loss parameter as close as possible to zero.

−2 −2 The quantities |S 41| and |S 32| represent quantity of power of one polarisation mode reaching the undesired port, deﬁning therefore the cross polarizations, XPi j.

2.2 OMT Typologies

Varying types of OMTs exist with associated characteristics in terms of performances, working frequency bands, geometry and production process. A useful classiﬁcation for these systems are based on the geometrical structure of the device, as presented in the following three sections:

2.3. Planar

2.4. Waveguide based

2.5. Finline

2.3 Planar OMTs

Planar OMTs use dielectric probes in rectangular or circular waveguides, representing the typical and most researched conﬁguration since the early 2000s. This comprises four probes at right angles within a cylindrical waveguide, after which the two orthogonal polarisations are extracted by combining the signals from each pair of probes. This design is compact, simple to construct and easily scaled to most frequencies.

44 Design and Feasibility Study of an Orthomode Transducer for the FAST Experiment 2.3: PLANAR OMTS

Due to advantages in integration, scalability and the low mass nature of a planar OMT compared to other OMT methods[11], a planar transducer coupled to a corrugated horn is a good solution for future astronomical research, in particular at sub-millimetre wavelengths such as those involved in the investigation of the Cosmic Microwave Background.

The realisation of a high performance planar OMTs to achieve the stringent requirements of new polarisation cosmology instruments, requires extreme precision and some corrective ex- pedients, either to increment the bandwidth or to reduce the cross-polarisation, which in turn requires higher costs.

Typical materials for the production of a planar device under standard lower frequency conditions include metallic materials such as gold, copper or aluminium alloys, or at higher frequencies a superconducting highly conductive materials, such as silicon nitrides or niobium are commonly used.[12]

A microstrip, as in the one shown in ﬁgure.2.2 belongs to the family of planar devices used largely in modern microwave applications. Comprising essentially a single-mode port, its single fundamental mode supports modes propagating in the z-direction from a dc frequency band upwards.

Louis Smith 45 2: CURRENT STATE OF OMT RESEARCH

Figure 2.2: Reference diagram of a microstrip waveguide component. As shown this is com- prised of a number of diﬀerent dielectric substrates [7]

It can be seen that a microstrip is formed by the combination of a conductive strip of width w and thickness t placed within a substrate of relative dielectric constant and thickness h grounded on one side by a conducting layer, this layer results in some major advantages over more traditional production mediums. These include:

− Enabling fabrication using a low cost printed circuit board technology resulting in good mechanical tolerances in the microwave range.

− It allows easy integration of elementary linear and nonlinear devices, making it possible to realise complex circuits directly on a single board (integrated circuits).

− It can be easily coupled with a square or circular waveguide to form an OMT as illustrated in figure 2.4. A major drawback associated however with the an OMT design based on the microstrip technology is associated with the medium in which the EM field must propagate being non-homogeneous. This is different from other systems, where propagation is facilitated in either air or dielectric material, but not both thus the propagation constant does not depend linearly on frequency causing an extra distortion within the propagating wavepacket.

46 Design and Feasibility Study of an Orthomode Transducer for the FAST Experiment 2.3: PLANAR OMTS

The strip acts as a guide for the EM wave in the z-direction with the energy being concentrated by the dielectric medium, in the region between the strip and the ground plane. Such is the effect of this configuration as to emphasise the increasing dielectric constant. The fundamental mode in this configuration is termed quasi-TEM, because the longitudinal component of the associated EM field exists, but is very small compared to its transverse cousin.

The most practical and widely used planar OMT conﬁguration, ﬁgure 2.3, is formed by the junction of two microstrip lines on a common substrate[7], with the strips intersected by another at 90◦. These microstrip lines are typically enclosed by a metallic box connected electrically to the waveguide walls where the lower side of the box representing the microstrips ground plane, within a region inside the waveguide usually being removed to ensure conditions which are favourable for optimum coupling.

Figure 2.3: Reference diagram of a basic microstrip OMT.[7]

In this conﬁguration one side of the waveguide is typically short-circuited by a metallic plane while on the other side the two orthogonal modes TE11V and TE11H, associated with ports one and two, respectively, can propagate.

Louis Smith 47 2: CURRENT STATE OF OMT RESEARCH

The optimisation of this transition between the microstrip and a waveguide is currently a highly researched topic, due to its structure being heavily used within the satellite communication industry. Although, the lack of symmetry in the polarisation plane does not provide high performance and broadband operation, this conﬁguration nevertheless has two major advantages:

− An OMT can be easily fabricated and network matched networks using present state of the art microstrip technologies.

− It is very easy to accommodate on a microstrip the active circuitry required to eﬃ- ciently process the incoming radio frequency signals. Thus, on a microstrip card the OMT, matching network, low noise ampliﬁers and wave integrated circuit technology can all be facilitated without an appreciable degradation of the quality of the signal itself.

A typical performance for this type of OMT design has been recorded to be between 10-15 percent bandwidth with a minimum return loss of 15-20dB and an isolation characteristics of typically 30-40dB.

2.4 Waveguide OMTs

Waveguide based OMTs as in ﬁgure.2.4 exhibit unequalled performances demonstrated at millimetre wavelengths which can be produced using a wide variety of techniques. As with any waveguide devices, its broadband operation is tied to its symmetric properties with symmetrical and non-symmetrical transitions within a waveguide producing high order modes which, though evanescent, subtract power from the desired principle modes.

An initial classiﬁcation system of OMTs based on rectangular waveguide technology and their associated level of symmetry was presented by B∅ifot[13]. This method of classiﬁcation enabled B∅ifot to split the copious OMT designs based on waveguides, into three main groups related to their increasing symmetry, with class one representing the simplest and class III the most mechanically complicated and symmetric approach.

48 Design and Feasibility Study of an Orthomode Transducer for the FAST Experiment 2.4: WAVEGUIDE OMTS

Figure 2.4: High performance Class III waveguide based OMT[7]

Typically, the common port has a square or circular section, since it must host both vertical and horizontal principle modes coming from its incoming source, while the output due to its singular transverse mode has a standardised rectangular shape with a typical dimension ratio of 1:2 between the two faces due to its singular transverse mode. A major advantage to a circular port is that can be directly joint to a feed horn waveguide, whilst a square input would require a circular−to−square transition, which would potentially introduce a mismatch between an OMT and its corresponding coupled device. Section transformers for circular to square to rectangular standard ports, just like junctions, are of critical importance with good matching properties a necessary for this reason.

The B∅ifot classiﬁcation is a suitable and logical system as, for any waveguide OMT since the broadband operation of the transducer is tied to its symmetric properties, therefore non- symmetric transitions when present in the constituent OMT waveguides produce discontinuities consequently higher order modes are produced, most of which are evanescent and do not propagate. Uncompensated higher order modes however store reactive energy preventing the broadband operation of the device, therefore the production of these higher order modes often dictates the broadband isolation and input matching capacity of a waveguide device.

Hence it can be seen that several asymmetric OMTs have been designed to cover bandwidths of less than 30 percent[13], whilst highly symmetric structures enabling the avoidance of higher

Louis Smith 49 2: CURRENT STATE OF OMT RESEARCH order mode excitation enables a broad bandwidth (of 40 percent or more)[14]. The adoption of symmetrical structures, such as a B∅ifot[15] or turnstile junction[16], improves the channel isolation and return loss characteristics of the OMT, although at the cost of a greater mechanical complexity. As a consequence of their symmetry, the isolation and cross-coupling in these conﬁgurations are, in principle, inﬁnite and zero respectively.

2.4.1 B∅ifot Classiﬁcation, Class I

The ﬁrst class of waveguide OMTs represents the simplest and most common approach consisting of a main arm used for one mode and an orthogonal side arm. These resultant structures are symmetric in respect to the primary mode yet not for the secondary, thus creating an asymmetric device see ﬁgure 2.5.

Figure 2.5: Class I OMT, where port 1 represents the input common port while ports 2 and 3 are the output.[13]

Historically, these designs were driven by a desire to minimise the volume, mass and transmission losses incurred in achieving polarization discrimination all within an undemanding mechanical framework. Asymmetric OMTs are commonly used for polarization diplexing in microwave applications due to their ease of design, with the performance of these structures being limited in practice to a fractional bandwidth of 10 to 30 percent caused by the excitation of higher order modes in the common arm by discontinuities caused through the construction of symmetrical higher-order modes. These modes have their cut-oﬀs within the frequency range of operation, reducing the hypothetical performance, however, owing to cancelling effects, leakages to the side arm ideally does not occur.

50 Design and Feasibility Study of an Orthomode Transducer for the FAST Experiment 2.4: WAVEGUIDE OMTS

It is therefore possible to achieve a full broadband isolation for a mode in the main arm, however it has been observed that at higher bandwidths (approx. 30 percent)[17] an OMT based on an asymmetric configuration, is burdened by a strong dispersion towards the lowest frequencies and by a very faint attenuation of the TE11 and TM11 modes at the highest frequencies. Owing to this non-symmetrical nature, the sidearm for this mode causes a configuration of imbalance, thereby leading to the generation of odd-symmetrical modes. This non-symmetry also causes the higher-order modes to leak to the main arm and negatively affect the polarization purity. Thus it is difficult to achieve good isolation over a wide frequency scale for the mode in the side arm, as well as low return loss. Several tuning screws or other reactive components have been suggested[18] to achieve reasonable matching, however the use of these have shown to result in a higher level of complexity removing one of the major advantages of this design, as well as limiting the scalability over which a class I design may operate at higher frequencies due to the the reactive components size becomes unsuitable.

The highest performing example of a class one OMT can be seen in [17] et al A. Dunning, S. Srikanth and A.R. Kerr, where the resultant complexity resulting from a more symmetric component would have meant considerable complication compared with the ﬁnal class I asymmetric designs. In this case a return loss of -24dB was achieved with an isolation characteristic of 37dB across a 30 percent bandwidth.

2.4.2 B∅ifot Classiﬁcation, Class II

A secondary class of OMT as defined by B∅ifot comprises a more complex configuration whereby the sidearm is split into two symmetrical elements from the main as illustrated in figure 2.6. As in class one, a field in the main arm sees a symmetrical device, therefore coupling only to symmetrical higher-order modes, thus causing a removal of unwanted effects resulting in natural broadband behaviour. Dissimilarly however, to group one OMTs a class two configuration also observes a symmetrical splitting and combining junction in side arm.

These designs built on the ideas by Brain conducted at Marconi Research Laboratory[41] and ﬁrst reported in its true split block conﬁguration by B∅ifot with coupling occurring from the

Louis Smith 51 2: CURRENT STATE OF OMT RESEARCH main arm through two symmetrical H-planes bends to a sidearm where it is recombined con- structively. The symmetrical nature of the splitting and combining junctions of the sidearm enables good isolation over a wide frequency range within both the main and side arms.

There are three main subgroups within the class II division which have been developed for broadband applications (fractional bandwidth ≥ 26 percent) in respect to both the millimetre and sub-millimetre range:

− B∅ifot junction with septum and pins[2].

− B∅ifot junction with a double ridge[19].

− Reverse coupling structure[20]. These designs can prove to be complex to manufacture and spacious in size due to the presence of the recombining side ports, while RF losses are higher for the recombined side port in comparison to the through port.

B∅ifot Junction

The B∅ifot junction is a class II OMT, but it can be thought of as a turnstile junction (Class III section 2.4.3) with two of the outputs ports having been folded parallel to the common port. The main arm’s dual components are separated by a metal septum, recombined by a square waveguide and then transformed into a standard full-height waveguide; this design can be seen in ﬁgure 2.6, in both its pin and double ridge form. Numerous waveguide OMT designs based on the B∅ifot junctions have been demonstrated to work at millimetre wavelengths [3][20][21] where within the sidearm, the septum can be thought of as a back-to-back mitered bend.

B∅ifots control over modal symmetry is of considerable importance for an OMTs performance with the common arm supporting six modes of propagation over a standard 2 : 1 rectangular waveguide band, two of which are desired. The bandwidth, isolation and return losses are ul- timately determined by the level of modal conversion, the septum length and the achievable symmetry, due to their ability to control the excitation of the resulting evanescence, thus resulting in them not being propagated, therefore the associated reactants must be compensated. Since it is desirable for both the polarization modes to propagate within the common arm, the

52 Design and Feasibility Study of an Orthomode Transducer for the FAST Experiment 2.4: WAVEGUIDE OMTS higher order modes cut-oﬀ frequency is lower than that of the upper chosen frequency bands edge.

The length of the side arms must be kept as close as possible to each other in order to ensure coherent signal recombination within the power combiner. Phase errors manifest themselves by means of constructive/destructive interference or beating at the side arm output. The usual cause of this fault is manufacturing error. This can be remedied by a side arm power combiner septum to compensate for minimal reﬂection, thus employing adiabatic transformation in its guide height to match the output guide size.

Figure 2.6: Reference diagram of a class II OMT; A)With septum and pins OMT with septum and pins, B) Shows the double ridge formation.

B∅ifot Junction with Septum and Pins

Within this conventional conﬁguration the number, diameter and location of the pins are a compromise between the tuning of the septum reactance, produced in the sidearm ports and allowing a low impedance return path for the main-arm currents. From the main-arms perspec-

Louis Smith 53 2: CURRENT STATE OF OMT RESEARCH tive, it is useful to think of the pins as a pair of short-circuit waveguide-stubs which are used to tune out discontinuities from the sidearm junctions this design can be seen in ﬁgure.2.6.A. While these pins provide an adequate match for the OMT, their small diameter and particular placement result in the advanced complexity of assembly, therefore making them unsuitable for scaling to terahertz frequencies.

The main and side-arm junctions are twofold symmetric about the vertical and horizontal guide planes, thus, the TE11 and TM11 excitations can be avoided in the square common-arm of the junction. Isolation above -40dB has been found to be common within this design with a return loss of -20dB.[3][22]

B∅ifot Junction with a double ridge

Numerous waveguide OMT designs based on the B∅ifot junction have been demonstrated to work at the millimetre wavelengths, resulting in ever decreasing pin diameters with increasing frequency. The complexity of assembling these, as previously stated, poses a significant challenge for the reliable and cost-effective production of this device, especially at higher frequencies. Other B∅ifot based designs with a thicker septum are however also possible, whereby the pins are eliminated in favour of numerous of short capacitive steps, or alternatively standard multistep transitions on the side-arms as seen in figure.2.6.B. This results in the signal being coupled to the sidearm then being transformed with an adiabatic taper and recombined; this can be thought of as a thick septum from which the main-arm is carved. A configuration allowing the use of this relatively compact and wideband E-plane bends with power combiners is therefore allowed.

This design beneﬁts from the mechanical realisation of the blocks giving a simpliﬁed assembly, the alignment of the septum inside the waveguide however still remains critical. This symmetric OMT achieves full waveguide band performance by limiting the excitation of TE11 and TM11 modes from the square common port. Isolation above -40dB has been found to be achievable within this design with a return loss of -20dB, similar to the pin based B∅ifot OMT.[3]

54 Design and Feasibility Study of an Orthomode Transducer for the FAST Experiment 2.4: WAVEGUIDE OMTS

Reverse-Coupling structure

The third subclass of this type is a reverse-coupling OMT method as shown in ﬁgure 2.7. This type of OMT was developed at the Australia Telescope Facility by G. Moorey and P. Axtens for the 77-177 GHz band in 2006. This conception processes a square waveguide input propagating two orthogonally linear polarized signals which enables, during any period, the wavelength to be below the cut-oﬀ value. Beside the fundamental modes, some higher order modes can propagate within the square waveguide frequency bands due to inherent discontinuities.

Higher order modes such as the TE11 and TM11 have the same cut-oﬀ frequency; therefore, in theory these modes are excited by a discontinuity created in the aperture of the side arms. However as long as the two-fold symmetry of the structure (a requirement of its class II status) is maintained, these excitations can be limited. As with most class two OMTs its adopted symmetry enables broadband operation allowing a bandwidth for this device of over 30 percent. [18]

The symmetric coupling structure of the common square waveguide arm splits the incoming signal with opposite phases; the incoming TM11 signal into the two rectangular waveguide side arms. Signals coupling to each sidearm are obtained with a broadband 90◦ hybrid coupler realised with an E-plane branch line coupling structure. Isolation below -50dB has been found to be common within this design with a return loss of -17dB, representing a current maximum. [21]

Louis Smith 55 2: CURRENT STATE OF OMT RESEARCH

Figure 2.7: Reverse coupling class 2 structure showing both input and output modes[21]

The transformer stepped sections have the same physical length and height in the sidearm and common arm to guarantee that the line input port sees the same impedance while looking straight on and through the coupled ports of the hybrid. A disadvantage of this design is the relative complexity of high accuracy machining. The tiny features of this design can lead to average low return losses, as higher order modes can easily be propagated within the structure as previously stated especially with narrow stepped double ridged centred in the middle of the square waveguide input.

2.4.3 B∅ifot Classiﬁcation, Class III

The third and ﬁnal B∅ifot OMT is even more complex in comparison to the previous two. Here both the sidearm and main arm are split symmetrically. This results in forming a turnstile junction or a variant of this design.[23]

Numerous orientations have been suggested for the splitting then recombining of this class of OMT with some having one arm been split into two symmetrical E-plane bends, while the other branches are split into two symmetrical H-plane bends [6]. For some applications it is also possible to split both arms into symmetrical E-plane bends [24].

56 Design and Feasibility Study of an Orthomode Transducer for the FAST Experiment 2.4: WAVEGUIDE OMTS

The highly symmetric nature if this OMT in the main arm and for the mode in the side arm causes unwanted higher-order unsymmetrical modes to be abated therefore for this reason these OMTs have a naturally high broadband isolation capacity, with components being highly complex and therefore potentially expensive to manufacture.

Turnstile Junction

As a valid alternative to a class two B∅ifot junction, the turnstile junction OMT design does not require pins or septums to achieve accurate polarization separation and low return loss over wide bandwidths; in addition, all the rectangular waveguides can be split along their mid planes.

Developed at the MIT Radiation Laboratory by R. Dicke, the turnstile junction is a natural candidate for wideband performance as a result of its four-fold symmetry. This structure is inherently three dimensional and presents manufacturing challenges at the high frequency limit ﬁgure.2.8).

Figure 2.8: Reference diagram of a class three turnstile junction, showing both the common- arm and the resultant four side arms. As seen port three and four are coupled as are ports one and two by a 180 degree phase diﬀerence[3]

Louis Smith 57 2: CURRENT STATE OF OMT RESEARCH

The turnstile junction processes a circular or square waveguide input port and four single-mode rectangular waveguide outputs. This then enables the two orthogonal TE11 modes from the input circular waveguide to be split equally into two TE10 modes by a scattering element as shown in ﬁgure 2.4.B).

The ﬁrst higher order mode generated in a circular waveguide input that can propagate in this structure is TM11 mode enabling theoretically up to 70 percent bandwidth. On the other hand, in a rectangular waveguide the ﬁrst propagated higher order mode is that of the TE20 which enables a bandwidth of 66 percent. Therefore, the maximum theoretical bandwidth that a turnstile junction can operate at just below one octave.[25]

A metallic tuning stub or scattering element is located at the base of the commonly circular orientated waveguide, designed to maintain natural symmetry and enable an enhanced broadband operation of above 40 percent to be achievable[25]. The shape and symmetry of this metallic element is critical. A square prism has been used as a tuning stub together with an E-plane bends within a full height waveguide configuration obtaining a return loss better than 19dB [26] in the 18-26 GHz bend; a pyramid tuning stub orientation using a full height waveguide yielding a return loss of -23dB respectively within the 9.2-12.4GHz band (30 percent bandwidth)[27][28]. A double cylindrical structure using a full height waveguide covering the 75-115GHz band (38 percent bandwidth) achieved a return loss of -35dB thus improving the performance by 10dB over previous designs[6]. This orientation is illustrated in figure 2.9. these finding were repeated during the course of this thesis providing similar results

58 Design and Feasibility Study of an Orthomode Transducer for the FAST Experiment 2.4: WAVEGUIDE OMTS

Figure 2.9: Metallic element it situ within the turnstile junction. As shown this can take the form of a number of cylindrical varying steps located at the centre of the junction.[25]

Signals split by the turnstile junction exit opposite waveguides 180◦ out of phase. These signals are then recombined in a power combiner which experiences a similar phase shift, implemented using an E-plane Y junction as seen in ﬁgure2.4. The electrical lengths of the waveguides from the turnstile to the power combiner are kept equal to maintain this phase variant.

The sidearm bends and impedance transformers are a compromise between two characteristics; the ohmic and return losses. In addition, they are required to maintain the same electrical path diﬀerence in order to maintain the appropriate phase diﬀerence once recombined. Isolation above -35dB has been found to be common within this design.[6]

Coaxial Cable Turnstile Junction

Coaxial Cables are used in OMTs as a single mode port because its fundamental excitation has a single polarization conﬁguration avoiding the possibility of propagating two uncoupled signals. This structure enables the propagation of electromagnetic energy in the whole frequency spectrum with the fundamental mode of propagation, (TEM) where both the electric and magnetic ﬁeld vectors travel in a the plane orthogonal to the direction of propagation.

Figure 2.10 shows a common coaxial cable which usually comprises two materials: an homogeneous dielectric material and an inter-conducting medium to provide mechanical stability. This structure is rotationally symmetric, therefore by applying a potential diﬀerence V between

Louis Smith 59 2: CURRENT STATE OF OMT RESEARCH the two conductors, a TEM ﬁeld is propagated within the medium.

Figure 2.10: Reference sketch of a coaxial cable.[9]

A very easy to fabricate and low cost OMT is shown in ﬁgure 2.11.[9] This junction is formed by the insertion of two coaxial cables whose inner conductors intersect a circular waveguide section, where the axis of the three guided structures are mutually orthogonal and the coaxial external conductor is electrically connected to the circular waveguide wall.

One side of the waveguide is then short-circuited by a metallic plane, called back-short. The two input ports are then located at the common circular input. Inside the waveguide, the inner 1 conductor of each coaxial cable is typically a 4 wavelength long to maintain maximum matching.

As can be seen in figure 2.11 the vertical TE11v mode produced by port one has a symmetric electric field pattern that couples with port three, where the inner conductor behaves as a vertical dipole. At first order, this field configuration induces no current in port four, resulting in absence of coupling between ports one and four. By analogy, the horizontal TE11H mode produced by port two couples to port four and, at first order, does not produce any excitation in the coaxial cable of port three.

It is diﬃcult to obtain perfect matching at all ports of this junction with a realistic value for measured return losses being between -15 to -20dB or when a matching element is present, a bandwidth no greater than 10-15 percent can be achieved.[9] This is mainly due to a lack of

60 Design and Feasibility Study of an Orthomode Transducer for the FAST Experiment 2.4: WAVEGUIDE OMTS symmetry with respect to the two polarisation planes, which are defined in the common-port waveguide by the field polarisation of the two fundamental modes and the waveguide axis. In this case the structures configuration breaks key symmetries within the region of interaction with the coaxial cables, leading to severe performance degradation.

Figure 2.11: Reference sketch of a basic coaxial cable orthomode transducer. As shown the two coaxial cables constituting the output ports of the OMT are located at 90 degrees to the main waveguide port.[29]

Another example of a coaxial cable conﬁguration consists of a turnstile junction and two identical 180◦ hybrid power combiners, as shown in ﬁgure 2.12 enabling four-fold symmetry of the structure to be maintained. The metallic tuning stub located at the base of the circular waveguide does not break this symmetry. The axis of the probe/ coaxial connector assembly is 1 located approximately a 4 wavelength from the plane of a reactive load.

Louis Smith 61 2: CURRENT STATE OF OMT RESEARCH

Figure 2.12: Systematic diagram showing a coaxial cable turnstile junction OMT, with coaxial cable ports acting as the required bends. The coaxial cable probes have been illustrated with there respective diameters. [29]

The four coaxial cables are then required to be combined with a hybrid power combiner for the out of phase signals available at the four coaxial outputs of the turnstile junction. This conﬁguration results in an improved broadband conﬁguration of 25-40 percent and a return loss of -31dB over the entire band. This however substantially increases the complexity of fabrication.[29]

62 Design and Feasibility Study of an Orthomode Transducer for the FAST Experiment 2.5: FINLINE

2.5 Finline

As previous stated symmetry is of considerable importance for the broadband operation of a waveguide device, as any discontinuity within the waveguide produces higher order modes. These evanescent mode stores reactive energy thus preventing a broadband device, it is however almost impossible to avoid some form of discontinuity within a waveguide, however simple guidelines can be adopted to minimise these eﬀects.

In such an environment where a symmetric consideration is key, the obvious choice of a broadband OMT would be a class three transducer, described by B∅ifot. The main problem with the adoption of this class three design for sub-millimetre wave is its perceived diﬃculty in fabrication.

As frequency increases, waveguide dimensions decrease and the tolerences in production become extremely critical. Wollack reported a B∅ifot OMT which was suitable for the (18- 27GHz)[21] but clearly indicated machining challenges it posed to fabrication such as a device at higher frequencies up to the W-frequency band (75-115GHz). A method of design beyond 100GHz is a septum OMT with a fractional bandwidth of approximately 20 percent, which falls out of the requirements stated at the beginning. A Finline OMT is a possible candidate at millimetre wavelengths.[30]

A septum OMT can be built beyond 100GHz but has about a 20 percent bandwidth a width which falls short of our requirement as stated above. For these purposes a Finline OMT is a possible candidate at millimetre wavelengths.

First proposed by Robinson in 1956[31] a Finline OMT has the potential to be a superior approach for the THz applications. This design has also be investigated at lower frequencies by Skinner and James (1991) [32], while being considered for millimetre wave applications by Chattopadhyay and Carlstrom who tested a scale model device across the X-band.[30]

Figure 2.13 consists of a square or circular waveguide ﬁtted with diametrically opposite thin

Louis Smith 63 2: CURRENT STATE OF OMT RESEARCH tapered metallic fins. In this configuration, the dominant mode, whose electric field is parallel to the fins, is gradually transformed to the Finline mode whose energy is essentially confined into a narrow gap between the fins located at the centre of the waveguide. This energy can then be removed from the waveguide by curving the finline and bringing it out through the sidewall of the guide.

Figure 2.13: Schematic view of the Finline OMT; A) illustrated the overall design consisting of a thin metallic ﬁn set inside a waveguide inorder to split the incoming dually polarised input wavefront, B) illustrates the thin metallic ﬁns set inside a circular or square waveguide. Conventional resistive layers are used to suppress the excitation of unwanted modes (region pointed by arrow) [31]

The mode which is polarized orthogonal to the fins passes through the guide virtually unper- turbed with a sufficiently thin fin, enabling fabrication at milli-metric frequencies with a higher level of ease than either class two or class three OMT, thus it is sometimes seen as more viable in these bands.

Within the Chattopadhyay design[30], the ﬁns were realised as two separate metallic plates held at the proper separation with alignment pins. This design was scaled to a design of 1THz with a ﬁnal gap of 5µm.

Conventional Finline OMTs use a resistive card seen in ﬁgure 2.14 as a means of suppressing the excitation of unwanted higher order modes simulated by the termination of the ﬁns. It has

64 Design and Feasibility Study of an Orthomode Transducer for the FAST Experiment 2.5: FINLINE

Figure 2.14: A Finline OMT sketch with the resistive card illustrated at the base of the output port.

been shown that these resistive cards on the Finline signiﬁcantly complicates the fabrication process. Instead of these resistive cards an alternative has been demonstrated which enables the suppression of the oscillations by reducing the Finline length causing a transmission loss of the horizontal waves and narrowing operational bandwidth.

Louis Smith 65 2: CURRENT STATE OF OMT RESEARCH

66 Design and Feasibility Study of an Orthomode Transducer for the FAST Experiment 3

Detailed Development of a Turnstile Junction, appropriate for the FAST Experiment

3.1 The Turnstile Junction Waveguide OMT

A waveguide-based OMT is preferable for our application due to its compacted size and ability to be linked to the wider waveguide based component, such as in this case a feed horn. It has been decided that the small diameter and high complexity in respect to assembly of a compensation pin or septum based system poses a signiﬁcant challenge for a reliable and cost-eﬀective production of this device as if a class two method were to be chosen, especially during the scale model feasibility stage. For this reason, as well as the reduced bandwidth experienced due to it slight asymmetry results, this procedure has being discounted. An alternative to the Boifot OMT as previously stated shall be used in this design, a class three turnstile junction as described by Meyer and Goldberg in 1955. [33]

This configuration has been chosen due to its high performance characteristics in respect to return losses and isolation especially across a relatively broad bandwidth as specified in the performance requirements (this required broadband nature not being achievable using an asymmetric class one or planar microstrip design). A full waveguide configuration also reduces the

Louis Smith 67 3: DETAILED DEVELOPMENT OF A TURNSTILE JUNCTION, APPROPRIATE FOR THE FAST EXPERIMENT required complexity of this design in comparison to a hybrid form and thus alleviates manufacturability problems associated with the positioning and eﬀective transfer between the varying technologies i.e. the position and length of a coaxial probe within a waveguide turnstile junction.

A brief description of the various constituent parts required to produce an OMT based on a turnstile junction network follows. We start with the characterisation of the turnstile junction itself.

3.1.1 The Turnstile Splitting Junction

As previously mentioned the turnstile junction is a ﬁve-port microwave network connecting a circular or square input port and four single mode rectangular waveguide outputs so providing separation of the two input polarisations. The turnstile junction is an inherently broadband component with excellent isolation and return losses. First developed by R. Dicke during the second world war at the MIT Radiation Laboratory then expanded upon by Gehin and Tourneur in 1986[34] into its modern wideband ridge-guide form. ﬁgure.3.1 shows the inherently three dimensional structure of a turnstile junction with a metallic stub within the branching region.

68 Design and Feasibility Study of an Orthomode Transducer for the FAST Experiment 3.1: THE TURNSTILE JUNCTION WAVEGUIDE OMT

Figure 3.1: Turnstile Junction splitting a dually polarised TE11 mode into its constituent parts. The splitting junction is located at the geometric centre of the device in order to maintain the highly symmetric nature of the device. [6]

Within this design, the turnstile junction processes two orthogonal TE11 modes within the input waveguide which are then split equally into two TE10 modes by a concentric matching tuning scattering element located within the common waveguide component; the shape and size of which is critical to the final design. This element has been shown to act as a fork enabling the selection of the working bandwidth by only changing the stub but maintaining the same overall OMT shape. This facilitates the manufacture and design of these OMTs which have the possibility to tune the frequency band over which they operate thus providing an important reconfigurability function. This can be achieved by varying the central tuning stub position, size or shape by screwing it in and out figure.3.2. Signals split by the turnstile junction exit through opposite waveguides 180 degrees out of phase with a good match being achieved by careful determination of the optimum dimensions of the constituent ports and stubs.

Louis Smith 69 3: DETAILED DEVELOPMENT OF A TURNSTILE JUNCTION, APPROPRIATE FOR THE FAST EXPERIMENT

Figure 3.2: Detailed view of a designed scatterer, the base chamfer assures a good electrical continuity with the turnstile base in case of poor ﬂatness in the scatterer base

The input port, taking either the form of a square or circular waveguide, operates between the cut-off frequency of the fundamental modes in the circular/square waveguides (TE11 and TE10 respectively) and the cut-off frequency of the first higher order modes propagating within the structures. The first higher order modes generated within a circular waveguide is the TM11 which enables theoretically up to 70 percent bandwidth. In comparison the rectangular waveguide first higher order TE20 modes enables a bandwidth of 66 percent. Therefore, the maximum theoretical bandwidth achievable within a turnstile junction is just below one octave. This has been supported by EM simulations and mechanical designs, where similar returns were achieved by varying a square or circular input waveguide although a fractional bandwidth for fundamental modes was found to be slightly reduced.

From these simulations using a circular waveguide, the band was shown to extend up to a fractional value of 2.08 (calculated by the division of the fundamental modes i.e. vc(TM11)/vc(TE11)) while in a square waveguide it achieved a fractional signiﬁcance of 2.0 (vc(TM10)/vc(TE10)). It is therefore preferable for the input port of the turnstile junction to process a circular waveguide due to its higher bandwidth potential in respect to the input TE11. However, the rectangular waveguide outputs are TE10 modes with the same bandwidth arguments.

The electrical performance of the standard turnstile junction has been drastically improved by compensating the junction with the use of a tuning stub, regardless of the use of square, pyra-

70 Design and Feasibility Study of an Orthomode Transducer for the FAST Experiment 3.1: THE TURNSTILE JUNCTION WAVEGUIDE OMT midal, multi-stepped cylindrical or other imaginative scattering elements as described in the previous chapter. The use of eﬀective EM computational tools has resulted in the quality of this waveguide component being dramatically improved. As previously aﬃrmed a recent preference for a two, three or four stub waveguide scatter has been established, due to the higher performance in terms of bandwidth in comparison to other more exotic designs.

3.1.2 Compact 90 degree Twist

Within assemblies of rectangular waveguides for microwave systems various components are required for the purpose of joining the waveguides, one being a twist section which itself can be sub-divided into either a ﬁxed or rotary system. Traditionally 90 degree twists, created by a smooth variation of the waveguide walls have been employed for this purpose however these have become less frequently utilized due to their diﬃculty in manufacture and by their inherent exaggerated proportions.

The most frequent in respect to employment is a fixed twist section consisting merely of a twisted singular section of waveguide while a rotary approach has become atypical. As a functional element, twists are used for the provision of progressing a plane polarised wave by rotating an output branch which itself is orientated at a variant angle. The main requirement of a waveguide twist is its ease of design and manufacture, its provision for minimal reflection and its operation within any specified frequency band. A secondary requirement unique for this general purpose is also its compact characteristics so as not to excessively affect the overall size of the entire OMT component.

A stepped twist is formed by a number of adjoining sections of straight rectangular waveguides, a conﬁguration suited for both ﬁxed and rotary twist sections. It comprises two or more adjoining sections of straight rectangular waveguides which are twisted about their common axis at one or more junction faces.

The idea of the step twist in rectangular waveguides was ﬁrst proposed by J.C. Slater during his work at the Radiation Laboratory as a by-product from a vertebra type ﬂexible waveguide;

Louis Smith 71 3: DETAILED DEVELOPMENT OF A TURNSTILE JUNCTION, APPROPRIATE FOR THE FAST EXPERIMENT made of a series of short interlocking sections. It was found that these sections could be twisted at the flange to form a rotary twist joint with the space between faces being equivalent to the vertebra i.e. a quarter wavelength to facilitate the cancellation of their reflection. Commonly a fixed step twist is utilised due to its numerous advantages over a twisted waveguide including but not limited to its shape being of a prescribed dimension without any deforming process enabling a more sophisticated design to be compressed.

Therefore, if the bandwidth within a guide is relatively narrow then a tuned system can be made through the use of quarter-wave spacing between the ﬁxed twist faces, thus the design is termed tuned. This is to distinguish from a wideband design in which such spacing is not eﬀective over the bandwidth that is to say that the frequency bandwidth is about 12 percent, or the guide wavelength bandwidth is about 18 percent. Such spacings are advantageous, however if these respective bandwidths are increased to within a 40 to 80 percent range this system can become unsuitable.[35]

Recently there has been a development away from standard faced twists towards wideband compensation steps. A wideband stepped twist utilizes the principle of enlarging the width of the waveguide to compensate for the constriction at the twisted faces, this usually takes the form of deforming the shape of the waveguide. This compensation is nearly independent of frequency, as is adapted to several twist faces to give a total angle of 90 degrees.

It has been suggested that a multi-section wideband step with a bow-tie shaped cross section represents the best orientation for a waveguide based twist. This bow-tie shape[36] as illustrated in figure 3.3 removes the corners present within the steps which can suffer from high electric field intensity while at the same time providing enough degrees of freedom to achieve excellent performance such as stringent return losses, bandwidth or rotation angle while at all times maintaining an extremely compact profile. It has been shown that a return loss in excess of -30dB is achievable with a bandwidth of approximately 40 percent. This smooth helix bow-tie structure has however proven difficult to manufacture especially in conjunction with certain manufacturing techniques.

72 Design and Feasibility Study of an Orthomode Transducer for the FAST Experiment 3.1: THE TURNSTILE JUNCTION WAVEGUIDE OMT

Figure 3.3: General conﬁguration of the multi-section bow-tie steps twist : A) shows the basic bow-tie section with its parameters; B) a basic rotation with one section; C) the input and output parameters; D) a reference system for the input, output and steps; E) the cross sections for n=3 sections while F) is a 3D view of the N=3 case. [36]

A major wideband alternative to the bow-tie design is that investigated by Rudd [37]. This twist design while also compact whilst maintaining high performance consists of two overlapping rectangular apertures, as shown in ﬁgure 3.4. Although this design is geometrically simple and compact the inner corners of the design makes fabrication of a terahertz scaled version impractical with standard manufacturing methods, it has however been successfully used for applications over the microwave bandwidths, which are under consideration for this design. This conﬁguration represents the most common approach to producing a compact microwave twist.

In order to calculate the cut-off frequencies and eigenfunctions of the TE and TM modes in the stepped corner ridge waveguides a full EM computational modeller is required. This solver allows the basis of the TE and TM modes whose cut-off frequencies do not exceed at a given a s value. This variation of the cut-off frequency parameter λ with the normalised cut size a for

Louis Smith 73 3: DETAILED DEVELOPMENT OF A TURNSTILE JUNCTION, APPROPRIATE FOR THE FAST EXPERIMENT the first two TE modes in a studied waveguide with a various cut-off size h. At s=h, they correspond to the degenerated TE10 and TE01 modes in the a by a square waveguide and their a cut-off parameter λ = 0.5. As s increases, the degenerated TE10 and TE01 modes become coupled and form two combined TE modes with the electrical field distributions parallel or perpendicular to the plane passing through the corner vertices.

Figure 3.4: Rectangular waveguide twist. A) Principle layout; B) Plane junction of the rectangular and double-corner cut square waveguides (with their common aperture being outlines by the dashed lines). [37]

s As expected, the larger a , the greater difference in the cut-off parameters of the studied TE modes. Such modes shall be called the TE1m and TE1e possessing magnetic and electric wall symmetry, respectively. With increasing s, the waveguide enclosure tends to transform into two a a+h (if h = 0 and s = 2 or three (if h > 0 and s = 2 isolated square waveguides. This explains the cut-off dependence for h = 0 within figure.3.3.

3.1.3 H and E plane Bends

An H-plane waveguide bend allows for an electromagnetic guided wave to change its orientation from one direction to the orthogonal one. This enables waveguide circuits on varying planes to be interconnected, thereby permitting compact systems to be constructed. A rectangular waveguide is the most versatile structure of this application due to the ease over which it

74 Design and Feasibility Study of an Orthomode Transducer for the FAST Experiment 3.1: THE TURNSTILE JUNCTION WAVEGUIDE OMT can be used both for a single mode and common port. Signals are thus transmitted through an OMT via an E or H plane bend ﬁgure 3.5.

Figure 3.5: Rectangular waveguide bends. A) Principle H plane bend layout; B) Principle E plane bend layout.

When considering the construction and design of waveguide bend, the shape, size and dielectric material of the constituent waveguide must be taken into consideration due to the fundamental mode presenting a non-zero frequency cut-off below which no energy can be propagated; therefore the bandwidth of a frequency is restricted at the lower end of the cut-off. The composition of this bend must however be consistent throughout its length in order to minimise reflections within the waveguide which would themselves inhibit the flow of energy from one end to the other. Reflections losses can be caused by an abrupt change in the waveguide shape, therefore these bend transitions must satisfy certain conditions.

Waveguides may however be bent in several ways that do not cause significant reflection. The decision on the type of bend is dependent on its orientation when determining which field is being used, however in order for the bend to avoid unwanted reflections the bends must have a radius greater than twice the length of the waveguide wavelength. Neither the E nor the H bends change the normal mode of operation within the waveguide. There are however variations between these two planes, with the E-plane bends exciting the higher order TM11 mode, whereas an H bend produces a TE20 mode. In a standard waveguide, the degenerated modes

TM11 and TE11 have a higher cut-oﬀ frequency than the TE20 modes, with the theoretical bandwidth of an H-plane bend being independent of the waveguide height. The E-plane bend height is linked conversely with the cut-oﬀ frequency due to this variation in its degenerated modes with the frequency given by equation 1.11 where a represents the waveguides width and

Louis Smith 75 3: DETAILED DEVELOPMENT OF A TURNSTILE JUNCTION, APPROPRIATE FOR THE FAST EXPERIMENT b represents its height. The usable bandwidth for both types of bends is smaller than that of an equivalent straight section of waveguide.

f √ a 2 cT E11 = 1 + (3.1) fcT E10 b It can be seen with the aid of equation 3.1 that by using an E-plane bend rather than a waveguide H bend a wider bandwidth with a minimum of complexity can be achieved for balanced phase operation. Additionally, since the cut oﬀ frequency for the TM11 is higher for reduced height waveguide (a=4b), a further improvement in terms of matching has been reported to have been achieved by reducing the waveguide height. The only limitation to this height reduction is in the manufacturability and in the theoretically increase in losses; for this reason the use of reduced height waveguides was investigated for this application to ensure that the design was practical and provided minimal return losses.

3.1.4 Y Junction Tapered Power Combiner

Y junctions are useful as power dividers or combiners in situations in which the more complex four port 180 degree hybrid (magic T) is not required. This device can be used to combine the two signals produced by a turnstile junction that requires also an additional 180 degree phase shift between them. This is illustrated in ﬁgure 3.6 where pol.1 and pol.2 represent the two input ports and pol.3 the output port. This device has been highly investigated by Kerr in [38], whose HFSS simulations indicated that a return loss value above -35dB is readily achievable.

The bend for this device follows the same basic theory as that prescribed in the E-plane bend as in section 1.2 and follows on from the less symmetric T based system which is unsuitable for the blanket use of the FAST OMT due to its geometry being incompatible with the chosen design. In order to reduce the volume and maximise the broadband nature of this junction, the number of tapers within this junction (which are akin to a Chebyshev Transformer) can be altered, as well as their individual lengths, widths and spacings. It has been reported than an increase in the frequency of branches within the body of the combiner (a minimum of two being required

76 Design and Feasibility Study of an Orthomode Transducer for the FAST Experiment 3.1: THE TURNSTILE JUNCTION WAVEGUIDE OMT

Figure 3.6: Standardised simulated layout of a Y junction combining section as shown this consists if two incoming polarisations processing a relative phase shift of 180 degrees which are then combined at the base of the system to form the output port. It can be seen that this component processes a high level of symmetry [38]

to produce a suitable performance) resulted in the bandwidth of the device being broadened. This increase is delivered at the cost of greater branch lengths and volume measurements. A compromise has therefore been calculated resulting in an optimum number of branches having been found to be four, beyond which the performance of the device is improved at a dispropor- tionate cost in terms of mechanical fabrications and size. It was also found that a symmetric combiner provides the best overall performance.

A lossless reciprocal three port device cannot present three matched ports simultaneously. The coupling between port one and port two or three in this limit is 3dB, as such the resultant isolation from ports two to three is 6dB. It is also required that the frequency sensitivity of a component is minimized to the extent that the total stored energy is the same for all eigen- soultions. This would suggest the following design rules are desirable to achieve broadband response:

Louis Smith 77 3: DETAILED DEVELOPMENT OF A TURNSTILE JUNCTION, APPROPRIATE FOR THE FAST EXPERIMENT

1. The dominant mode symmetry should be preserved by junction geometry.

2. The guide heights of the three ports are linked by the power division ratio, R = b1 b2 where all variables can be seen in ﬁgure.3.6.

3. A desire to minimise the frequency dependence of the junction discontinuities so as

such b0 = b1 + b2.

78 Design and Feasibility Study of an Orthomode Transducer for the FAST Experiment Part II

Design and Results

Louis Smith 79 80 Design and Feasibility Study of an Orthomode Transducer for the FAST Experiment 4

Simulated Disign and Results

4.1 Overview

In this final part of the report, a design and the simulated results of a broadband slenderised OMT as a means of producing a feasibility study for our chosen design shall be presented. This is composed of a waveguide turnstile junction with a cylindrical dual stub and compact 90 degree twist with a thin combiner/divider. This class three waveguide OMT is suitable for realising a thin and simple structure with excellent return losses over a wide bandwidth. In particular, a circular to square waveguide transition located at the summit of the turnstile junction is effectively used to obtain a good reflection characteristic, this structure contributes to low-profile of the system.

The combiner/divider used in this structure was ﬁrst reported by A. Yoji et al. 2003,[24] composed of an E-plane stepped impedance transformer with an H-plane bend, contributing to the low height almost planar nature of this OMT design.

It was decided at the beginning of the design phase of this thesis that is OMT would be modelled using a higher frequency band (with the same percentage bandwidth) with an eye towards the possibility of building a prototype to be tested in our RF labs, equipped with a W-Band VNA. The chosen frequency range is between 75-115GHz, a range with the same percentage bandwidth as those speciﬁed with a model to actual scaling factor of 1:78.95. All values speciﬁed

Louis Smith 81 4: SIMULATED DISIGN AND RESULTS within the ﬁgures presented within this chapter can be found in the table found in appendix.1, thus enabling any component to be reproducible if necessitated. All components presented within this chapter were designed used Ansofts HFSS 13 and optimised in order to minimise return losses, in other words provide the maximum match between the various waveguide faces.

4.2 H-Plane Bend with E-Plane Stepped Impedance Transformer

The two branches of the FAST turnstile junctions waveguide configuration are interconnected by H plane bends first proposed as previously stated by A. Yoji[24] which themselves were augmented from the basic theory stated in the previous chapter. These combiners are designed to enable a cross-over of turnstile junction branches as such enabling the overall OMT design to operate with a class three approach while maintaining a flat structure. The use of H-plane bends combined with an E-plane stepped impedance transformer, enables the waveguide structure to be reduced to a compact configuration while still maintaining high performance.

Figure 4.1: Design concept of E-plane transformer with bend [24]

As shown in ﬁgure 4.1, the dimensions of the adopted E-plane impedance transformer combined with an H-plane bend being derived from the designed straight stepped impedance waveguide transformer with an angle of segmented bend being given by equation 4.1.

L a θ = − (4.1) R 2

82 Design and Feasibility Study of an Orthomode Transducer for the FAST Experiment 4.2: H-PLANE BEND WITH E-PLANE STEPPED IMPEDANCE TRANSFORMER

This design was then produced and optimised using the commercial finite element analysis program HFSS 13 with the resultant design being shown in figure 4.2. The various stepped height parameters defined as the h variants in figure 4.1 were determined through the use of an optimisation program inbuilt into Ansofts HFSS package which enabled a value to be formulated within a pre determined range set by the user.

Figure 4.2: Simulated 90 degree H-bend with an E-plane transition, as can be seen in A) and B) the designed bend consists of five sections each of varying heights however processing the same angle of transition from one to another (30 degrees). H1 and H5 represent the initial height of a standard waveguide for this frequency band of 2.54mm while H5 has a relative height of 0.45H1 or 1.245mm, thus enabling the two OMT branches to pass over one another. As seen in section C) the wave passes consistently through the bend without significant reflections

Figure.4.2 indicates the final designed H-bend design as seen on by the CAD program HFSS, this device those similar to that first proposed by A.Yoji, however as can be seen in figure 4.3 significant improvements have been made in the defined return loss characteristics in comparison to those first proposed in the 2005 paper stemming from numerous varying step ratio

Louis Smith 83 4: SIMULATED DISIGN AND RESULTS experiments having been conducted to ascertain the optimum orientation for this device. It was found that a constant thirty degree variant between the three angled sub-sections resulted in the most advantageous conclusions, it was also decided that in order for the two branches to overlap with a suitable gap, a height reduction was set to 40 percent of the initial: from a full height of (1.3mm) to reduced height (0.637mm).

As can be seen in ﬁgure 4.3 this H-plane bend represents a high-quality solution for a full to reduced height H-bend. The return loss is below -25dB over a 80 percent bandwidth. The average return is -32dB. Better performance is achieved in the middle of the band whereas values up to -18dB are achieved at the edge of the band.

84 Design and Feasibility Study of an Orthomode Transducer for the FAST Experiment 4.2: H-PLANE BEND WITH E-PLANE STEPPED IMPEDANCE TRANSFORMER Figure 4.3: Return loss vs frequency graphis for -32dB, the as reduced shown height in H-bend black, transition as as shown shown in the black; average well return below loss the minimum value for deﬁned speciﬁcation this of component -25dB

Louis Smith 85 4: SIMULATED DISIGN AND RESULTS

4.3 Turnstile Junction

In the design of our OMT I have adopted the turnstile junction design as discussed in the previous chapters. A standard solution was used as a starting point (after experimentation with variations in the branch rectangular waveguide diameters failed to yield any worthwhile results) consequently few alterations were applied in order to get the required high performance. The major alteration which as applied was the re-optimisation of the tuning stub, speciﬁcally the number of steps and the related parameters. This design is shown in ﬁgure 4.4 with the tuning stub being illustrated in part C.

Figure 4.4: FAST OMT Turnstile Junction. A) The dimensions of the output waveguides have the standard values whereas the R3 parameter has been optimised to get the correct cut- oﬀ frequency for the fundamental TE11 mode. B) Electromagnetic simulation showing the incoming wave propagating through the turnstile junction: a 45 degrees mode is split into its constituent components. C) Turnstile junctions scatterer made with two cylindrical stubs. D) Field distribution of turnstile junction cross section

It was found that the FAST OMT turnstile junction shown in ﬁgure 4.4.A provides a suitably

86 Design and Feasibility Study of an Orthomode Transducer for the FAST Experiment 4.3: TURNSTILE JUNCTION low return loss performance across the frequency band, as illustrated in ﬁgure 4.5. As shown, the dimensions of the four output ports are standardised and equal in order to maintain the symmetrical nature of the device, thus inducing the highest possible bandwidth. Further bandwidth enhancements are achieved by use of the scattering stub in the geometric centre of the devices bottom wall. It has been foreseen that, for mechanical simplicity, the stub should be manufactured independently from the body of the device and then screwed into place once the entire component is completed. This has been suggested previously by Cano in 2009 where no measurable degradation was recorded if a small amount of conductive epoxy or silver paint was applied to the base of the scatterer to improve the electrical contact in the device. A base chamfer must also be applied in order to apply the required M4 thread to accommodate the screw and the stub.

As illustrate in figure 4.4.B the common circular input is handles the orthogonal dual-polarized wave. The vertically polarized wave is divided between between port one and port three, and isolated from port two and port four. On the other hand, the horizontal polarized wave is divided between port two and port four and isolated from port one and port three. figure 4.4.D shows the propagated electric fields within the turnstile junction. For each of the polarized waves, the turnstile junction can be represented as approximately two symmetrical E-plane waves propagating through two E-plane bends. A good match can therefore be achieved if the turnstile stub figure 4.4.C is optimised in order to ensure that the reflection characteristics are matched. Figure 4.5 shows the simulated return loss characteristics of the turnstile junction across the scaled frequency band. These results represent a high-quality solution for the need of splitting the incoming dually polarised waves into their constituent parts in a passive manner. This design has a return loss much lower than -25dB, required by the global OMT components specifications of table 1. It was calculated that the average return losses for this component was 41.5dB with the performance improving significantly across the central section of this band with the peripherals representing the worst attainment figures (-29dB at its highest point) which is still well below the threshold point.

Louis Smith 87 4: SIMULATED DISIGN AND RESULTS Figure 4.5: Simulated return loss characteristics forthat the the independent average Turnstile return Junction loss across for the this chosen component scaled was frequency -41dB. band, it can be seen

88 Design and Feasibility Study of an Orthomode Transducer for the FAST Experiment 4.4: COMPACT NINETY DEGREE TWIST

4.4 Compact Ninety Degree Twist

A compact 90 degree twist made by rotating a waveguide section along its longitudinal axis was required in order to limit the overall OMT size. As detailed in the previous sections there are numerous methods by which this can be achieved, however, it was decided that the wideband

fixed step configuration which could rotate the incoming polarised TE10 wave as suggested by Rudd would result in the most satisfactory choice result (figure 4.6).

Figure 4.6: Simulated Compact 90 degree twist.

This design was made through the realisation that the use of this method would result in the best overall design due to its relative ease of manufacture and design in comparison to a bow- tie fixed twisted waveguide component. While being more compact than a smoothly slowly tapered configuration. This compact twist also has the relative advantage of processing the ability to be scalable over numerous frequency bands achieving return loss and frequency band attributes figure 4.7 suitable for the umbrella purpose of the FAST OMT.

As seen in ﬁgure 4.6 this ﬁnal simulated design resulted in a compact (approximately 2.5mm

Louis Smith 89 4: SIMULATED DISIGN AND RESULTS along the longitudinal axis) arrangement which can be easily manufactured and is suitable for incorporation. Figure 4.6a illustrates the fact this design is composed of two identical waveguide lines of standardised proportions one of which has been rotated by a ninety degree angle along the x-axis separated by an intersecting splitting junction composed of a double rectangular overlapping elements which when combined have a variable length b in both its vertical and horizontal direction. Symmetry is maximised as to limit possible discontinuities, thus the bandwidth over which this component operates, once the suitable cut-oﬀ calculations have been considered is suitably high to enable it to be appropriate for its purpose.

The simulated return loss characteristics for the compact 90 degree twist across the scaled frequency band can be seen in figure 4.7. This design represents an arrangement below the cut-off threshold of -25dB required of it by the overall OMT. It was calculated that the average return losses for this component was -35.2dB with the performance improving significantly across the central section of this band whilst the peripherals represented worst attainment figures (-24dB at its highest point). The components performance is slightly below that registered in some lit- eral sources due to certain boundaries applied upon it in order to maintain the compact nature of the device as a whole.

90 Design and Feasibility Study of an Orthomode Transducer for the FAST Experiment 4.4: COMPACT NINETY DEGREE TWIST Figure 4.7: Simulated return losscalculated characteristics average return for loss the for this separate device compact(-24dB was at 90 -35dB its with highest degree the point) twist scale across operating with the a chosen lower performance scaled within frequency the band. extremities of the The band

Louis Smith 91 4: SIMULATED DISIGN AND RESULTS

4.5 Y Junction Tapered Power Combiner

For the purpose of combining the two constituent input waves, each of which experiencing a relative phase shift of 180 degrees into a singular output port a Y-junction tapered power combiner was elected; similar to those by Kerr in 2001 and detaled in the preceding literature. As previously stated in order to reduce the length and amplify the broadband nature of this device a tapering system was employed in which both the length and width of each individual section was determined with the preliminary values chosen in accordance with binomial rules then optimised using HFSS. This optimisation was also conducted in respect to the other variables as illustrated in ﬁgure 4.8, with the matching resulting in said design.

It was found that an atypical arrangement of four independent tappers resulted in a suitable compromise between a satisfactory selection of measurements in respect to the overall FAST requirements whilst still maintaining its manufacturable which could be enhanced by a reduction in said graduation, however at an unsuitable cost to performance.

Figure 4.8: Simulated Y junctions. Sections A) and B) in this figure comprises the final HFSS design as described in the previous literature as seen this processes similarities to those first proposed by Kerr with the input and output waveguides having been given the standardised universal dimensions present throughout the entire design.

92 Design and Feasibility Study of an Orthomode Transducer for the FAST Experiment 4.5: Y JUNCTION TAPERED POWER COMBINER

As can be seen in figure 4.8 this structure was kept symmetrical along both the z and y planes resulting in the broadest bandwidth possible while still maintaining a good return loss. In the Kerr orientation, the two incoming full-height rectangular waveguide meet in square waveguide sections which are then transformed back into rectangular waveguides. The resultant combiner design is thus relatively long (approximately 8mm within the W-band). It was seen as vital to maintain a minimum length for this section of the device as its presence in the final OMT design represents a significant limitation in the final compactness of the design therefore a reduction of 25 percent was applied while some of the more mechanically challenging smooth bends were replaced by a reductive step based system.

This design produced simulated return losses as displayed in ﬁgure 4.9 across the scaled frequency band, it can be seen that the average return losses for this component was -34dB with a range of between -30dB at the fringes to -45dB across the central region of the band. These simulated measurements results in the component being deemed as suitable for the purpose for which it was design as its characteristics were within the speciﬁcations for the FAST component.

Louis Smith 93 4: SIMULATED DISIGN AND RESULTS Figure 4.9: Simulated return loss characteristics forvalue the of personalised -34dB. Y junction across the chosen scaled frequency band with an average loss

94 Design and Feasibility Study of an Orthomode Transducer for the FAST Experiment 4.6: SIMULATED FAST OMT DESIGN

4.6 Simulated FAST OMT Design

Once the various constituent sections of the OMT were identified and simulated to a suitably high standard so as not to representing a potentially limiting factor. Each of these subcompo- nents were then united to form a global model following a predetermined blueprint. Interac- tions between the sub-components, i.e. mismatches and phase differences, were automatically considered and rectified within a first order approximation by human intervention then fine- tuned with the use of an optimisation function. An electrical conductivity of σ = 1.5x107 mho/m was applied to compensate for surface roughness and discontinuities of the assumed gold-plated external walls of the waveguides. This value was established from comparisons taken from electroformed components to measurements of other WR10 systems, the scaled wave on which this L-band component is based[6]. It was foreseen that this method shall be used as the initial feasibility models method of production due to its superior results in at the chosen frequency.

The structure of this OMT design could have taken numerous forms, with the main influencing factors being the decision to produce a waveguide based transducer, with a high symmetry and physically compact design being made paramount it was also decided that for ease of manufacturability and reproduction a closely planar approach was advantageous. This resultant OMT design can be seen in figure 4.10 where the simulated H bend was used as a means of connecting the outgoing turnstile junction branches with combining junction via the use of a reduced height waveguide. This design facilitated the two branches to overlap one other within the same general plain by means of flipping the orientation of the H bends in the z-direction thus reducing the size of the overall design in comparison to similar formations. For this reason an H-plane bend was seen as necessary as it alone facilitates this compact design to be achieved in this manner.

This system of stepped impedance H bends has been applied previously in other waveguide based OMTs were a component of high performance was achieved at a reduced size. The unique nature of this device however lies with the use of a compact 90 degree twist, enabling the OMT to operate over a generalised plane, thus facilitating a reduction in complexity of

Louis Smith 95 4: SIMULATED DISIGN AND RESULTS design. This component can therefore be produced with a reduced complexity while improving the compactness of the system in comparison to these previous designs as a reduction in dead space is facilitated by the removal of the need to elongate the system along its zenith to facilitate the inclusion of the Y junction, this ﬁnal design can be seen in ﬁgure 4.10.

Figure 4.10: Planar waveguide based OMT for the FAST experiment. A), B), C) and D) Waveguide based OMT from top, bottom and sides as shown this system benefits from the use of the turnstile junction based in the centre of the symmetric system with the tuning stub being located at the geometric centre (as seen in figure B) of the transducer. This system has a total volume of approximately 212mm3 and measures a total length of 18mm from end to end with the Y junction representing a considerable proportion of this length. E) Shows the wave being passed through the orthomode transducer as seen the incoming wave passes through the component with very few simulated discontinuities and reflections.

It was seen that the configuration illustrated in figure 4.10 resulting in a design which met all the specified requirements whilst maintaining a compressed fabrication measuring just 212mm3 in volume, 972mm3 in displacement or 6λ at its longest point. This displacement measurement

96 Design and Feasibility Study of an Orthomode Transducer for the FAST Experiment 4.6: SIMULATED FAST OMT DESIGN represents one of the most compact in its class facilitated through its unique semi-planar shape, thus the FAST OMT representing suﬃcient savings in respect to space if an array of devices were to be necessitated at some future point. As previously stated this transducer will make use of a tunable screw in stub as previously described.

Figure 4.11: FAST planar OMT systematic diagram. As illustrated this component is com- prised of the numerous sub-components which were described and simulated in the previous sections of this report. This design resulted in the H-plane bend being rotated around 180 degrees in the z-plane enabling the two waveguides to overlap one another. The wave is then rotated again by the same bend rotated by a 90 degree transition and combined by the Y junction. All four H-bends and 90 degree junctions as well as the two Y junctions were matched to ensure that their variables are standardised to ensure ease of manufacture.

As described and illustrated in ﬁgure 4.11 the FAST OMT was simulated using the researched and individually designed components described in the previous sections of this thesis. It can be seen that this design resulted in the H-plane bend being rotated 180 degrees in the z-plane enabling the two waveguides to overlap one another these waves are then transformed by a

Louis Smith 97 4: SIMULATED DISIGN AND RESULTS mirror image of this initial bend, then transformed by a 90 degree twist and combined using a Y junction. All components were maintained within a standardised set of parameters in order to ensure ease of manufacture. This configuration yielded a sufficiently high set of results as to fulfil the predetermined specifications see figure 4.12, figure 4.13 and figure 4.14.

Figure.4.12 and figure.4.13 characterize the return loss and isolation measurements across the chosen scaled frequency band as seen both these characteristics; return loss averaged at -28dB across the band (attaining results beyond the stipulated limits across 73 percent of the band) and isolation averaged at -49dB (resulting in a performance beyond the stipulated limits across atleast 93 percent of the band) represent suitably high attainment figures as to fulfil its initial purpose of separating the dually polarising incoming wave into its constituent parts by means of a passive device. It can also be seen in figure.4.14, that the cross polarisation measurement was well below the significance threshold stipulated with an average value of -55dB proving that this design has a suitably high polarisation purity, an important feature in defining the quality of a OMTs performance.

It can therefore be seen that the simulated Orthomode transducer based on this semi-planar design is potentially suitable for its initial perceived purpose of being placed within FAST. It must also be noted that the simulated results across the chosen frequency band represent, an on the whole, a relatively stable and unvarying polarisation purity and loss value, therefore, providing any future measurements taken using this component a measure of stability. Without the presence of large sharp variations within the band.

98 Design and Feasibility Study of an Orthomode Transducer for the FAST Experiment 4.6: SIMULATED FAST OMT DESIGN . As seen the average return losses for this device are -28dB below those 11 Figure 4.12: FAST OMT Simulated return lossesrequired for of the this ﬁrst device port within S the brief while operating below or at this minimum for over 73 percent of the band.

Louis Smith 99 4: SIMULATED DISIGN AND RESULTS . As can be seen the average isolated for this device was 21 S measured to be below the operational -35dB precondition whiletendency behaving for below or this at device this lays signiﬁcance at across a 93 value percent of of -49dB. the band. The central Figure 4.13: FAST OMT Simulated Isolation measurements for the second ports

100 Design and Feasibility Study of an Orthomode Transducer for the FAST Experiment 4.6: SIMULATED FAST OMT DESIGN . As can be seen the average cross polarisation 21 S Figure 4.14: FAST OMT Simulated Cross Polarisationfor measurements this for device the was measured second to ports be belowbe the seen operational this -20dB this precondition device with has an a suitably average value high being polarisation recorded purity. at -55.6dB, therefore it can

Louis Smith 101 4: SIMULATED DISIGN AND RESULTS

102 Design and Feasibility Study of an Orthomode Transducer for the FAST Experiment 5

Conclusions and Future Work

5.1 Conclusion

This report has demonstrated the feasibility, design and simulation of a waveguide based orthomode transducer using a compact twist 90 degree module, turnstile junction splitter, H-plane bend and Y junction power combiner. Various approaches were outlined as means of solving the FAST requirement speciﬁcation, however a ﬁnal design based on a class three waveguide turnstile junction approach was chosen due to its broadband high performance nature stemming from its highly symmetric nature.

This ﬁnal design is compact and is compatible with a circular input required to operate over the 0.95−1.45GHz L-band however this latter simulated design was a scaled version operating at a chosen higher frequency of 75−115GHz due to its ability to be assessed using the Manch- ester Universities W-band VNA. This therefore enables the design to be manufactured using electroforming techniques and assessed in its scaled form expanding the potential scope of this feasibility report while instantly indicating the natural progression which the author feels should be taken during the future work conducted towards proving the feasibility of this design.

The finally simulated scaled OMT has been extensively optimised to operate over a 35 percent bandwidth centred at 90GHz, while maintaining an average return loss and isolation figure in excess of those specified as the threshold values of -25dB and -35dB respectively. This

Louis Smith 103 5: CONCLUSIONS AND FUTURE WORK waveguide based OMT has shown excellent polarization separation and purity with a calculated average isolation in excess of -49dB across most of the desired frequency band ﬁgure 4.13. Similarly it was found that this design provided above expectation cross polarization 4.14(averaged at -55dB) and return losses 4.12(averaged at -28dB) providing competitive or superior results than most existing standard waveguide based alternatives especially which the compact planar nature is taken into account resulting in an extremely attractive compact construct. The results of this design have been summarised in table 4.1.

Table 5.1: OMT Requirements vs simulated results according to the FAST documentation

Due to timeline limitations and some delays experienced during the completion of simulations conducted as well as financial limitations, an initial suggestion of partial construction of the device was shelved yet based on previous experience and research conducted during the course of this report I would expect a close agreement between the measured and HFSS simulated results. It has also been suggested that the project would benefit from the production of a secondary tuning stub being initially simulated and finally manufactured in order to demonstrate the highly re-usable nature of this device.

It is the belief of the author that with further research this design has the potential to be further optimised in respect to its magnitude especially if the dimensions of the Y junction are to be further investigated in order to minimise its size while still maintaining the overall OMTs performance characteristics.

104 Design and Feasibility Study of an Orthomode Transducer for the FAST Experiment Part III

Appendices

Louis Smith 105 106 Design and Feasibility Study of an Orthomode Transducer for the FAST Experiment

References

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Appendix.1.

Table A.1 FAST OMT Variables.

Variable Value (mm) B 1.303 A 2.54 Yh1 1.122 Yh2 1.009 Yh3 1.023 Yh4 0.875 Yw1 2.608 Yw2 2.245 Yw3 1.738 Yw4 1.406 Yw5 1.305 L 0.751 H 1.031 K 0.998 F 0.299 G 0.559 S 0.985 R3 0.889 R2 0.450 R1 1.315 T1 0.232 T2 0.491 H1 1.303 H2 1.268 H3 1.098 H4 0.954 H5 0.652