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Synthesis of Filters for Digital Wireless Communications

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Synthesis of Filters for Digital Wireless Communications Synthesis of Filters for Digital Wireless Communications Evaristo Musonda Submitted in accordance with the requirements for the degree of Doctor of Philosophy The University of Leeds Institute of Microwave and Photonics School of Electronic and Electrical Engineering December, 2015 i The candidate confirms that the work submitted is his own, except where work which has formed part of jointly-authored publications has been included. The contribution of the candidate and the other authors to this work has been explicitly indicated below. The candidate confirms that appropriate credit has been given within the report where reference has been made to the work of others. Chapter 2 to Chapter 6 are partly based on the following two papers: Musonda, E. and Hunter, I.C., Synthesis of general Chebyshev characteristic function for dual (single) bandpass filters. In Microwave Symposium (IMS), 2015 IEEE MTT-S International. 2015. Snyder, R.V., et al., Present and Future Trends in Filters and Multiplexers. Microwave Theory and Techniques, IEEE Transactions on, 2015. 63(10): p. 3324- 3360 E. Musonda developed the synthesis technique and wrote the first paper and section IV of the second invited paper. Professor Ian Hunter provided useful editorial comments, suggestions and corrections to the work. Chapter 3 is based on the following two papers: Musonda, E. and Hunter I.C., Design of generalised Chebyshev lowpass filters using coupled line/stub sections. In Microwave Symposium (IMS), 2015 IEEE MTT- S International. 2015. Musonda, E. and I.C. Hunter, Exact Design of a New Class of Generalised Chebyshev Low-Pass Filters Using Coupled Line/Stub Sections. Microwave Theory and Techniques, IEEE Transactions on, 2015. PP(99): p. 1-11. Supervisor (Professor Ian Hunter) proposed the initial physical realisation of a basic section and reviewed the final papers. E. Musonda developed the initial idea, developed the complete synthesis technique including the required transfer functions and circuit transformations, and wrote the papers. Chapter 4 is based on the following paper: ii Musonda, E. and Hunter I.C., Microwave Bandpass Filters Using Re-Entrant Resonators. Microwave Theory and Techniques, IEEE Transactions on, 2015. 63(3): p. 954-964. Supervisor (Professor Ian Hunter) proposed the idea of integrated resonance and transmission zero using the re-entrant transmission line and reviewed the final paper. E. Musonda developed the equivalent circuits, synthesis and design theory and wrote the paper. This copy has been supplied on the understanding that it is copyright material and that no quotation from the report may be published without proper acknowledgement. © 2015 The University of Leeds and Evaristo Musonda iii Acknowledgements My utmost gratitude goes to Professor Ian Hunter, my supervisor and research chair of Royal Academy of Engineering/Radio Design Ltd - Microwave Signal Processing, for his exemplary role and encouragement during my PhD research work. I am grateful to Radio Design Limited for their technical support toward our research group at the University of Leeds. I am grateful to various individual supports from within School of Electronic and Electrical at Leeds University and my colleagues. I also incessantly thank my PhD sponsors namely the University of Leeds under the oversight of Professor Ian Hunter, the Beit Trust for part funding towards my PhD and RS Microwave for providing equipment funding. Lastly, I thank my family, my wife Caroline, my son Crescens, and daughters Whitney and Charlotte, for their endurance, emotional support and comfort rendered to me during the course of my research. I am forever indebted to my sister Mable, who has been like my mother and always been there for me whenever I needed someone to lean on. iv Abstract Firstly, a new synthesis method for the generation of the generalized Chebyshev characteristic polynomials has been presented. The general characteristic function is generated by a linear combination of Chebyshev basis characteristic functions. The basis functions for different filtering functions may easily be determined based on the number and position of reflection and transmission zeros. These basis functions enable direct synthesis of both lumped and distributed filter networks. Different filter functions including but not limited to low-pass, bandpass and dual bandpass filters, have been synthesised to demonstrate the general application of the synthesis method. Secondly, a new method for the design of a new class of distributed low-pass filter has been presented that enables exact realisation of the series short circuited transmission lines which are normally approximated via unit elements in other filter realisations. The filters are based on parallel coupled high impedance transmission lines which are terminated at one end in open-circuited stubs. The approach enables realisation of both finite and quarter-wave frequency transmission zeros hence giving improved stopband performance. A complete design is presented and the fabricated low-pass filter demonstrates excellent performance in good agreement with theory. Finally, design techniques for microwave bandpass filters using re-entrant resonators are presented. The key feature is that each re-entrant resonator in the filter generates a passband resonance and a finite frequency transmission zero, above the passband. Thus an Nth degree filter can have N finite frequency transmission zeros with a simple physical realization. A new synthesis technique for pseudo-elliptic low-pass filters suitable for designing re-entrant bandpass filter has also been show-cased. A physically symmetrical 5 pole re-entrant bandpass prototype filter with 5 transmission zeros above the passband was designed and fabricated. Measured results showed good correspondence with theories. v Table of Contents Acknowledgements .................................................................................... iv Abstract ........................................................................................................ v Table of Contents ........................................................................................ vi List of Tables ................................................................................................ x List of Figures ............................................................................................ xv Motivation .................................................................................................. xxi Thesis Organisation ................................................................................ xxv Chapter 1 Microwave Filters – Fundamentals ........................................... 1 1.1 Microwave Filter Networks – Analysis and Synthesis .................... 1 1.1.1 Filter Transfer Function, Characteristic Function and Characteristic Polynomials ..................................................... 2 1.1.2 S-Parameters, ABCD Matrix and Y Admittance Matrix .......... 8 1.1.3 Coupling Matrix Synthesis Method ...................................... 13 1.1.4 Cascaded Synthesis Method ............................................... 30 1.2 Design of Microwave Filters ......................................................... 38 1.2.1 Lumped Lowpass Prototype Filters ...................................... 38 1.2.2 Frequency Transformation and Impedance Scaling ............ 39 1.2.3 Distributed Elements Filters ................................................. 39 1.2.4 Numerical EM Techniques ................................................... 40 1.2.5 Other Design Considerations ............................................... 52 1.3 Conclusion ................................................................................... 53 Chapter 2 Method for Generating Generalised Chebyshev Polynomials ............................................................................................................. 54 2.1 Introduction .................................................................................. 54 2.2 Generalised Chebyshev Characteristic Function ......................... 54 2.3 General Recursive Technique - Determining the characteristic polynomials .................................................................................. 57 2.4 Basis Characteristic Functions ..................................................... 58 2.4.1 Lumped Generalised Chebyshev Low-pass Filters .............. 60 2.4.2 Distributed Generalised Chebyshev Low-pass Filters ......... 65 2.4.3 Lumped Generalised Chebyshev Bandpass Filters ............. 66 vi 2.4.4 Lumped Chebyshev Low-pass Prototype Filter for Interdigital Bandpass Filter .................................................................... 78 2.4.5 Distributed Generalised Chebyshev Bandpass Filters ......... 83 2.4.6 Lumped Chebyshev Narrow Dual Bandpass Filters ............ 86 2.4.7 Lumped Generalised Chebyshev Dual Bandpass Filters ..... 89 2.5 Procedure for Generating the Filter Characteristic Polynomials 101 2.6 Examples ................................................................................... 101 2.6.1 Direct Synthesis of Generalised Distributed Chebyshev Low- pass Filter .......................................................................... 102 2.6.2 Direct Synthesis of Generalised Distributed Bandpass Filter 104 2.7 Conclusion ................................................................................. 106 Chapter 3 Synthesis and Realisation of a New Class of Distributed Low- pass Filters ......................................................................................
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