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FILTERS and MULTIPLEXERS By DESIGN METHODS FOR MICROWAVE FILTERS AND MULTIPLEXERS by SAOD ABDUL AZIZ ALSEYAB B .S c ., M.Sc. Submitted in fulfilm ent of the requirements fo~ the degree of Doctor of Philosophy The University of Leeds Department of Electrical and Electronic Engineering October 1979 Research carried out between June 1976 and June 1979, under the Supervision of Professor J.D. Rhodes. LIBRARY H S I l l V i a IMAGING SERVICES NORTH Boston Spa, Wetherby West Yorkshire, LS23 7BQ www.bl.uk BEST COPY AVAILABLE. VARIABLE PRINT QUALITY I**-* **■ IMAGING SERVICES NORTH » j' I! IsJwfTi 1 CO-Q Boston Spa, Wetherby &f i.mmm_*Wt West Yorkshire, LS23 7BQ. I G il www.bl.uk PAGE NUMBERS ARE CUT OFF IN THE ORIGINAL ( i) ABSTRACT This thesis is concerned with developing synthesis and design procedures for microwave filt e r s and m ultiplexers. The core of this thesis presents the following topics. 1) New classes of lumped lowpass prototype filters satisfying generalized Chebyshev characteristics have been investigated. Exact synthesis procedures are given using a relatively new technique termed the alternating pole synthesis technique to solve the accuracy problem. The properties of these filt e r s and th e ir practical advantages have been discussed. Tables of element values for commonly used specifications are included. 2) A new design procedure has been developed for bandpass channel multiplexers connected at a common junction. This procedure is for multiplexers having any number o f Chebyshev channel f ilt e r s , with arb itrary degrees, bandwidths and inter-channel spacings. The procedure has been modified to allow the design of multi-octave bandwidth combline channel f i l t e r multiplexers. I t is shown that this procedure gives very good results for a wide variety of sp ecification s, as demonstrated by the computer analysis of several multiplexers examples and by the experimental resul t s . 3) A compact exact synthesis method is presented for a lumped bandpass prototype filte r up to degree 30 and satisfies a generalized Chebyshev response. This prototype has been particularly utilized in designing microwave broadband combline f ilt e r s . 4) Different forms of realization have been discussed and used in design and construction of different devices. This includes a new technique to realize TEM networks in coaxial structure form having equal diameter coupled circ u la r cylin d rical rods between p arallel ground planes. Other forms of realization have been discussed ranging from equal diameter posts, direct coupled cavity waveguide filters to microwave integrated circuits using suspended substrate stripline structure. The experimental results are also given. In addition, the fundamentals of lumped c irc u its and distributed circuits have been briefly reviewed. The approximation problem was also discussed. ( I l l ) ACKNOWLEDGEMENTS I wish to express my sincere gratitude to the people of Yorkshire whose hospitality and friendly nature w ill stay alive in my memory for long years to come. I would like especially to thank the many members of the Department of Electrical and Electronic Engineering at Leeds University. First of a ll, I am in debt to Professor J.D. Rhodes who supervised the research which led to this thesis in his unique and distinguished way, for a ll the help and encouragement during the work. It is a privilege indeed working with him. My thanks should go to: Mr. P. Clark Mr. J.L . Gibbs and his s ta ff o f the Workshop. Messrs. R.C. Hawkes, O.L. Clarke and N. Banting for their efforts in building the devices. The technical s ta ff of Dec-10 system of the Department of Computer Studies at Leeds University for use of the facilities and their ready help whenever needed. Miss S.D. Salmon for preparing neat drawings of a ll the illustrations and graphs in this thesis. Mr. S . J . A lja d ir who devoted a lo t of his time for going through the fin a l manuscript and correcting many spelling and grammatical mistakes. Mrs. S. Moore and Mrs. J. Lowe for their expert typing. V .f. A. Payne for his help in photocopying this thesis. Finally, The Ministry of Higher Education and Scientific Research of the Government of Iraq for the financial support without which I would not be here in the f i r s t place. CONTENTS PAGE NO ABSTRACT ( i ) ACKNOWLEDGEMENTS ( i i i ) CHAPTER!: FUNDAMENTALS OF LUMPED CIRCUITS THEORY. 1 1.1 INTRODUCTION. 1 1.2 BASIC CONCEPTS. 2 1.2.1. Lumped Element Networks. 5 1.2.2. Driving Point Functions and Transfer Functions6 1.2.3. Properties of Driving-Point Immittance Functions. 8 1.2.4. Properties of Transfer Functions. 9 1.3 TWO-PORT NETWORK PARAMETERS. 10 1.3.1. The z-Parameters. 11 1.3.2. The y-Parameters. 12 1.3.3. The Forward and Reverse Transfer Matrix Parameters. 13 1.3.4. Relationships Between z, y and ABCD Parameters. 14 1.4 SYMMETRICAL AND RECIPROCAL TWO-PORT NETWORKS. 16 1.5 LOSSLESS NETWORKS. 16 1.5.1. One-Port Lossless Network. 17 1.5.2. Two-Port Lossless Network. 18 1.6 TWO-PORT NETWORK TERMINATED BY AN ARBITRARY LOAD. 19 PAGE NO. 1.7 INSERTION LOSS OF DOUBLY TERMINATED NETWORK. 21 1.8 IMAGE PARAMETERS AND IMAGED-MATCHED NETWORKS. 24 1.8.1. The Image Parameters. 24 1.8.2. Image-matched Lossless Networks. 26 1.9 SCATTERING PARAMETERS (MATRIX) 27 1.9.1. Definition of Scattering Variables. 27 1.9.2. Scattering Parameters of Two-Port Parameters 29 1.9.3. Relationship Between The Scattering Parameters and other Parameters. 31 1.9.4. Properties of the Scattering Matrix. 32 1.10 DOUBLY TERMINATED LOSSLESS NETWORK. 32 1.10.1. Darlington's Theorem. 35 1.11 ZEROS OF TRANSMISSIONS. 35 1.12 CONCLUDING REMARKS. 38 CHAPTER 2: APPROXIMATION AND SYNTHESIS OF PROTOTYPE FILTERS. 39 2.1 INTRODUCTION. 39 2.2 THE IDEAL LOW-PASS FILTER. 40 2.3 MINIMUM PHASE TRANSFER FUNCTIONS. 42 2.4 THE APPROXIMATION PROBLEM. 43 2.4.1. The Maximally F la t Response. 44 2.4.2. ine Equiripple Response. 48 2.4.3. The Chebyshev Response. 51 2.4.4. The E llip t ic Function Response. 57 PAGE NO. 2.5 THE EXPLICIT DESIGN FORMULAS. 62 2.5.1. The Modified Low-Pass Prototype Ladder Network. 64 2.5.2. E x p lic it Formulas For Element Values in Chebyshev F ilte rs . 66 2.5.3. The Singly Terminated Low-Pass Prototype. 72 2.6 THE GENERALIZED CHEBYSHEV RESPONSE. 77 2.7 THE GENERALIZED CHEBYSHEV LOW-PASS PROTOTYPE FILTERS. 83 2.7.1. Prototypes Having A Single Transmission Zero at In fin ity . 83 The z-Transformed Variable Techniques. 87 The Alternating Pole Synthesis Technique. 95 Results. 100 2.7.2. Prototype Having 3-Transmission Zeros at Infinity. 114 Results. 119 2.8 IMPEDANCE AND FREQUENCY SCALING. 128 2.9 FREQUENCY TRANSFORMATION. 128 2.9.1. Low-Pass To High-Pass Transformation. 129 2.9.2. Low-Pass to Band-Pass Transformation. 131 2.9.3. Low-Pass to Band-Stop Transformation. 136 2.10 CONCLUDING REMARKS. 140 PAGE NO CHAPTER 3: DESIGN PROCEDURE FOR BAND-PASS CHANNEL MULTI­ PLEXERS CONNECTED AT A COMMON JUNCTION. 141 3.1 BASIC CONCEPTS. 141 3.2 INTRODUCTION. 142 3.3 THE DESIGN PROCEDURE. 144 3.4 PROTOTYPE EXAMPLES AND COMPUTER ANALYSIS. 158 3.5 CONCLUSIONS. 172 CHAPTER 4: DESIGN AND PERFORMANCE OF EXPERIMENTAL MICROWAVE MULTIPLEXERS. 173 4.1 INTRODUCTION. 173 4.2 DIRECT COUPLED-CAVITY WAVEGUIDE FILTERS. 174 4.3 THE MULTIPLEXER DESIGN SPECIFICATIONS. 182 4.4 CALCULATION OF THE PROTOTYPE VALUES. 182 4.5 CONVERTING THE PROTOTYPE INTO WAVEGUIDE STRUCTURE. 191 4.6 THE PERFORMANCE OF THE MULTIPLEXER. 199 4.7 CONCLUDING REMARKS. 200 4.8 APPENDIX. 204 CHAPTER 5: FUNDAMENTALS OF DISTRIBUTED NETWORKS AND DESIGNS OF TEM-MODE MICROWAVE FILTERS. 206 5.1 INTRODUCTION. 206 5.2 BASIC CONCEPTS. 207 5.3 MULTI-WIRE-LINE NETWORKS. 213 PAGE NO 5.4 THE COMBLINE FILTER. 215 . 5.4.1. Background. 215 5.4.2. Exact Synthesis Procedure For Lumped Band- Pass Prototype. 217 5.5 DESIGN AND PERFORMANCE OF MICROWAVE BROADBAND COMBLINE FILTER. 226 5.5.1. The Specifications. 226 5.5.2. The P.ototype Element Values. 227 5.5.3. Conversion of the Lumped Element Values to Commensurate Lines. 228 5.6 MIXED LUMPED/DISTRIBUTED COMBLINE FILTER. 239 5.7 DESIGN TECHNIQUES FOR TEM-NETWORKS HAVING COUPLED CIRCULAR CYLINDRICAL RODS. 245 5.7.1. Method. 246 5.8 MICROWAVE INTEGRATED CIRCUITS (MICs) 259 5.8.1. The MICs F ilte rs . 262 5.8.2. Design and Construction of SSS Microwave Low-Pass F ilt e r . 263 5.9 CONCLUDING REMARKS. 274 5.10 APPENDIX 278 CHAPTER 6: DESIGN PROCEDURE FOR MULTI-OCTAVE COMBLINE-FILTER MULTIPLEXERS. 280 6.1 INTRODUCTION. 280 6.2 DESIGN FORMULAS FOR BROADBAND COMBLINE FILTER. 282 PAGE NO. 6.3 THE MULTIPLEXER DESIGN PROCEDURE. 289 6.4 PROTOTYPE EXAMPLES AND COMPUTER ANALYSIS. 296 6.5 DESIGN AND PERFORMANCE OF COMBLINE FILTER- DIPLEXER. 300 6.6 CONCLUSIONS. 303 CHAPTER 7: GENERAL CONCLUSIONS. 310 1 CHAPTER 1 FUNDAMENTALS OF LUMPED CIRCUITS THEORY 1.1 INTRODUCTION. F ilte rin g is a fundamental signal process in electronics, i t includes such diverse operations as channeling, demodulating, equalizing, detecting, decoding, phase slitting, integrating and differentiating. Nowadays, any two-port network that is designed to process signals is loosely called a f i l t e r , whether i t is lin ear or non lin ear, time invariant or time-varying, and whether the signal is continuous or d ig ita l.
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