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Investigation of Advanced Butler Matrices with Integrated Filter Functions

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Investigation of Advanced Butler Matrices with Integrated Filter Functions INVESTIGATION OF ADVANCED BUTLER MATRICES WITH INTEGRATED FILTER FUNCTIONS by Vittorio Tornielli di Crestvolant A thesis submitted to the University of Birmingham for the degree of Doctor of Philosophy School of Electronic, Electrical and Systems Engineering College of Engineering and Physical Sciences University of Birmingham July 2015 University of Birmingham Research Archive e-theses repository This unpublished thesis/dissertation is copyright of the author and/or third parties. The intellectual property rights of the author or third parties in respect of this work are as defined by The Copyright Designs and Patents Act 1988 or as modified by any successor legislation. Any use made of information contained in this thesis/dissertation must be in accordance with that legislation and must be properly acknowledged. Further distribution or reproduction in any format is prohibited without the permission of the copyright holder. Vittorio Tornielli di Crestvolant (ID 1188203): Investigation of advanced Butler matrices with integrated filter functions, School of Electronic, Electrical and Systems Engineering, University of Birmingham, July 2015. Plagiarism checked on 14th July 2015, Turnitin ID 46086594. Submitted on 15th July 2015. Viva Voce examination held on 17th September 2015 in Birmingham, UK; panel composed by Dr P. Tricoli (chairperson), Dr R. Cameron (external examiner) and Dr F. Huang (internal examiner). Revised on 6th October 2015; date of current version 24th October 2015. Printed using LATEX 2"with ClassicThesis and ArsClassica, mathematical fonts stand- ard of the . AMS COPYRIGHT © Vittorio Tornielli di Crestvolant July 2015 The copyright in this document is vested in University of Birmingham. This document may only be reproduced in whole or in part, or stored in a retrieval sys- tem, or transmitted in any form, or by any means electronic, mechanical, photocopy- ing or otherwise, either with the prior permission of Vittorio Tornielli di Crestvolant or in accordance with the terms of Partnership Agreement No. 4000107492/13/NL/GLC/fe. No other copyright statement will be accepted. ABSTRACT This study presents a novel synthesis technique for Butler matrices that include fil- ter transfer functions through a circuit based only on resonators. The Butler matrix is the fundamental building block to split and recombine the signals in Multi-port Power Amplifiers, where multiple inputs are delivered to a bank of amplifiers shar- ing them, and later recombined through an output network. However, to suppress spurious frequencies generated by the amplifiers or to provide near-band rejection in order not to interfere with other transmission/receiving bands, separate filtering is often required. Here, the traditional properties of the Butler matrix are included together with filtering selectivity into one single device based only on coupled res- onators. An analytical synthesis procedure of the coupling matrix is presented here for the first time. The proposed solution has shown significant advantages in terms of size reduction compared to the traditional baseline consisting of a Butler matrix plus a bank of band-pass filters. Based on the technique proposed, three prototypes are designed and manufactured: a 180° hybrid coupler based on resonators and two versions of a 4 4 Butler matrix with filtering, built with additive manufacturing and × with milling. Experimental measurements are in good agreement with simulations and theoretical expectations. «il bel paese ch’Appennin parte, e ’l mar circonda et l’Alpe.» Petrarca, Canzoniere, CXLVI, vv. 13-14 ACKNOWLEDGEMENTS This work is the outcome of a 3 years PhD programme in partnership between the University of Birmingham, the European Space Agency (ESA) and Airbus Defence and Space under the Networking Partnering Initiative No. 4000107492/13/NL/GLC/fe. In this context, the work has been carried out at the University of Birmingham, UK, at the European Space research and Technology Centre (ESTEC) in Noordwijk, The Netherlands, and at the Airbus Defence and Space facilities of Stevenage, UK. The Author wishes to thank Prof. Michael Lancaster for the continuous support over the whole period of the study. A special and grateful thank is for Mr. Petronilo Martin Iglesias who firmly and tirelessly gave support during the period spent at ESTEC, for his availability and openness in discussing problems, other than for always find- ing opportunities to make this work visible and acknowledged among colleagues. A thank goes to Mr. Paul Booth, who was the referee during the intern-ship at Airbus Defence and Space, for his comments and suggestions. The Author also thanks Dr. Piero Angeletti, head of the ESA RF Equipment and Technology section, for his feed- backs and interest in this work, to Hanno Ertel and Andre Zandvliet of the ESTEC workshop for planning, designing, and producing the physical devices with milling. Also, a thank goes to the friends and people met during all these years: in particular to the YGT community of ESTEC and to all other friends with whom was a pleasure to work with and to share time and experiences together. A special thought and thank also goes to my family for the continuous support and to those people who always have been close, providing invaluable help and support throughout all this experience. Birmingham, UK, July 2015 CONTENTS 1 1 2 introduction 7 2.1 The Butler matrix and its developments 7 background 2.2 Multi-port power amplifier 9 2.3 Coupled resonators based networks 13 2.3.1 Main-line band-pass filters 13 2.3.2 Coupling matrix of 2-port circuits 26 2.3.3 Multi-port circuits 34 2.4 Limitations of general synthesis techniques 35 2.5 Resonator based Butler matrix 40 2.6 Physical realisation of coupled resonator networks 43 2.6.1 Lumped element synthesis 43 2.6.2 Extraction of the coupling coefficient 47 2.6.3 Extraction of the external quality factor 50 2.7 Power handling capability 57 3 62 3.1 Basic concepts of the 90° hybrids 62 quadrature hybrids based on resonators 3.2 The equivalence method 72 3.3 Extension to multiple branches 79 3.4 Polynomials based synthesis 85 3.5 Analysis of 4-resonator hybrid 93 3.5.1 Analytical analysis 93 vii 3.5.2 Topological approach 99 contents viii 3.6 Implementation of 8-resonator hybrid 102 3.7 Butler matrix based on quadrature resonant hybrids 108 3.8 Final considerations 112 4 115 4.1 Electrical behaviour of the rat-race coupler 115 butler matrix with inherent filter functions 4.2 180° hybrid with filtering 118 4.3 Virtual open circuit 120 4.4 Analytical synthesis of Butler matrix formed by 180° hybrids 126 4.4.1 Transfer function requirements 127 4.4.2 Set of polynomials 128 4.4.3 Topology 131 4.4.4 Formulation of the coupling matrix 134 4.5 Example of 4 4 Butler matrix with filtering 136 × 4.6 Extension of the filtering characteristic 139 4.6.1 Sub-networks 140 4.6.2 Example with symmetric response 142 4.6.3 Example with transmission zeros 144 4.7 Multi-port excitation of N N Butler matrix 149 × 5 151 5.1 Electromagnetic model 151 prototypes and experimental results 5.1.1 Selection of the type of resonator 151 5.1.2 Negative coupling introduced by planar H-plane cavity 152 5.1.3 Design 153 5.2 Hybrid 180° with filtering 155 5.2.1 Physical implementation 155 5.2.2 Measurements 158 5.2.3 Multipactor analysis 162 contents ix 5.3 Butler matrix 4 4 based on resonators 170 × 5.3.1 Milling model 174 5.3.2 Additive manufacturing model 181 5.4 Size reduction 189 6 193 a conclusions 197 a.1 General analysis 198 synthesis of branch-guide couplers a.2 The approximation problem 211 a.2.1 Butterworth specification 213 a.2.2 Tchebycheff specification 214 a.3 Synthesis procedure 217 a.4 Examples 220 a.4.1 Three branches Butterworth asymmetric coupler 220 a.4.2 Four branches 3 dB Butterworth symmetric coupler 226 a.4.3 Five branches 3 dB Tchebycheff symmetric coupler 232 b 241 b.1 Synthesis procedure 242 synthesis of multi-port resonant networks b.1.1 Characterisation of the circuit 242 b.1.2 Coupling matrix formulation 245 b.1.3 Scattering parameters 249 b.1.4 Analytical synthesis of multi-port circuits 252 b.1.5 Transversal networks 259 b.1.6 Matrix transformations 264 b.1.7 Low-pass to band-pass transformation 267 b.1.8 Steps of the synthesis 268 b.2 Cauchy Method 270 b.3 Examples 275 contents x b.3.1 Fully canonical filter 275 b.3.2 Diplexer formed by two box-sections 288 b.4 Conclusive notes 300 c 302 list of publications303 bibliography LISTOFFIGURES Figure 1.1 Example of Ka-band multi-beam satellite system 2 Figure 1.2 Conventional payload amplification architecture 3 Figure 1.3 Non uniform allocation of users and power 4 Figure 2.1 Schematic of 4 4 Butler matrix 7 × Figure 2.2 Butler matrix used to shape signal beams 8 Figure 2.3 Multi-port Power Amplifier 10 Figure 2.4 Low-pass filter prototype 13 Figure 2.5 Prototype low-pass filter characteristics 14 Figure 2.6 Lumped elements band-pass filter 17 Figure 2.7 Ideal immittance inverters. 19 Figure 2.8 Practical realisation of inverters 20 Figure 2.9 Filter transformation with ideal immittance inverters 22 Figure 2.10 Equivalence with filters with inverters included 23 Figure 2.11 Band-pass filter with distributed resonators 26 Figure 2.12 Two ports inter-coupled resonant circuit 28 Figure 2.13 Example of generalised Tchebycheff filter 30 Figure 2.14 Coupling matrix defined by blocks 34 Figure 2.15 Transversal network of a 3-port circuit with 4 resonators 37 Figure 2.16 General multi-port all resonators network 38 Figure 2.17 Proposed solution of MPA including filtering 41 Figure 2.18 Electric and magnetic
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