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DESIGN METHODOLOGY FOR MULTILAYER MICROWAVE FILTERS AND BALUN CIRCUITS by CHOONSIK CHO B.S., Seoul National University, Seoul, 1987 M.S., University of South Carolina, 1995 A thesis submitted to the Faculty of the Graduate School of the University of Colorado in partial fulfillment of the requirements for the degree of Doctor of Philosophy Department of Electrical and Computer Engineering 1998 i Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. UMI Number: 9916780 UMI Microform 9916780 Copyright 1999, by UMI Company. All rights reserved. This microform edition is protected against unauthorized copying under Title 17, United States Code. UMI 300 North Zed) Road Ann Arbor, MI 48103 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. This thesis for the Doctor of Philosophy degree by Choonsik Cho has been approved for the Department of Electrical and Computer Engineering by K.C. Gupta Richard C. Booton, Jr. tw We The final copy of this thesis has been examined by the signators, and we find that both the content and the form meet acceptable presentation standards of scholarly work in the above mentioned discipline. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Choonsik Cho, (Ph.D., Electrical Engineering) Design Methodology for Multilayer Microwave Filters and Baiun Circuits Thesis directed by Professor K.C. Gupta A systematic and efficient approach to the design for a broad class of passive microwave circuits in multilayer configurations is presented. Multilayer configurations are becoming popular at microwave frequencies due to their sev eral advantages over single layer configurations. However, systematic design procedures for multilayer circuits have not been yet available. Design proce dures for several types of microwave circuits in multilayer configurations have been developed. Parallel coupled-line band-pass filters, end-coupled band pass filters and three-line baluns have been designed with the systematic de sign procedures developed. Procedures developed have been verified by com paring the results with full-wave electromagnetic simulations. These circuits have also been fabricated and measured to verify the design procedures. Wide bandwidth, size/volume compaction, flexible design and physically realizable dimensions are the factors th at multilayer structures provide compared to sin gle layer configurations. A network modeling is employed to characterize multilayer m ulticonductor transmission line systems. Since the microwave circuits developed utilize multiple coupled lines in multilayer configurations, the characterization of these coupled lines plays a significant role in derivation of design equations and generation of design procedures. Using this modeling approach, a multiple coupled line system can be transformed to a multiple uncoupled line system. These equivalent uncoupled lines are used to derive network parameters ([S], Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. iv [Y] or [Z] matrix) for coupled lines. The normal mode parameters (NMPs) for coupled lines derived in terms of system specifications are utilized to obtain the physical geometries. An optimization process is employed to find the geome tries which yield the desired NMPs calculated from circuit specifications. For optimizing the geometry, a quasi-static field analysis program, Segmentation and Boundary Element Method (SBEM), is employed to calculate inductance and capacitance matrices for specific dimensions of the multilayer configura tions. A general optimization algorithm, Simplex method, is used in conjunc tion with SBEM to obtain the physical geometry for various coupled lines. Sometimes, this optimization process generates local minima and takes consid erable time in computer simulation. Therefore, an Artificial Neural Network Modeling (ANN) is used to save the optimization time. Because end-coupled band-pass filters employ gap coupled sections, the 2-dimensional SBEM is not applicable for optimizing the gap dimensions. In this case, an ANN model has been developed and used to design this kind of filters based on the procedure developed here. Two case studies of parallel coupled-line band-pass filters are pre sented following the design procedure developed. A quasi-static analysis by SBEM and simulation result from a full-wave electromagnetic simulator are presented along with measurements for verification. Two designs of paral lel coupled filter carried out in coplanar waveguide (CPW) are also reported. Three-line baluns have been designed in two layer structures, simulated and verified by measurement results. Two examples of multilayer end-coupled band-pass filters have been designed using the procedure developed. One ex ample of these filters is also designed with an ANN model for comparison. A Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. discussion of results from these circuits and suggestions for future work presented. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. vi ACKNOWLEDGMENTS I would like to thank many people who helped continuously to make this dissertation come true without any difficulty. I am preferably thankful for Dr. K. C. Gupta, the dissertation advisor, for his endless encouragement directing the correct way to aim, patient guidance and invaluable advice. Also, I appreciate Jaeheung Kim, Zhiping Feng and Dr. Wenge Zhang who always assisted me with difficult fabrication of many circuits. I thank Dr. Roop L. Mahajan and Martin Hausler for installing and running a software of the artificial neural network model. I wish to thank Dr. Zoya B. Popovic and her many students for assisting experiments. Besides, I am grateful for Dr. Melinda Picket-May and Dr. Richard C. Booton, Jr. for serving on my committee. I am also grateful for my parents, brother and sister for encouraging me from a distance. Finally I want to express my gratitude from the bottom of heart to my wife, Misoo Kwon, for her endless devotion and speechless encouragement. This dissertation would not have been possible without her love and endurance. Also, I thank my child, Yeonjoo, for being always patient of not having enough time to play with me. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. CONTENTS CHAPTER 1 IN TR O D U C TIO N ............................................................................ 1 1.1 Advantages of Multilayer C i r c u i t s ....................................... 1 1.2 The Need for Developing Design Procedures....................... 3 .................................................... 5 1.3 Organization of the Thesis 2 A REVIEW OF MULTILAYER 2.1 Two Types of Multilayer C ircuits.......................................... 8 2.2 Multilayer Integration of MicrowaveC i r c u i t s ..................... 9 2.2.1 MMICs (Monolithic Microwave Integrated Circuits) 9 2.2.2 MCM (Multi-Chip M o d u les)................................... 9 2.3 Multilayer Circuits Using Multilayer Transmission Lines . 12 2.3.1 3 MICROWAVE CIRCUITS . .8 Circuit Functions Realized with Multilayer Trans mission L in es................................................................ 12 2.3.2 Coupled-Line C o u p le rs ............................................. 14 2.3.3 Parallel Coupled-Line Band-Pass F i l t e r s 16 2.3.4 End-Coupled Band-Pass F i l t e r s ............................. 18 2.3.5 Planar B a l u n s ............................................................. 19 2.3.6 Other Multilayer C o m p o n e n ts ................................ 20 DESIGN M E T H O D O L O G Y ......................................................... 21 3.1 Network M o d eling.................................................................... 22 3.2 Analysis Approach for Multilayer C irc u its .......................... 31 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. viii 3.3 Circuit S ynthesis...................................................................... 33 4 DESIGN OF PARALLEL COUPLED-LINE BAND-PASS FIL TERS IN MULTILAYER CONFIGURATIONS.......................... 37 4.1 Derivation of Design P ro ced u re............................................ 37 4.1.1 Z-M atrix for 2-Port Coupled Line Sections . . . . 39 4.1.2 Evaluation of the Normal Mode Parameters for Homogeneous C onfigurations................................... 4.1.3 Evaluation of the Normal Mode Parameters for Inhomogeneous C o n fig u ratio n s................................... 4.1.4 4.2 4.3 4.4 44 45 An Alternative Approach to the Evaluation of NMPs in Inhomogeneous Configurations............................. 47 Description of Design Procedures......................................... 48 4.2.1 Homogeneous C onfigurations................................... 48 4.2.2 Inhomogeneous C onfigurations................................ 50 Design E xam ples...................................................................... 53 4.3.1 Homogeneous Filters ................................................ 53 4.3.2 Inhomogeneous F ilte rs ................................................ 59 4.3.3 CPW F i l t e r s ................................................................ 66 Discussion ................................................................................ 70 5 DESIGN OF END-COUPLED BAND-PASS FILTERS IN MUL TILAYER C O N FIG U R A TIO N S................................................... 73 5.1 Derivation of Design P ro ced u re............................................. 73 5.2 Description of Design P r o c e d u re .......................................... 77 5.3 Design E xam ples...................................................................... 79 5.4 Design of End-Coupled Filters with ANN M odels 85 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. ix 5.4.1 ANN M odeling............................................................ 85 5.4.2 ANN Modeling Methodology for Multilayer EndCoupled Filters ......................................................... 88 5.4.3 The Design of Multilayer End-Coupled Filters Us ing ANN M odels......................................................... 5.5 Discussion .............................................................................. 90 94 6 MODELING FOR THREE-LINE BALUNS IN MULTILAYER C O N FIG U R A TIO N S...................................................................... 96 6.1 In tro d u c tio n ........................................................................... 96 6.2 Description of Design P r o c e d u re ........................................ 97 6.2.1 Representation of a Baiun by Two Coupled-Line C o u p le rs ...................................................................... 97 6.2.2 Design of 3-Line B alu n s............................................. 102 6.2.3 Physical Geometry for the 3-Line B a iu n ................. 104 Design Exam ples...................................................................... 106 6.3.1 Single-Layer 3-Line B a lu n s....................................... 106 6.3.2 Two-Layer B a lu n s....................................................... 107 D is c u ss io n .............................................................................. 117 7 SUMMARY AND FUTURE W O R K ............................................ 118 6.3 6.4 7.1 Multilayer Microwave Circuit DesignMethodology . . . . 118 7.2 Multilayer Microwave Circuit E x a m p le s ........................... 120 7.3 7.2.1 Parallel Coupled-Line Band-Pass F i l t e r s 120 7.2.2 End-Coupled Band-Pass F i l t e r s .............................. 121 7.2.3 Three-Line B aluns....................................................... 122 Future W o r k ............................................................................ 123 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. X 7.3.1 Compaction of F ilt e r s ................................................ 7.3.2 Bandwidth Considerations in Designing Three-Line 123 B a l u n s ......................................................................... 125 7.3.3 Other Multilayer C irc u its ......................................... 125 BIBLIOGRAPHY ......................................................................................... 126 APPENDIX A AN OPTIMIZATION OF PHYSICAL GEOMETRY USING “SIMPLEX” ALGORITHM ............................................................ 138 A .l Main f u n c t io n ........................................................................ 138 A.2 Link to S B E M ........................................................................ 141 A.3 “Simplex” function.................................................................. 143 B DATA FLOW FROM EM-ANN MODELS TO HP-MDS . . . . 145 B.l User-defined linear m o d e l..................................................... 145 B.1.1 Creating and preparing a directory .......................... 145 B .l.2 Run the “makemod” ................................................... 145 B.1.3 Editing the C-code template f i l e ............................. 145 B.2 The feed-forward ANN function ........................................ 150 B.3 An EM-ANN weight f ile ........................................................ 151 B.4 Compiling and linking the m o d e l........................................ 152 B.5 Read design icons file into M D S ........................................ 152 B.6 Notes on model u s a g e ........................................................... 153 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. xi TABLES TABLE 1.1 A sensitivity analysis of the S-parameters for coupled lines on same layer (left side in Figure 1.1) and coupled lines on different layer (right side in Figure 1.1) with respect to the spacing (5 )........................................................................................ 4.1 The specifications for homogeneous parallel coupled-line band pass f i l t e r s .......................................................................................... 4.2 ............................. 58 The filter specifications used for inhomogeneous parallel coupledline band-pass filters 4.6 56 Center frequency, bandwidth and ripple level for homoge neous parallel coupled-line band-pass filters 4.5 56 Physical dimensions for a homogeneous 4-layer parallel coupledline band-pass filter (units in m m ) ................................................ 4.4 54 Physical dimensions for a homogeneous 3-layer parallel coupledline band-pass filter (units in m m ) ................................................ 4.3 3 ....................................................................... 59 Physical dimensions for the inhomogeneous (a) 3-layer par allel coupled-line band-pass filter and (b) 5-layer parallel coupled-line band-pass f i l t e r .......................................................... 4.7 62 Center frequency, bandwidth and ripple for inhomogeneous parallel coupled-line band-pass f i lte r s .......................................... Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 65 x ii 4.8 The specifications used for multilayer CPW parallel coupledline band-pass filters ................................................................... 66 4.9 Physical dimensions for 3-layer CPW parallel coupled-line band-pass filters, (a) Topology A (b) Topology B ................... 68 4.10 Center frequency, bandwidth and ripple for 3-layer CPW par allel coupled-line band-pass filter d e s ig n s ................................ 71 5.1 Specifications for multilayer end-coupled band-pass filters . . 80 5.2 Physical dimensions of a two-layer end-coupled band-pass filter (units in mm) for Design A. Dimensions W \, W2,g and I are shown in Figure 5 . 1 ............................................................ 80 5.3 Physical dimensions of a two-layer end-coupled band-pass filter (units in mm) for Design B. Dimensions W \, W2,g and I are shown in Figure 5 . 1 ............................................................. 82 5.4 Center frequency, bandwidth and ripple level for multilayer end-coupled band-pass filte rs ...................................................... 84 5.5 Physical dimensions of a two-layer end-coupled band-pass filter (units in mm) with ANNs (Design A ) ............................. 93 5.6 Center frequency, bandwidth and ripple for a two-layer endcoupled band-pass filter with A N N s .......................................... 94 5.7 Design times and required iterations for end-coupled filters with ANN modeling and without A N N s ................................... 95 6.1 Some choices of Zoi,Zq 2 for balun input/output impedances Zin = = 50ft .......................................................................... 101 6.2 Parameters for the design example of a single-layer 3-line balun 106 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 6.3 Parameters for the design example of a two-layer 3-line balun (Topology A ) .................................................................................. 6.4 Parameters for the design example of a two-layer 3-line balun (Topology B ) .................................................................................. 6.5 108 Summary of a two-layer 3-line balun performance (Topology A ) ..................................................................................................... 6.6 107 115 Summary of a two-layer 3-line balun performance (Topology B ) ..................................................................................................... Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 116 x iv FIGURES FIGURE 1.1 Coupled-line couplers used for determining the sensitivities of the S-parameters with respect to the spacing dimension (left : hi = 20 mil, /i2 = 10 mil, er i = er2 = 9.6, rig h t: hi = 20 mil, h2 = 5 mil, /i3 = 5 mil, erl = er2 = er3 = 9 .6 ) ............. 2.1 The layout of a 3-D multilayer MMIC (from Ref. [1]) 2.2 The cross-sectional view of an MCM used for multilayer inter connects 3.1 .... ......................................................................................... 2 10 11 Cross sectional view of various examples of multilayer coupled lin es................................................................................................... 22 3.2 A system of n-conductor transmission li n e s ................. 22 3.3 A network model of n-conductor transmission line system . .30 3.4 Anetwork model of two-coupled l i n e ....................................... 31 3.5 A 32 3.6 A flow diagram for analysis of multilayer circuits consisting network model of three-coupled lin e ........................... of sections of multi-conductor lines 3.7 ......................................... A flow diagram for synthesis of a single coupled-line section of a multilayer c ir c u it ................................................................... 3.8 33 34 Synthesis of multilayer circuits consisting of several coupled line s e c t io n s ................................................................................... Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 35 XV 4.1 The layout of a parallel coupled-line band-pass filter using 4 coupled line sections (top view )................................................... 4.2 A typical filter section consisting of a coupled line with two ports o p e n ...................................................................................... 4.3 38 An admittance inverter model used for modeling a 2-port coupled section shown in Figure 4 . 2 .......................................... 4.4 38 38 An equivalent circuit using admittance inverter models for a coupled-line band-pass filter similar to one shown in Figure 4.1 39 4.5 An equivalent circuit for the transmission line of the length 29 39 4.6 An equivalent circuit for the admittance inverters at both ends of Figure 4 . 4 .......................................................................... 4.7 An equivalent network corresponding to the parallel coupledline band-pass filter circuits shown in Figure 4 . 1 ................... 4.8 40 40 A lumped element equivalent circuit for the band-pass filter configuration................................................................................... 4.9 The cross-sectional view of a typical homogeneous configuration 40 43 4.10 The cross-sectional view of a typical inhomogeneous config uration ............................................................................................. 45 4.11 The procedure for the design of multilayer parallel coupledline band-pass filters in homogeneous configurations............. 49 4.12 The procedure for the design of multilayer parallel coupledline band-pass filters in inhomogeneous configurations . . . . 52 4.13 The cross-sectional view of a 4-layer homogeneous parallel coupled-line band-pass f i l t e r ....................................................... 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Further reproduction prohibited without permission. 53 xvi 4.14 The layout used for simulation of a homogeneous 3-layer par allel coupled-line band-pass f i l t e r ........................................... 55 4.15 The layout used for simulation of a homogeneous 4-layer par allel coupled-line band-pass f i l t e r ........................................... 55 4.16 The performance of a 3-layer parallel coupled-line band-pass filter embedded in a homogeneous dielectric........................... 57 4.17 The performance of a 4-layer parallel coupled-line band-pass filter embedded in a homogeneous dielectric........................... 58 4.18 (a) The cross sectional view and (b) the layout of an inho mogeneous 3-layer parallel coupled-line band-pass filter. . . 60 4.19 (a) The cross sectional view and (b) the layout of an inho mogeneous 5-layer parallel coupled-line band-pass filter. . . 61 4.20 The photograph of multilayer parallel coupled-line band-pass filters fabricated on RT/Duroid 5880 (right: 3-layer filter left: 5-layer filte r)................................................................................. 63 4.21 The performance of an inhomogeneous 3-layer parallel coupledline band-pass f i l t e r ...................................................................... 64 4.22 The performance of an inhomogeneous 5-layer parallel coupledline band-pass filters ................................................................... 65 4.23 The layout of 3-layer CPW parallel coupled-line band-pass filter configuration for (a) Topology A, (b) Topology B . . . . 67 4.24 The performance of a 3-layer CPW parallel coupled-line band pass filter for topology A ............................................................. 69 4.25 The performance of a 3-layer CPW parallel coupled-line band pass filter for topology B ............................................................. 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Further reproduction prohibited without permission. 70 xv ii 5.1 The layout of a multilayer end-coupled band-pass filter . . . 74 5.2 An equivalent transmission line circuit for end-coupled band pass f i l t e r s ..................................................................................... 74 5.3 A modified transmission line model for end-coupled band pass f i l t e r s ..................................................................................... 75 5.4 An equivalent circuit using admittance inverters and A/2 res onators (<t> = 180°)......................................................................... 75 5.5 The relation between an admittance inverter and a gap ex pressed by susceptances and transmission l i n e s ...................... 5.6 A design procedure for multilayer end-coupled band-pass filters 76 78 5.7 The physical layout for a two-layer end-coupled band-pass filter (Design A ) ............................................................................ 81 5.8 The performance of a two-layer end-coupled band-pass filter (Design A ) ..................................................................................... 81 5.9 The photograph of two-layer end-coupled band-pass filters fabricated on RT/duroid 5880 (bottom: Design A, top: De sign B ) ............................................................................................ 82 5.10 The physical layout for a two-layer end-coupled band-pass filter (Design B ) ............................................................................ 82 5.11 The performance of a two-layer end-coupled band-pass filter (Design B ) ..................................................................................... 83 5.12 The architecture of typical single hidden layer artificial neural netw ork............................................................................................ 87 5.13 Analysis ANN model for gap coupled sections.......................... 89 5.14 Synthesis ANN model for gap coupled s e c tio n s ....................... 89 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. x v iii 5.15 Flow of data for linking EM-ANN models to commercial mi crowave circuit sim ulators............................................................ 91 5.16 A synthesis procedure for gap coupled sections using ANN m o d e ls ............................................................................................ 92 5.17 Performance of a two-layer end-coupled filter using ANNs . . 93 6.1 The general configuration of a 3-line b a l u n ............................. 97 6.2 The block diagram of b a l u n s ...................................................... 98 6.3 The bifurcated block diagram of b a lu n s ................................... 99 6.4 A 3-line balun composed of two 2-line couplers....................... 99 6.5 Equivalence between (a) a section of 3-coupled lines and (b) a 6-port network combination of two couplers.......................... 103 6.6 A design procedure for 3-line b a lu n s ......................................... 105 6.7 The physical layout of a single-layer 3-line b a lu n ......... 106 6.8 The physical layout of a two-layer 3-line balun (Topology A)107 6.9 The physical layout of a two-layer 3-line balun (Topology B)108 6.10 The performance of two-layer 3-line balun (Topology A) de signed by the procedure developed and comparison with an ‘ideal’ b a l u n ................................................................................... 109 6.11 The performance of two-layer 3-line balun (Topology B) de signed by the procedure developed and comparison with an ‘ideal’ b a l u n ................................................................................... 110 6.12 The phase imbalances of two-layer 3-line baluns designed by the procedure developed................................................................ 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Ill x ix 6.13 (a) The layout of a two-layer 3-line balun fabricated on Duroid RT5880, (b) the photograph of a two-layer 3-line balun fabricated on Duroid RT5880 ......................................... 112 6.14 The measured performance of a two-layer 3-line balun (Topol ogy B) designed by the procedure developed and comparison with a full-wave sim u latio n ......................................................... 113 6.15 The measured phase imbalance of a two-layer 3-line balun designed by the procedure developed......................................... 7.1 A possible layout of a more compact parallel coupled-line band-pass f i l t e r ............................................................................ 7.2 124 A possible layout of a more compact end-coupled band-pass filter 7.3 114 ................................................................................................ 124 A possible layout of a cascaded three-line b a l u n ................... 125 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. CHAPTER 1 INTRODUCTION 1.1 Advantages of Multilayer Circuits Most of the microwave circuits have been developed in single layer configurations since microstrip lines were introduced to replace striplines. Mi crowave integrated circuits (MICs) and monolithic microwave integrated cir cuits (MMICs) have mainly been realized on the top of a single-layer substrate material on which active circuits and passive circuits are placed. This single layer substrate environment provides a simple and convenient method to design and fabricate microwave components. However, as the need to reduce the size of area and volume has increased, substantial efforts have been made to im plement MICs and MMICs in multilayer substrate environments. As a result, passive and/or active microwave components are now being integrated in a single multilayer module [1, 2]. Furthermore, some circuits are of themselves becoming more compact using multilayer configurations [3-5]. There are two strong motivations for implementing the designs of MICs and MMICs in multilayer configurations. One of these is the need to inte grate microwave components (as many as possible) within a given size/volume constraint. In this case, circuits developed in the single layer configuration may be utilized and the effect of multiple substrates that is not considered before is now taken into account. Many low frequency and digital systems are adapting Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 2 this methodology to reduce the overall size and volume. The other motivation that is mainly considered in this thesis is to develop designs for novel components and circuits using multilayer configu rations. Using this, an enhanced performance is expected when the multiple layers are used. The use of multilayer multiple coupled-lines is an example for this purpose. They create a tight coupling when used for directional cou plers, and a wide bandwidth when used for coupled line filters, baluns, etc. These performances are usually not obtained from single-layer coupled-lines. Multilayer configurations also provide more topological freedom in circuit lay outs because the components can be placed more flexibly than the single layer structures. In addition, because single-layer designs can frequently cause a difficulty in obtaining physical geometry with reasonable fabrication tolerance, multiple layers can be used to overcome this problem. 1^2 )^r2 h i >£ri Figure 1.1. Coupled-line couplers used for determining the sensitivities of the S-parameters with respect to the spacing dimension (le ft: h\ = 20 mil, hi = 10 mil, eri = er2 = 9.6, right : hi = 20 mil, /i2 = 5 mil, /i3 = 5 mil, eri = er2 = er3 = 9.6) Another advantage is a lower sensitivity as compared to single-layer topology. The sensitivity analysis [6] can be performed for a coupler consisting of 2 conducting strips placed at different layers. This circuit is compared to a coupler consisting of 2 conducting strips placed at the same layer as shown Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 3 Table 1.1. A sensitivity analysis of the S-parameters for coupled lines on same layer (left side in Figure 1.1) and coupled lines on different layer (right side in Figure 1.1) with respect to the spacing (S ). Sensitivity ISnl l-Snl to il \S a i \ Coupled lines on same layer 0.5999 0.0753 0.0811 0.2230 Coupled lines on different layer 0.0204 0.0062 0.0103 0.0186 in Figure 1.1. Table 1.1 shows a comparison of sensitivities 1 of S-parameters between these two different structures. We alter the spacing dimensions (ex pressed as S) for two cases with holding constant widths for two conducting strips (expressed as W\ and W->). As shown in Table 1.1, the sensitivities of Sparameters for the coupler on same layer are larger than those for the coupler on different layer. In other words, the coupler on different layer is less sensitive to a change of the spacing dimension than the coupler on same layer, therefore, the multilayer configurations using conducting strips placed at different layer are more tolerable to the spacing dimension. 1.2 The N eed for Developing Design Procedures Continuous efforts have been going on for development of multilayer microwave components and circuits to overcome the difficulties associated with single layer configurations and even to compact their size and volume. Direc tional couplers designed in a single layer have created difficulties in providing tight couplings. Therefore, two-layer circuits have been utilized for obtaining 1The sensitivity (F) of P with respect to 5 is calculated as F £ = ^ coupling or the isolation, and S is the spacing dimension in this example where P is the Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 4 tight couplings (around 3 dB) and wide bandwidth. Research on two-layer directional couplers has resulted in design procedures for implementing these directional couplers. Parallel coupled-line band-pass filters have also been ex plored recently using multiple layers to achieve wide bandwidths th at are not attainable in single-layer structures. However, the design procedures for de signing these filters to desired specifications have not been available until now. In the research reported in this thesis, design procedures have been developed for multilayer parallel coupled-line band-pass filters. Multilayer end-coupled band-pass filters have also been reported in the literature [7] earlier. How ever, this work had been limited to only striplines and coplanar waveguide (CPW) configurations. In this thesis, microstrip version of end-coupled multi layer filters have been investigated and design procedure is developed for their implementation. Baiuns have attracted much attention for several application areas at microwave frequencies. Two-layer planar Marchand baluns [8] have been in use for almost a decade for obtaining a wide bandwidth and a good balance performance. More compact version for baluns is a three-line balun. The two-layer version of this class of baluns provides compactness, flexibility and physically realizable dimensions compared to the single-layer version. A design procedure for these baluns has been developed in this thesis. In this thesis, more efficient and systematic procedures for the design of multilayer microwave circuits and components (such as filters and baluns) are presented and verified. For illustrating these methods, several design examples are included. A quasi-static analysis and a full-wave electromagnetic simula tion program have been used for enhancing the circuit performance. Design procedures have also been verified by fabricating several designs and measuring Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 5 their performance. 1.3 Organization of the Thesis This thesis begins with an investigation of the multilayer configura tions suitable for microwave circuits. In Chapter 2, a review of multilayer structures at microwave frequencies is described. The current status in the de sign of multilayer circuits is reviewed for various applications such as couplers, filters, baluns, antennas and so on. Chapter 3 presents the design methodol ogy used throughout this thesis. Since multilayer multi-conductor transmission lines are employed to model parallel coupled line filters and three-line baluns, the network modeling of these lines plays a crucial role in deriving design pro cedures for various multilayer circuits. This network model is used to derive network parameters such as [Z], [Y], and [S] matrices needed for setting up the design equations. The network parameters used can be obtained from the nor mal mode parameters (NMPs) which include voltage ratios, impedances and phase velocities for various modes existing in multi-conductor line sections. A quasi-static field analysis method, SBEM [9, 10], is used to determine these NMPs for various cases. An analysis using SBEM used to analyze multilayer multi-conductor lines is presented. Using the analysis process, a synthesis ap proach to the design of circuits is discussed later. This synthesis approach makes the circuit design possible because a procedure to find out the physical geometry appropriate for desired circuit specifications can be based on this synthesis process. An optimization process has been employed to optimize the physical geometry for designing parallel coupled line filters and three-line baluns. Commonly used optimization processes can often converge to local Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 6 minima and therefore require considerable computer time resource. Therefore, an alternative modeling based on the use of ANNs has been used in the design of end-coupled band-pass filters. This ANN modeling reduces the CPU time requirement dramatically. The remaining chapters of this thesis constitute various examples of multilayer microwave circuits th at have been developed. In Chapter 4, paral lel coupled-line band-pass filters are modeled using network modeling method discussed in Chapter 3. Because the traditional method had been developed for only symmetrical coupled lines in single layer configurations, non-symmetrical coupled lines in multiple layers are employed and a design procedure for this kind of filters is derived. A wide bandwidth can be obtained in this multilayer configurations, and more freedom is possible in the choice of physical geome try. Filter examples in homogeneous, inhomogeneous and CPW configurations have been used to verify the design procedure developed. Simulated and mea sured results are presented and compared with calculated performance using SBEM. In Chapter 5, end-coupled band-pass filters are designed in multilayer configurations. Since this filter configuration utilizes gap coupled sections, twodimensional SBEM is not appropriate for this design. Instead, the capacitances associated with the gap geometry have been determined using a full-wave sim ulator (HP-Momentum [11])- These capacitances have been calculated repeat edly to optimize gap geometry needed for desired parameters. The desired parameters for each gap-coupled section have been derived for non-symmetric and multilayer configurations. To speed up the optimization process, an ANN modeling has been employed successfully. In Chapter 6, three-line baluns in two layers are presented along with the design procedure developed. These Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 7 baluns are more compact than the planar Marchand balun [8]. The design procedure begins with bifurcation of the 3-line configuration into two identical 2-line couplers. Design procedure for 2-line couplers using two layers is an intermediate step for the balun design. Once the couplers are designed from balun specifications, desired normal mode parameters (NMPs) for 3-coupled lines are derived, then these NMPs are evaluated using SBEM and an optimiza tion process. Detailed design equations are presented. Two designs have been performed and presented together with simulation and measurement results to verify the design procedure developed. The thesis concludes with a discussion of results and some suggestions for future research in Chapter 7. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. CHAPTER 2 A REVIEW OF MULTILAYER MICROWAVE CIRCUITS This Chapter reviews various kinds of multilayer circuits reported in the literature. 2.1 Two Types of Multilayer Circuits From the point of view of design methodology, multilayer circuits can be divided into two groups. In the first group of these, one integrates various single-layer circuits into a single multilayer module, whereas the second group represents planar components employing multilayer transmission line structures. For the multilayer circuits in the first group, passive components and/or active devices are integrated into a single module for miniaturization and cost-effective production [1]. When these circuits are integrated, verti cal vias between different layers and apertures in the ground plane are placed appropriately considering miniaturization, crosstalk and productivity. Multilayer couplers, filters, baluns, inductors, etc. belong to the sec ond group because these employ multilayer transmission structures to overcome difficulties associated with single-layer designs. The research reported in this thesis relates to multilayer circuits in this group. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 9 2.2 M u ltilay er In te g ra tio n of M icrow ave C irc u its 2.2.1 M M IC s (M onolithic M icrow ave In te g ra te d C ircu its) Multilayer MMICs [1,12] are constructed using a semiconductor substrate and multilayer passive circuits integrated with active devices on the semiconductor substrate. Active devices, resistors and MIM (M etal-insulator-metal) capaci tors are formed on the surface of a semiconductor wafer. Dielectric films and conductors are stacked on the wafer, and transmission lines and the ground lay ers are connected through via-holes. This structure allows transmission lines with reduced line widths, vertical interconnections with short signal delays and miniaturized connections in a small area. In addition, this provides miniature but low-loss transmission lines, and high design flexibility. As examples of this multilayer topology, several miniature passive circuits such as directional couplers, Wilkinson dividers, transmission lines, and planar baluns have been designed and fabricated. Active circuits such as mixers, amplifiers, phase shifters and up-converters are integrated with passive circuits in planar forms. Figure 2.1 [1] shows the typical configuration of a multilayer MMIC. In Figure 2.1, a 3-D multilayer MMIC fabricated on a GaAs substrate integrates active devices, resistors, and MIM capacitors on the surface of a semiconductor wafer. A thin film microstrip line offers a compact meanderline configurations while thin polyimide films and conductors are stacked on the wafer and a ground metal is inserted between layers. 2.2.2 M C M (M u lti-C h ip M odules) An MCM [13-15] as shown in Figure 2.2 is defined as multilayer sandwiches of dielectric and con ducting layers, on which integrated circuits and passive components (if any) are mounted directly on (or inside of) the sandwich structure, without separate Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 10 Vertical ground plane Ground metal between layers Vertical via Active device Semiconductor Substrate Figure 2.1: The layout of a 3-D multilayer MMIC (from Ref. [1]) Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 11 Inductor Substrate Figure 2.2. The cross-sectional view of an MCM used for multilayer inter connects packaging for each of the active components. That is, the chips are mounted bare onto the MCM’s, which then provide the required power and ground, as well as all the signal interconnect and the electrical interface to the external environment. The entire MCM, including chips and passive components, may be placed in a hermetic package much like a large single-chip carrier, or may be directly covered with a sealant material (such as epoxy or a glass passivation coating) to protect the components from physical damage. Three general categories of MCM’s are MCM-C (for MCM-Ceramic), MCM-L (for MCM-Laminates) and MCM-D (MCM-Deposited). MCM-C’s are manufactured by stacking unfired layers of ceramic dielectric, onto which liquid metal lines are “silk screened” using a metal ink process. The individual inked layers are then aligned, pressed together, and cofired into a solid pla nar structure, onto which integrated circuits can be installed. MCM-L’s are manufactured through the lamination of sheet layers of organic dielectrics, and are very similar to traditional printed circuit board technology. MCM-D’s are manufactured through the deposition of organic or inorganic dielectrics onto a silicon or alumina support substrate. After each dielectric layer is deposited, one of several techniques is used to pattern metal lines as well as metal vias. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 12 The chips are then installed on the upper surface. MCM-D technology can provide a versatile platform for the integra tion of GaAs MMICs and silicon devices for microwave circuits where perfor mance, size and weight are critical factors. Multilayer circuits such as spi ral inductors, baluns, coupled-line couplers, Lange couplers, transmission line transformers, filters, amplifiers, and voltage controlled oscillators have been integrated using this technology [13, 14]. 2.3 M u ltila y e r C irc u its U sing M u ltila y e r T ran sm issio n Lines 2.3.1 sio n Lines C irc u it F u n ctio n s R ealized w ith M u ltila y e r T ran sm is Couplers [16-31], filters [4, 5, 32-39], baluns [8, 40-43], hybrid circuits [44-47], and microstrip antennas [48-52] are several examples of multi layer microwave components developed so far. Multilayer configurations have recently received increasing attention because they make design more com pact, increase design flexibility, and often lead to better performance. In the design of coupled-line directional couplers, single-layer coupled-line couplers are well suited for weak coupling only [7]. Consequently, multilayer structures have been widely explored [16-31] in the design of high directivity coupledline couplers and re-entrant type couplers. Since a tight coupling is possible in multilayer coupled lines, a high coupling like 3 dB is easily obtained. Be sides, multilayer configurations are inherently non-symmetrical with reference to the two-coupled lines at different layers, thus they provide much flexibility in design. Coupled-line couplers and re-entrant type couplers developed in mul tilayer configurations also show compact design and often better performance Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 13 compared to single layer configurations. For microwave filter circuits, paral lel coupled-line band-pass filters and end-coupled band-pass filters have been extensively explored in multilayer configurations. In designing coupled-line filters, single-layer configuration, based on the traditional design procedure, is adequate when the bandwidth is less than 15 % [7]. This bandwidth limitation can be easily overcome by using multilayer coupled-lines because they can be designed for a tight coupling in each coupled section. Non-symmetry also adds more flexibility to the design of these filters. Designs for these multilayer filters are discussed in Chapter 4. In the designs for end-coupled band-pass filters, the bandwidth has been restricted to about 15 % due to the limit of gap be tween microstrip lines [7]. As in the case of parallel coupled-line band-pass fil ters, multilayer end-coupled filter configurations can also be designed for wide bandwidth by using the tight coupling caused by overlapping gap between two conductors at different levels. Designs of these filters are discussed in Chap ter 5. In the design of balun circuits, multilayer geometry has been utilized to obtain more compact and flexible designs for planar Marchand baluns and three-line baluns. Since coupled lines are used for these classes of baluns, wide bandwidth and flexibility are very important advantages achievable compared to single-layer baluns. These circuits are presented in Chapter 6. In addition to couplers, filters and baluns; hybrid circuits like magic-T and branch-line couplers and microstrip patch antennas have also been developed in multilayer configurations. Microstrip patch antennas fed from a lower layer provide wider bandwidth than those implemented in a single layer [48-52]. Branch-line cou plers and m agic-T’s designed in multilayers show some advantages [44-47]. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 14 However, for the various microwave circuits reported in multilayer configura tions, we do not have systematic procedures available for engineers to arrive at specific designs starting from circuit performance specifications. In this thesis, we discuss a systematic design methodology for a broad class of multilayer mi crowave circuits (like filters and baluns) th at make use of coupled transmission line sections as basic circuit elements. This design approach is discussed in Chapter 3. 2.3.2 C o u p le d -L in e C o u p lers For coupled-line directional couplers to function ideally, they should have perfect matching at all the four ports, perfect isolation and quadrature phase outputs over all frequency range of interest. Matching at the four ports is closely related to perfect isolation and directivity. Also, a tight coupling is frequently required in the design of coupled-line directional couplers for several applications. Single layer config urations show a considerable difficulty in achieving the tight coupling because of narrow spacing between adjacent lines and correspondingly increased sen sitivity to dimensional tolerances. As an alternative, various efforts to obtain ideal performance for coupled-line directional couplers have been made by us ing multilayer configurations and by modifying geometries topologically. Since multilayer configurations allow a tight coupling for coupled lines, they are in creasingly utilized for obtaining better performance for coupled-line couplers. Horno and Medina [25] used broadside couplers in multilayers to obtain a high directivity. They designed several coupled-line couplers with 3 dB to 20 dB coupling based on the graphs drawn based on a number of calculations. They also implemented high directivity couplers with directivity values ranging from 53 dB to 61 dB by equalizing the two phase velocities. However, these designs Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 15 were restricted to symmetrical geometries. In addition, a systematic proce dure for designing these couplers is not available. Masot et al. [26] designed a coupled-line coupler using suspended multilayer coupled lines and showed how to optimize the physical geometry. This design is restricted to suspended sym metrical coupled lines. Schwab and Menzel [53] proposed various multilayer topologies to be used in couplers and filters, and have reported a coupler using slots and coupled lines in a multilayer configuration. This coupler has a very narrow bandwidth and poor directivity as seen by theoretical and measured results. Prouty and Schwarz [27] developed a two-level coupler showing 3 dB coupling around 300 MHz, but this design has a poor directivity. Mernyei et al. [18] presented a coupled-line coupler in CPW using two layers. This coupler shows the control of the coupling in -3 to -30 dB range with a 100 % bandwidth at 30 GHz, but has poor directivity and matching at all ports. However, it has been pointed out [18] th at CPW structure in multilayers leads to a good possibility for obtaining better performance of coupled-line couplers. Fan and Pennock [28] presented two examples of broad side couplers using inset dielec tric guide (IDG). Again no design procedure is available for design and broad bandwidth is not obtained even in multilayer structure. Person et al. [17] developed a 3 dB coupler in multilayer thick-film technology showing a wide bandwidth, but not good matching and directivity. Banba and Ogawa [19] reported multilayer MMIC couplers using thin dielectric layers. They used symmetrical coupled lines along with an extra conductor located in a different layer. Engels and Jansen [16] designed quasi-ideal couplers in multilayer con figurations. They have presented design equations for coupled-line couplers and obtained wideband, high directivity and matched performance by use of Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 16 a full-wave simulation. In this design, a slot in ground plane is used which makes fabrication more complicated. Also equal port impedances are used leading to limited freedom for choosing those impedances. In the literature [20], a systematic design procedure for multilayer coupled-line couplers having no additional conductors and/or slots has been proposed. Using this proce dure, a 3 dB coupler can be designed to yield broad bandwidth performance and good directivity and matching. R e - E n tr a n t T y p e C o u p lers: When a directional coupler with high coupling is required, multilayer re-entrant type coupler is an attrac tive alternative. This configuration for tight coupling is a planar version of the re-entrant type couplers made up of two coupled lines on one layer and another wide microstrip line on the adjacent layer. This coupler makes a tight coupling possible without tight fabrication tolerance requirement of a narrow gap. After Cohn [29] proposed coaxial re-entrant type couplers, several planar versions of re-entrant couplers have been explored [27, 30, 31]. Pavio and Sutton [30] adapted multilayer structures for re-entrant type couplers based on the design procedure for re-entrant coaxial couplers. Prouty and Schwarz [27] have re ported multilayer re-entrant type coupler design connecting two coupled-line couplers, and obtained a tight coupling and a good directivity over a wide band. But they have not reported any detailed procedure for design. Hayes et al. [31] proposed a stripline coupler in cofired ceramic multilayer circuits showing 3-dB coupling and acceptable return loss. 2.3.3 P ara lle l C o u p le d -L in e B a n d -P a s s F ilte rs symmetrical coupled-line band-pass filters in single-layer configurations have been utilized for a long time and their design procedure is well documented Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Parallel 17 in [7]. Traditional single-layer coupled-line filters have an inherently narrow bandwidth due to weak coupling, caused by single-layer parallel coupled lines. Therefore multilayer configurations have been explored to obtain broad band width. Since the design procedure in [7] was developed for symmetrical coupled lines in single-layer configurations, a modified design method has been devel oped [33] in this thesis (Chapter 4) for using asymmetrical coupled lines in multilayer structures. Tran and Nguyen [35] reported the development of par allel coupled-line band-pass filters in a two-layer configuration. They used the topological freedom in choosing geometry to achieve a wide bandwidth, and verified their designs by experimental measurements. However, the design procedure for how to calculate the desired parameters and to obtain physical geometry was not presented. Lutz et al. [4] presented a multilayer coupledline band-pass filter showing an example. Also, design equations for desired J-param eters to be optimized were reported. But, further procedure leading to filter layouts is not available. In Chapter 4, designs for these filters are discussed. P a ra lle l C o u p led—L ine B a n d -P a s s C P W F ilte rs: Mul tilayer coupled-line band-pass filters can also be implemented in Coplanar Waveguide (CPW ). CPW circuits have drawn much attention due to their sev eral advantages over microstrip circuits. CPW circuits are easily fabricated, are relatively insensitive to the substrate thickness and can have low disper sion effect because their structure is uni-planar (with all conductors in a single plane). Menzel et al. [36] developed multilayer coupled-line filters in CPW circuits showing what kind of CPW-microstrip transitions can provide better performance. But they restricted their design to around 10 % bandwidth, and Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 18 this narrow bandwidth needs to be extended for several applications. These CPW filters can be designed using the same procedure for parallel coupled line filters as discussed in Chapter 4. 2.3.4 E n d -C o u p le d B a n d —P a ss F ilte rs Single-layer end- coupled band-pass filters are well documented in [7, 54], where a design pro cedure has been described for finding the desired admittances for each gapcoupled section and for obtaining the physical geometry based on the graphs showing the relation between the gap dimension and corresponding capacitance in single-layer symmetry. Since single-layer circuits are suitable for narrow bandwidth only, multilayer circuits have been investigated for achieving a wide bandwidth in the design of end-coupled band-pass filters. Schwab and Menzel [53] proposed a two-layer end-coupled band-pass filter using striplines, but this work is only applicable to narrow bandwidth and restricted to a stripline structure. Nguyen [37] presented a wideband end-coupled filter using CPW structure; but, any systematic design procedure is not given. Tzuang et al. [5, 38] proposed a considerably attractive physical layout for this class of filters. They designed it in stripline structure for obtaining a wideband. The design is limited to the stripline structure only and a design procedure is not available. Schwab et al. [34] and Williams et al. [39] have also presented this kind of narrow band filters in CPW configurations. They also implemented a wide band end-coupled filter in a two-layer stripline configuration, but wide band filters using microstrip lines have not been reported. A design procedure for wide band end-coupled filters using microstrip lines in multilayer configu rations is presented in Chapter 5. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 19 2.3.5 P la n a r B alu n s Baluns transform a balanced signal to an unbalanced signal and vice versa. A large number of balun configurations have been reported in literature. For use in microwave integrated circuits (MIC) and microwave monolithic integrated circuits (MMIC), wide bandwidth and compactness are of prime interest. M a rc h a n d B alu n : A planar version of Marchand balun has been adapted in multilayer structure for this purpose. Pavio and Kikel [8] presented planar Marchand baluns in two dielectric layers using an equivalent transmission line model. Because coupled sections in two-layer configuration can provide an extremely tight coupling, these baluns showed a wide band performance in 6 to 18 GHz frequency range. In this paper [8], the return loss at the input port (Sn ) has not been reported. Also, the design procedure leading to the physical dimensions has not been reported. Schwindt and Nguyen [40] have described a computer-aided analysis of a planar Marchand balun based on [S] parameter description. Although they analyzed this kind of baluns quantitatively, it was not discussed how their configuration worked as a balun. Engels and Jansen [41] proposed a design of this class of baluns where they have used [S] and [Y] parameters to derive the design equations. T utt et al. [42] have described a low loss monolithic planar Marchand balun using two thick layers. They implemented a wide bandwidth of 5.5 to 20 GHz and 0.7 dB loss over 6 to 21 GHz, but no synthesis techniques was provided. T h re e -L in e B a lu n s: Three-line baluns have been proposed in [43], however, this balun is discussed in single layer configurations only fo cusing on theoretical analysis and not the synthesis procedure. Furthermore, Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 20 design procedure is not available and no method to obtain the physical geom etry has been reported. Since this class of balun is more compact and can be realized in double layers, design procedure and examples are presented in more detail in Chapter 6. 2.3.6 O th e r M u ltila y e r C o m p o n en ts Other components such as hybrids and patch antennas have also been developed in multilayer config urations. H y b rid s: Branch-line couplers [44] and magic-T’s [45-47] have been developed using multilayer configurations to produce better performance than what is realized in single layer structures. More flexible designs can be obtained when multilayer branch line couplers are utilized. More compaction and flexibility is obtained when a multilayer configuration is used for magicT ’s. P a tc h A n ten n as: Microstrip patch antennas have been developed in multilayer structures since this configuration can offer wider bandwidth than that obtained with single-layer patch antennas. Generally the feed line is placed at the lower layer and the patch is placed at the top surface. A large number of applications have been reported [48-52]. In this Chapter, the previous work on multilayer microwave circuits has been reviewed. The following chapters describe the design procedure de velopment and its applications to multilayer circuits including: (i) parallel coupled-line band-pass filters in microstrip lines and CPW, (ii) end-coupled band-pass filters, and (iii) three-line baluns. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. CHAPTER 3 DESIGN METHODOLOGY The approach for developing design procedures, for the class of mul tilayer circuits discussed in this thesis, has been arrived by recognizing that sections of coupled transmission lines constitute the basic building blocks for this class of circuits. Examples of these coupled-line configurations used as ba sic circuit elements for multilayer circuits are shown in Figure 3.1. The ports of a section of coupled lines, whose cross-sectional views are shown in Figure 3.1, could be terminated in many different ways. These different terminations lead to different characteristics of the sections. These appropriately terminated coupled line sections axe used in the design of different kinds of multilayer mi crowave circuits. In this Chapter, we have developed a general analysis and synthesis procedure of multilayer microwave circuits using the network mod els for multilayered coupled line sections. For the design examples performed throughout this work, we have utilized a quasi-static field analysis program, Segmentation and Boundary Element Method (SBEM) described in [9, 10], to calculate capacitance and inductance matrices for multilayer multi-conductor transmission lines. Computations based on other analysis methods could as well be used for implementing the multilayer circuit design methodology pre sented later. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 22 ground plane Figure 3.1. Cross sectional view of various examples of multilayer coupled lines 3.1 Network M odeling Since the circuits we discuss are made up of various coupled line sec tions with terminations, a generalized network modeling for multilayer multi conductor transmission lines is a key step in the analysis and synthesis of these circuits. This modeling has been discussed in the literature [9, 10, 20, 55] on multi-conductor lines, and we use it in developing the design methodology for multilayer circuits. V, (x), i,(x) V jx ) , irjlx) Figure 3.2: A system of n-conductor transmission lines Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 23 Although multi-conductor transmission lines in an inhomogeneous medium do not support a pure TEM mode, voltages and currents can be ap proximated by a quasi-TEM mode. The system of multi-conductor transmis sion lines shown in Figure 3.2 is characterized using these voltages and currents. Assuming the time dependence is e?ut and the wave flows along the x direction, dv -z i (3.1) = -y v (3.2) = dx m dx where v = Vx V2 ... vn 1 = Zl %2 ... In z = Zn Z\2 • • * Zin 221 322 ' ' ' Z2n 3 il 3 ,2 2/11 2/12 • • • 2 /ln 2/21 2/22 ' ' • 2/2n 2/nl Vn2 2inn ‘‘ * Z nn and y= Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 24 za and ya {i= 1, 2, n) are the self-impedance and admittance per unit length of line i in the presence of all the other lines. zi} and yij (i ^ j) are the mutual impedance and admittance per unit length between line i and j. It is noted th at both z and y matrices are symmetrical. The equations (3.1) and (3.2) can be transformed to the following two wave equations: 92v a * = zyv <3-3> d2i a ? = yzv . . <3-4> By assuming x dependence of the voltage vector as e71, Eq. (3.3) becomes a typicalcharacteristic equation for n conductorlines.This equation has n eigenvalues: 2 2 2 2 7 = 7 i >72) • • • > m and a matrix E consisting of eigenvalues along the diagonal can be defined as E = 7l 72 ••• (3.5) 7n diag These n eigenvalues are related to the phase velocities of n orthogonal modes and the corresponding eigenvector for each eigenvalue represents the voltage ratios for n conductors in each mode. The n eigenvectors form the voltage eigenvector matrix R as: Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 25 1 1 1 i?21 R-22 ' *‘ R2n R = Rnl Rn2 ' ' ' (3-6) Rnn From linear algebra about eigenvector and eigenvalues [56], it is known that R " 1(zy)R = E (3.7) Taking the transpose of Eq. (3.7), R T(y z )(R -1)T = E T = E (3.8) This equation implies that, if Eq. (3.4) is solved instead of Eq.(3.3), the same eigenvalues are obtained and the corresponding current eigenvector matrix becomes (R T)_1. This eigenvector matrix can be normalized as all the elements in the first row are 1. Therefore, the current eigenvector matrix S can be defined as S= (R ^ P (3.9) where P= 151 151 fu fn ' 151 fn l (3.10) J diag Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 26 and fij is the cofactor of Rij. The characteristic impedance Z ^j (for the mode i, at the conductor j ) can now be solved using Eq. (3.1) or Eq. (3.2). How ever, only n out of these impedances are independent because the character istic impedances for the same modes at the different conductors are related by voltage and current ratios which are represented by voltage and current eigenvector matrices. Here, the characteristic impedances of conductor 1 in n different modes are selected to be calculated as Zm (3 1 1 ) where k is any integer between 1 and n. All other characteristic impedances can then be determined by the following equation. R21 521 Zc = ■'ell Jc21 •^2 n ■<Cl _ where Zcl = Rln R22 522 Rft1 Rn2 . . . 5nl 5n2 (3.12) Rnn 5nn - Jcn 1 diag It should be pointed out that only n (n + l) parameters (called “normal mode parameters”) are necessary to characterize the n-conductor transmission lines and these parameters are determined by solving the Maxwell’s equations with appropriate boundary conditions. In the above derivation, normal mode parameters are composed of n eigenvalues, n (n -l) variables in the voltage eigen vector matrix and n characteristic impedances. All the other parameters can also be determined by using these normal mode parameters. Now, consider Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 27 the system of n-conductor transmission lines of each line length I as shown in Figure 3.2 again. The voltage vector for 2n ports is assumed as: 0 0 R 1 1 (3.13) 1 M R D ”1 R 1__ RD A = O R G R l V = where V = Vi V2 A = Ai A2 vn vn+1 . . . • • • An j4n+1 ••• v2n • • • A2n and D = 3-7i i p-~ni o-yni diag The vector A is a voltage amplitude vector that solely depends on the external excitation and is used as a dummy variable. The matrix D represents the propagation delay of this multi-conductor transmission line system. It can be shown th at the corresponding current vector is expressed as I = h h - In In+1 - hn 0 0 szc-‘ -D 1 sz^1 rH SZJi D " A = rH -S Z ^ D -S Z ^ 1 1---- i SZ^1 D '1 (3.14) Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 28 Using Eq. (3.13) and Eq. (3.14), the impedance matrix Z of this 2n port network is given by Z = V I1 R 0 1 1 1 -1 ZciS- 1 0 R D D "1 -D D "1 0 R 0 1 1 1 -1 ZclP" 1 0 R D D "1 -D D 1 0 i -i 0 zcls0 ZclP- R 0 0 R (3.15) = XMXt where the matrix M is the product of the three inner matrices in Eq. (3.15). Since the m atrix M consists of the two matrices (the second and the third) for the propagation delay and the forth matrix involving the characteristic impedances, the operations performed by the matrix M can be represented by n uncoupled transmission lines with different electrical lengths and impedances corresponding to n different modes. This can be seen by writing the matrix M for 2 line case as: R = 1 1 Rc R* D = e- * 1 0 0 e~n*1 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 29 hx o 0 u 1*1 1*1 P -1= 0 1- R c / R r 1 0 1—R r / Rc ^c\ 1 —R c / R r -&JL 0 0 1 0 1 0 -1 o 0 1 0 1 0 1 0 -1 e-7J 0 end 0 1 0) 1 £ 0 f/Tcl 0 0 e - i,i o D7iri O ~e~ ^ 1 0 e1rl Z'l l-R c/R r 0 0 I-R r/R c 0 0 0 0 ------ 1 1 1 M = 1 -R r/R c 0 0 0 0 Jzx. 1 -R r/R c ZclCOth'Tcl ZelCSCh'ld 1- R c / R * l-R c /R r J 0 ZrXCOthlrl ZrlCsdl'Trl 1- R r / R c 1- R r / R c Z c\csch-fel ZclCOth'Tcl I-R e /fir l-R c /R r 0 ZrlCsdl'Trl l-R r/R c 0 -1 0 l-R c /R r 0 ____ 1 Z dP "1 = (3.16) 0 ZrlCOth'Trl I-R r /R c J The corresponding network is shown in Figure 3.4. Furthermore, a transformation of M by X (X M X T) is equivalent to a connection of these n uncoupled transmission lines (expressed by M ) with transformer banks (expressed by X ) at both ends. Since the matrix R represents the voltage ratios between conductors as shown in Eq. (3.6), the matrix X is expressed by transformers which correspond to these voltage ratios. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 30 Figure 3.3 represents this network modeling for a multi-conductor transmission line system. n+1 n+2 RntjRn.1,1 fel :&> Rn2 R32 1:R-»i R21 *31 R22IR32 Rn-u ;Rn; Figure 3.3: A network model of n-conductor transmission line system The network parameters such as [S], [Y] and [Z] parameters can now be calculated easily for any type of coupled line sections when this modeling approach is used. Two- and three-conductor lines are of important interest for different kinds of multilayer circuits investigated in this thesis. Generic models for two- and three-conductor coupled lines (special cases of the model in Fig ure 3.3 with n = 2 and 3) are shown in Figure 3.4 and Figure 3.5 respectively. It may be noted that these models represent coupled line sections in terms of characteristic impedances, voltage ratios and phase velocities of n-different normal modes of the n-conductor lines. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 31 4 ♦ ♦ 3 1 -R./R Figure 3.4: A network model of two-coupled line In Figure 3.4, R c and R* are the voltage ratios at c- and 7r-modes, Zci and Z ni are the characteristic impedances for the two modes, and 0C and 9n are the electrical lengths for the two modes. In Figure 3.5, Rij (i = m,n,p; j = 1,2,3) is the voltage ratio for the i mode at the conductor j , Zn 1 is the characteristic impedance at i mode, (0* is the electrical length at i mode, R is the voltage eigenvector matrix, and fa is the cofactor of Rij. 3.2 A nalysis A p p ro ac h for M u ltila y e r C irc u its Multilayer circuits consisting of multilayer coupled line sections can be analyzed step by step as shown in Figure 3.6. This analysis procedure is JThe subscript ‘c’ from Z cn representing the characteristic impedances for the i mode at the conductor 1 was removed for simplicity I Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 32 • 4 • 5 • 6 1 Rtnj2:Rm3< 1 J7~6 ml‘ml *Ni3 ;Rn2 Rn2 :Rn3 Figure 3.5: A network model of three-coupled line later used for developing design procedures for various multilayer circuits. As shown in Figure 3.6, the analysis of each of the coupled section in the circuit starts from the calculations of inductance and capacitance matrices for the coupled line section. Several different methods such as quasi-static analysis, spectral domain analysis, etc. can be used. For the research performed here, we utilized a quasi-static field analysis method, SBEM [9, 10], to calculate [L] and [C] matrices for a specific multilayer multi-conductor geometry. After the calculation of [L] and [C], the normal mode parameters (NMPs) are determined based on the equations derived in Section 3.1. The network parameters like [S], [Y] or [Z] are determined using these NMPs with appropriate port terminations. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 33 For simple circuits using only a single coupled line section, circuit performance is obtained from these [S], [Y] or [Z] parameters and any further calculation is not needed. For circuits consisting of several coupled line sections, the network parameters for all individual single sections need to be combined to yield the final network parameters of the overall circuit. Physical geometry [L] and [C] Normal mode parameters Port terminations [S], [Y] or [Z] Useful for circuits using single coupled sections Combined with other sections [S] for the overall circuit Figure 3.6. A flow diagram for analysis of multilayer circuits consisting of sections of multi-conductor lines 3.3 Circuit Synthesis The synthesis methodology for multilayer microwave circuits can be developed by rearranging the various steps in the circuit analysis procedure dis cussed in Section 3.2. The synthesis method aims at finding a set of physical Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 34 layout dimensions from the given circuit performance specifications. By revers ing the steps shown in Figure 3.6, synthesis procedure for a single section of multilayer coupled circuit may be expressed as shown in Figure 3.7. As seen in Figure 3.7, one starts with expressing the circuit specifications in terms of the network parameters, [S], [Y] or [Z]. For example, multilayer parallel coupledline filters can be designed for realizing the performance specifications such as the bandwidth, the center frequency, the ripple level, and etc. These fil ter specifications are used to represent desired [Z] parameters for each coupled section as discussed later. Specifications for a single coupled line section [S], [Y] or [Z] Normal mode parameters Optimization Physical geometry Figure 3.7. A flow diagram for synthesis of a single coupled-line section of a multilayer circuit In the next step of the multilayer circuit synthesis procedure, [Z] parameters for each coupled section can be expressed using the NMPs [9, 10, 20,57]. These NMPs are presented to an optimization process to find a physical geometry for the coupled section. This optimization process incorporates a field Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 35 Circuit specifications Evaluation of number of coupled line sections needed and specifications for each section Synthesis of each section as in Figure 3.7 Physical layout of the complete circuit Figure 3.8. Synthesis of multilayer circuits consisting of several coupled line sections analysis method of multilayer transmission lines. For the circuits consisting of several coupled sections, there is an addi tional initial step of obtaining characterizations for various coupled line sections from the circuit specifications. This is depicted in Figure 3.8. The synthesis procedure of Figure 3.7 is then repeated for different coupled line sections. For multilayer microwave circuits, coupled sections with conductors placed at dif ferent layers are mostly non-symmetrical. Thus, there is an additional design flexibility in the choices of terminal impedances for each coupled line section. This leads to an additional choice in the selection of the appropriate network parameters ([S], [Y] or [Z]) than th at available for the single-layer symmetrical coupled lines. This non-symmetry provides more freedom in the optimization process used for obtaining the physical geometry. This design methodology is used for the design of filters and baluns Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. discussed in Chapter 4,5, and 6. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. CHAPTER 4 DESIGN OF PARALLEL COUPLED-LINE BAND-PASS FILTERS IN MULTILAYER CONFIGURATIONS The design procedure of single-layer filters using symmetric coupled microstrip lines is well documented in the literature [7, 54, 58] and most of the filter designs make use of this procedure. These filters have been made possible by cascading quarter-wavelength coupled line sections which are openended at two of the ports. Often, very tightly coupled lines are needed, and these are difficult to be fabricated in single-layer configurations. Multilayer configurations overcome this difficulty because of the flexibility in overlapping coupled lines on different layers. Also, multilayer circuits can be implemented in both homogeneous (as embedded circuit components) and inhomogeneous (as microstrip-like circuits) layered dielectric media. In this Chapter, design procedures for homogeneous (stripline), inho mogeneous (microstrip) and coplanar waveguide (CPW) filters are investigated. 4.1 Derivation of Design Procedure A general configuration for parallel coupled-line band-pass filters made up of four coupled line sections (A/4 each at the design frequency) is shown in Figure 4.1. For multilayer circuit design, various conductors ( 1 ,2 ,3,4,etc.) may be located asymmetrically at different layers. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 38 Top view Figure 4.1. The layout of a parallel coupled-line band-pass filter using 4 cou pled line sections (top view) PORT 1 » O P E N C IR C U IT O P E N C IR C U IT « PO RT2 Figure 4.2. A typical filter section consisting of a coupled line with two ports open ^ 0 (N -1 ) 0 e Figure 4.3. An admittance inverter model used for modeling a 2-port coupled section shown in Figure 4.2 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 39 4.1.1 Z -M a trix for 2 - P o r t C oupled L ine S ections metrical coupled line sections with open ends at two of the ports have been widely utilized for the implementation of band-pass filters. For multilayer con figurations, asymmetrical coupled line sections as shown in Figure 4.2 allow more flexibility. The wave propagation and electrical behavior of asymmetrical coupled line sections are characterized by different voltage ratios (Rc and R^), mode impedances (Zcl, Z„i, Z c2 and Z v2) and phase velocities for the two nor mal modes (known as c- and 7r-modes) as discussed in Chapter 3. Following the conventional coupled line filter design procedure, the admittance inverter representation (shown in Figure 4.3) is utilized to derive the corresponding lumped element filter as explained in [7, 54, 58]. The general coupled line filter in Figure 4.1 may be redrawn as shown in Figure 4.4 by using the equivalent admittance inverter models. ------ , ■a » A A - a >----__ _ ^N+l r# J. -90° . _ ^]N_ -90° -90° M ^ •m m----- ^ Figure 4.4. An equivalent circuit using admittance inverter models for a coupled-line band-pass filter similar to one shown in Figure 4.1 -jZpjjCOte ZoN _* _ -jZnjjCOte i;_i T X sin29 Ljjij -p Cfj T Figure 4.5: An equivalent circuit for the transmission line of the length 26 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Sym 40 l:JZ r X/4- <=!> Figure 4.6. An equivalent circuit for the admittance inverters at both ends of Figure 4.4 Zo l J T F 7LN2 -J 7^ Zo Figure 4.7. An equivalent network corresponding to the parallel coupled-line band-pass filter circuits shown in Figure 4.1 u c; -j'm r —11— Ln’ Cn’ Figure 4.8. A lumped element equivalent circuit for the band-pass filter con figuration Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 41 The equivalent circuit shown in Figure 4.4 consists of cascaded trans mission lines of the length 2d and admittance inverters. The transmission line sections can be replaced by lumped element equivalent circuits shown in Fig ure 4.5 where L n = ^ ^ - , C n = 2zfN'uo• E dition, the admittance inverters at both ends (J\ and J n +i ) can be replaced by circuits containing transformers shown in Figure 4.6. Finally the filter circuit in Figure 4.1 is transformed to an equivalent network in Figure 4.7. The input admittance of this equivalent network for N = 2 is represented as : 1 y { . /Ci / UJ t M— U uo V ^ 0\ , - — ) + — 7= U *^2 — L*2 't J o -------------- } - ffi) + Z0JI (4.1) W Since the lumped element filter circuit as shown in Figure 4.8 can be equated to the equivalent circuit as shown in Figure 4.7, the input admittance for N = 2 is calculated where the frequency transformation and the impedance scaling have been used [54] (L\ = = ^ ,L '2 = ^ where A = Ui~“l , the fractional bandwidth, and gi,g2 are the prototype lowpass filter elements expressing L’s and C’s.). •— v i > <* “ V t (s (4-2) - “ ) + z » Equating the input admittances of Eq. (4.1) and Eq. (4.2), ./-parameters for N = 2 case may be written as: Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 42 2Z oZ o\Q\ 2y/ Z q\Z q29i 92 (4.3) 2Z qZ o292 Generalizing the number of coupled sections, J-param eters can be determined as: / = 1 JN = / V2ZoZoi9i .... 7r. ^ - . = 2 \ / Z o{n - i )Z on9n - i 9n , J n +i = (4.4) A 2ZoZo^g^g^+i 7T where N > 2, A is the fractional bandwidth, Zo is the impedance of the input and the output lines, J n is the admittance of an equivalent admittance inverter model for the N th coupled section, Z 0i, Z02 , • • • , Zqn are the line impedances at the two ports of coupled sections, and lg’ parameters are determined from the table for lumped element low-pass filter coefficients [7, 54, 58]. Once the admittance inverter model (value of J n ) corresponding to an asymmetrical coupled line section is derived by using Eq. (4.4), the normal mode parameters for each coupled section can be determined using the ABCD matrix or impedance matrix for the 2 -port asymmetrical coupled lines with open-ended ports as shown in Figure 4.2. The impedance matrix [Z] for a 2-port coupled line section is represented as [57, 59, 60]: Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. [Z] = Zyy Zy2 Z cy h -R c /R , Z2y Z 22 O O ct«?* 1 43 R ccsc 9C (4.5) R c esc 9C R 2 cot 9C cot 9„ Rn CSC9,r 1 1 R ttCSC9n R l cot 0, where R C, R ,r represent voltage ratios, Zci, Z^y represent mode impedances, and 9e, 9Wrepresent electrical lengths for the two modes of the coupled section. On the other hand, the impedance matrix for the admittance inverter model shown in Figure 4.3 can be expressed as: -j(JNZo(N-i)Zo* + zo(N-i)) sinScos9 Z\\ Z\2 Z21 Z22 -jJNZ0(N-l)ZoN x —jJ^ZoyN-iyZoN -j{J%z 0(N-i)ZlN + Zqn) sin0cos6 (4.6) where X = sin 2 6—J ^ Z 0^ - i )Z qn cos2 9 and 9 may be taken as 90° at the design frequency for the filter design. Until now, we have not made any assumption of homogeneity. Figure 4.9: The cross-sectional view of a typical homogeneous configuration Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 44 4.1.2 E v a lu a tio n of th e N o rm a l M o d e P a ra m e te rs for H o m ogeneous C o n fig u ra tio n s The cross-sectional view of a typical homo geneous configuration is shown in Figure 4.9. For homogeneous configura tions, phase velocities of 2 modes (9C and 9V) are equal (say 6). Equating the impedance matrices in Eq. (4.5) and Eq. (4.6) yields the normal mode param eters for the N th coupled section for a homogeneous configuration explicitly in terms of ^o(tv-i)j-^on' «md Jyv us: These normal mode parameters are used for obtaining physical dimen sions of the filter configurations since a set of physical dimensions corresponds to specific values of NMPs uniquely through the calculation of [L] and [C] ma trices [57, 59]. The designs are then analyzed by SBEM and/or a full-wave electromagnetic simulator. If the symmetric coupled sections are used in single-layer structures, the voltage ratio is 1 or -1 for the two modes. Therefore, the normal mode parameters for a symmetrical section can be written as: Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 45 Rc = -Rx = 1 Zq = Zoi = Zq2 — • • ■= Zqn Z c\ = 1 + JNZo + J ^ Z q (4.8) Z ni = 1 —JNZ 0 + J%2% These two impedances (Zci and Z nX) are exactly same as those derived for a single-layer symmetrical case in [54] using a different approach. air £n Figure 4.10. The cross-sectional view of a typical inhomogeneous configuration 4.1.3 E v a lu a tio n o f th e N o rm al M o d e P a ra m e te rs for In h o m ogeneous C o n fig u ratio n s The cross-sectional view of a typical “inho mogeneous” configuration is shown in Figure 4.10. For inhomogeneous dielec tric configurations, phase velocities for c- and 7r-modes are not equal, therefore, we cannot use the NMPs derived in Eq. (4.7) used for the homogeneous case. For the evaluation of desired normal mode parameters in an inhomogeneous case, we consider that for each A/4 section, tandc and tanO* are so large that .Z,riiCi tan 0,r,c Zo(v-i) and ^o(tv-i) tan0^iC >• Zxl)Cl. This approximation is justified because both 9C and 9W are close to 90°, and provides a reasonable method to proceed with the filter design. As mentioned in [9, 10, 20] earlier, Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 46 one additional intermediate design parameter (say ‘a’) is introduced to derive normal mode parameters for inhomogeneous configurations. For this parameter to be introduced, the coupling factor (5 (for the N th coupled section) between the port 1 and the adjacent open port of the four-port coupled line section in Sn S21 to 1 h— * 1 Figure 4.2 is used to find [S] matrix for the N th coupled section as: S12 - j 2/ V l - / ? 2 (4.9) 2(32 — 1 S22 The [S] matrix for the N th coupled section for the equivalent admit tance model can also be obtained from the [Z] matrix in Eq. (4.6) as: Sn Sn S21 S22 _ 2 \ / Z o(n - i )Z on 1 “ D 2y/Zo(N-i)ZoN j(JrfZ 0(N-.i)ZoN —1 JJ n ) (4.10) where D = (J n Z o(n - i )Z qn + l/«7iv)(j2sin20 —j + 2sin0cos0). Equating the [S] matrix in Eq. (4.9) to the [S] matrix in Eq. (4.10) for 9 = 90°, is found to be: /? = J n Z o(n - i )Z qn 1 + JtfZ0(N-l)ZoN (4.11) Once the coupling factor (3 is determined by Eq. (4.11) using J#, Zo(jv-i) and Z 0/v, one additional intermediate parameter ‘a’ is chosen for the N th coupled section, and lV is calculated [9, 10, 20] using: /? = (Vab—l )2 (1 + g )(1 + b) Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. (4.12) 47 From ‘a ’ and ‘6’ obtained in Eq. (4.12), normal mode parameters for the N th coupled section for an inhomogeneous configuration can be expressed as [9, 10, 20]: ry _ ry /a ( l + 6) ^ i- ^ - D V T T T •7^ j r l- — 7 ^ 0 ( A / - 1 ) 1 ' 1+ b 6(1 + a) This relation is used to find NMPs for each section and to find the physical dimensions to yield this set of NMPs. 4.1.4 A n A lte rn a tiv e A p p ro a c h to th e E v a lu a tio n o f N M P s in In h o m o g e n eo u s C o n fig u ra tio n s If the two electrical lengths are nearly 90°, NMPs are determined more easily equating ABCD-matrices of the 2-port coupled section in Figure 4.2 and the admittance inverter model in Figure 4.3. Assuming 6C~ 9* ~ 6 = 90°, the ABCD-matrix of the 2-port coupled section is [ABCD] = (^ ir^ c l [w jQCOS9 cO S^ RcRn(.Zcl Z^l) _* s in 9 R c R r { iZ c \ ' —Z -jr \) 9{RlfZel'~RcZxl)(RcZcl RieZirl) Rir Rc(Zci Zn\ P ^• COS^ COS2 B{^FCk Z c \ — R c Z i e \ } { R c Z c \ — R w Z l t \') — — R i r R c { LZ c \ — {RiF~‘&c)(.Zcl~Zxi')siTlQ (4.14) (ftc Z c i~ ftr^ ]ri)c o s 0 Z c 1—Z x l The ABCD-matrix of the admittance inverter model is also expressed as: Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 48 [ABCD] = (JivZo(Jv-i) + 7^ 7 ) sin 0 cos 0 i t j . v v o , sin2 6 ~ 3 {Jn Z 0(N- i )Z0N sin 2 0 - ^ cos2 0 ) cos2 *) sin 0 c o s 0 (4.15) Equating these two ABCD-matrices around 0 = 90°, the following relations are achieved. RnZci —R cZy\ _ R cR , ( Z c l - Z , x) ~ 1 N 0{n~1) + J n Z on R * ~ Rc _ _____ 1______ R cR tt{ZcI — Z 7ri) J n Z o(h - i )Z on RcZcl ~ RnZ.„\ _ j ry , 1 — - — - — = j n ^ qn + ------Ac\ — 6 -k\ J n ^Q(N-I) ^ The three equations in Eq. (4.16) consisting of 4 NMPs are now ex pressed using Jn,Zq(n-i) and Zqn- These new three parameters in the left hand sides in Eq. (4.16) can be used as the desired target parameters instead of 4 NMPs as derived in Eq. (4.13). Note th at only three parameters need to be optimized for determining the physical geometry. This provides a design flexi bility similar to the choice of the intermediate parameter ‘a’ in the procedure of Section 4.1.3. 4.2 Description of Design Procedures 4.2.1 Homogeneous Configurations Based on the discussion in Section 4.1, a design procedure for filters in a homogeneous multilayer config uration (Figure 4.9) may be summarized as shown in Figure 4.11. We start the Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 49 design from the filter specifications (bandwidth, number of coupled sections, ripple level, attenuation etc.) and then find ‘<7’ parameters (the prototype low pass filter elements) from the classical filter design tables available in the liter ature [7, 54]. From the given filter specifications, ‘<7’ parameters, and selected line impedances (Z0(at-i), Z on), we determine equivalent admittance parame ters as derived in Eq. 4.4 for each asymmetric coupled section. Desired target NMPs are then calculated explicitly using these admittance parameters. Once NMPs are determined from the filter specifications, these parameters are then used for obtaining an appropriate physical geometry. Part J Filter specifications Initial guess for w, and s Calculate [L]&[C] by SBEM Choose 5xn-d ^ Change wj ,w, ,s 5>n Bad Normal mode parameters for each coupled section Calculate Compare normal mode parameters Good Physical dimensions Part 3 Part 2 EM simulation Comparison Final Design Figure 4.11. The procedure for the design of multilayer parallel coupled-line band-pass filters in homogeneous configurations The overall design procedure can be broken up into following three parts: (1) Evaluation of desired NMPs as discussed in Section 4.1.2, (2) Determination of physical dimensions (width, spacing, etc.) to obtain Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 50 the desired mode parameters as computed in Part (1), and (3) Electromagnetic/network simulation and/ or experimental measurement of physical layouts obtained in P art (2) to verify the design. For Part (2), desired NMPs for each coupled section obtained from Part (1) are utilized to come up with physical dimensions for each coupled sec tion. In order to obtain physical dimensions for each coupled section, we have used an optimization method called ‘Simples? algorithm [61]. This optimiza tion process compares the desired NMPs obtained from the filter specifications mentioned in Part (1) with those calculated from capacitance and inductance matrices [57, 59, 60] for a geometry. The capacitance and inductance matrices can be determined using SBEM analysis [9, 10] of a specific physical structure. For Part (3) of the design procedure, S-parameters are determined for each coupled section starting from the physical dimensions finally arrived at, and then these S-parameters for various sections are combined for evalu ating the filter performance. The complete circuit combining all coupled sec tions is analyzed for determining the insertion loss and the return loss. Also, an electromagnetic simulation is carried out using the physical dimensions on Momentum ™ (an HP-EEsof product), a simulation package using the method of moments. The filter design is finally verified by comparing the performance obtained from EM simulations. 4.2.2 In h o m o g en eo u s C o n fig u ratio n s The design procedure for inhomogeneous configurations (Figure 4.10) is slightly different and may be summarized as shown in Figure 4.12. As in the case of homogeneous con figurations, we start the design from the filter specifications and then find Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 51 ‘g’ parameters from the classical filter design tables available in the litera ture [7, 54]. From the given filter specifications, ‘p’ parameters, and selected line impedances {Z q^ - \ ) i Z on), we determine equivalent admittance param eters for each asymmetric coupled section. For an inhomogeneous dielectric medium, one additional parameter (‘a’) needs to be introduced for specifying the coupling factor (5 (Eq. 4.12). Alternatively, 3 new desired target parame ters defined in Eq. (4.16) can also be used for synthesis process as discussed in Section 4.1.4. Therefore, the desired NMPs (c- and 7r-mode voltage ratios and impedances) are obtained from Eq. (4.13) or Eq. (4.16). Once NMPs are determined from the filter specifications, these pa rameters are then used for obtaining an appropriate physical geometry. Since we have one additional parameter (‘o’) or 3 desired target parameters for in homogeneous media, this configuration provides more flexibility in finding the physical dimensions of the filter. The overall design procedure can also be broken up into following three parts: (1) Evaluation of desired NMPs as discussed in Section 4.1.3 or Section 4.1.4. (2 ) Determination of physical dimensions (width, spacing, etc.) to obtain the desired mode parameters as computed in P art (1), and (3) Electromagnetic/ network simulation and/ or experimental measurement of physical layouts obtained in Part (2) to verify the design. For P art (2), desired NMPs for each coupled section obtained from P art (1) are utilized to come up with physical dimensions for each coupled section. In order to obtain physical dimensions for each coupled section, we have also used an optimization method called ‘Simplex1 algorithm [61]. The Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 52 Part 1 Filter specifications Wj ,w> and s for various sections from the homogeneous solution Choose Z W N -l) and Z Change w, ON ,s Bad Normal mode parameters for each coupled section Calculate Compare normal mode parameters Good Physical dimensions Part 2 EM simulation Comparison Final Design Part 3 Figure 4.12. The procedure for the design of multilayer parallel coupled-line band-pass filters in inhomogeneous configurations physical dimensions obtained from the design of homogeneous multilayer filters are used for an initial guess for the iterative evaluation of physical dimensions for an inhomogeneous medium. The line impedances, ZQi through Z qn at the interfaces between different coupled line sections, can be altered within the range of 10 Ct to 80 Q for obtaining more reasonable physical dimensions. For an inhomogeneous dielectric medium, the additional parameter (‘a ’) may also be selected iteratively for finding an appropriate physical layout. Alternatively, only 3 target parameters can be used as derived in Section 4.1.4 for the target parameters for synthesis. For Part (3) of the design procedure, S-parameters are determined for each coupled section starting from the physical dimensions finally arrived at, Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 53 and then these S-parameters for all sections are all combined together for eval uating the expected performance. The complete circuit combining all coupled sections is analyzed for determining the insertion loss and the return loss. Also, an electromagnetic simulation is carried out using the physical dimensions on Momentum ™ (an HP-EEsof product), a simulation package using the method of moments. The filter design is finally verified by comparing the performance obtained from EM simulations and experimental measurements. 4.3 D esign E x a m p les 4.3.1 H om ogeneous F ilte rs We illustrate this procedure by performing two examples of multilayer filters embedded in a homogeneous di electric as shown in Figure 4.9 and Figure 4.13. The filter specifications are selected as shown in Table 4.1 where Z on’s are line impedances at two ports of the n th coupled line section. These impedances are selected so as to avoid too narrow or too wide line widths and spacings. Figure 4.13. The cross-sectional view of a 4-layer homogeneous parallel coupled-line band-pass filter Following the design procedure developed and discussed earlier, and performing iterations with SBEM leads to the physical dimensions for the two Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 54 Table 4.1. The specifications for homogeneous parallel coupled-line band-pass filters Center frequency Bandwidth Ripple Number of resonators eT /14 h3 h2 h1 ^0 Z qi Zq2 Z 03 3-layer filter 10 GHz 40% 0.5 dB 3 4-layer filter 10 GHz 40 % 0.5 dB 3 2.2 2.2 120 mil 20 mil 20 mil 20 mil — 80 mil 20 mil 20 mil 50 Q 40 n 60 Q 40 Q 50 40 60 40 Q Q Q n filter examples as shown in Table 4.2 and Table 4.3, respectively. W i, W2, W0 and S are layout dimensions obtained as shown in Figure 4.1. The length of each line of all coupled sections is made shorter than the physical dimensions shown in Table 4.2 and Table 4.3 to take into account open-end discontinu ity reactances [62, 63]. The physical layouts of these two filters are shown in Figure 4.14 and Figure 4.15. Using the physical dimensions optimized for two examples, filter cir cuits are simulated on a full-wave EM simulator. Performances for two different multilayer filters in homogeneous dielectrics, as obtained by EM simulations and an ideal response from the Chebyshev filter, are shown in Figure 4.16 and Figure 4.17. Center frequency, bandwidth and ripple level for these two filters as obtained from SBEM analysis and EM simulations are compared in Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 55 Figure 4.14. The layout used for simulation of a homogeneous 3-layer parallel coupled-line band-pass filter Figure 4.15. The layout used for simulation of a homogeneous 4-layer parallel coupled-line band-pass filter Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 56 Table 4.2. Physical dimensions for a homogeneous 3-layer parallel coupled-line band-pass filter (units in mm) Section # Wi w2 S m ,w 0 1 2 4 3 1.304 1.368 1.136 1.119 1.119 1.136 1.368 1.304 -0.836 -0.525 -0.525 -0.836 2.3 22 Table 4.4. A good agreement with the desired values verifies the design proce dure proposed here. Note that SBEM is a program for quasi-static evaluation of [L] and [C] matrices for multilayer multi-conductor coupled lines. Results of SBEM axe used in a network simulator (HP-MDS) to obtain filter performance (marked as SBEM) in Table 4.4. These results do not incorporate discontinuity reactances and spurious mutual coupling among various sections. A full-wave simulation takes all these effects into account. We note that results from SBEM analysis and EM simulation are in close agreement. However, S2i at frequency above the pass-band as obtained from the EM simulation decays more rapidly than Table 4.3. Physical dimensions for a homogeneous 4-layer parallel coupled-line band-pass filter (units in mm) Section # Wi w 2 S W i,W 0 1 1.787 2.026 -0.572 3 2.638 0.642 0.642 2.638 -0.958 -0.958 3.4187 2 4 2.026 1.787 -0.572 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 57 0.0 dB — — -— -10.0 dB IS111 (Momentum) IS211 (Momentum) IS111 (Ideal) IS21I (Ideal) -20.0 dB -30.0 dB -40.0 dB 2.0 4.0 6.0 8.0 10.0 12.0 frequency (GHz) 14.0 16.0 18.0 Figure 4.16. The performance of a 3-layer parallel coupled-line band-pass filter embedded in a homogeneous dielectric th at obtained by connecting all S-parameters for coupled sections based on calculated NMPs. This may be caused by discontinuity reactances which were not taken into account in design process. Although the open end compensation was carried out in an approximate manner, the center frequency shift is also likely caused by other discontinuity reactances. An unwanted coupling between two different coupled sections affects the filter performance in that this can cause another pole at the stop band. Also, the optimization process used in determining physical dimension from [L] and [C] matrices is not perfect. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 58 0.0 dB — — -— -10.0 dB IS111 (Momentum) IS211 (Momentum) IS11I (Ideal) IS21I (Ideal) -20.0 dB -30.0 dB -40.0 dB 2.0 4.0 6.0 8.0 10.0 12.0 frequency (GHz) 14.0 16.0 18.0 Figure 4.17. The performance of a 4-layer parallel coupled-line band-pass filter embedded in a homogeneous dielectric Table 4.4. Center frequency, bandwidth and ripple level for homogeneous par allel coupled-line band-pass filters Center Frequency (GHz) Spec. SBEM 3-layer filter 4-layer filter Momentum 3-layer filter 4-layer filter 10 3 dB Bandwidth (%) 40 Ripple Level (dB) 0.5 10 10 42 42 < 0.378 < 0.378 10.13 9.85 40.97 42.33 < 0.546 < 0.935 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 59 Table 4.5. The filter specifications used for inhomogeneous parallel coupledline band-pass filters Center frequency Bandwidth Ripple Number of resonators £>5 £r4 Sr3 Sr2 Erl h$ 3-layer filter 6 GHz 50% 0.5 dB 3 — — 2.2 2.2 2.2 /14 — — h3 h2 hi 20 mil 20 mil 20 mil 4.3.2 In h o m o g en eo u s F ilte rs 5-layer filter 6 GHz 50 % 0.5 dB 3 2.2 2.2 2.2 2.2 2.2 20 20 20 20 20 mil mil mil mil mil The design procedure is demon strated by performing two inhomogeneous multilayer parallel coupled-line band pass filters, selected specifications of which are shown in Table 4.5. An opti mization process for evaluating physical dimensions, in this case also, has been carried out using the 'Simplex1 algorithm [61] (as performed in a homoge neous dielectric case [33]), and the line impedances and three desired target parameters as explained in Section 4.1.4 are optimized together with physical dimensions. Making iterations with SBEM leads to the physical dimensions appropriate for two filter examples as shown in Table 4.6. W\, W2 and S are layout dimensions as shown in Figure 4.1. The layouts of these filters using these physical dimensions are shown in Figure 4.18 and Figure 4.19. The length of each coupled section is taken Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 60 (a) (b) Figure 4.18. (a) The cross sectional view and (b) the layout of an inhomoge neous 3-layer parallel coupled-line band-pass filter. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 61 (a) (b) Figure 4.19. (a) The cross sectional view and (b) the layout of an inhomoge neous 5-layer parallel coupled-line band-pass filter. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 62 Table 4.6. Physical dimensions for the inhomogeneous (a) 3-layer parallel coupled-line band-pass filter and (b) 5-layer parallel coupled-line band-pass filter Section # Wi (mm) W2(mm) S(m m) Z on(Q) input 4.796 — — 50 1 2.445 0.557 -0.469 70 2 0.905 0.611 -0.568 60 3 0.611 0.905 -0.568 70 4 0.557 2.445 -0.469 output — 4.796 — 50 3 1.571 3.001 -0.176 55 4 2.013 3.908 -0.283 output — 7.993 — 50 (a) Section # W \(mm) W iim m ) S(m m) Z oh(Q) input 1.506 — — 50 1 0.755 1.206 -0.980 55 2 1.338 1.827 -0.274 60 (b) as the quarter-wavelength (at the center frequency) based on the arithmetic mean of the two phase velocities for the coupled section. The length of each line in all coupled sections is made shorter to take into account open end fringing capacitance [62, 63]. The physical layouts of these two filters (which were used by full-wave electromagnetic simulations) are shown in Figure 4.18 (b) and Figure 4.19 (b). Using the physical layouts, filter circuits are simulated on a full-wave EM simulator. Experimental measurements have been performed using the fabricated filters as shown in Figure 4.20. In Figure 4.20, the 3-layer filter is shown in the right side, and the 5-layer filter is shown in the left side. Performances for two different filters in an inhomogeneous dielectric, as obtained by EM simulations and an ideal Chebyshev filter response, are Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 63 \ ■ \ * Figure 4.20. The photograph of multilayer parallel coupled-line band-pass filters fabricated on RT/Duroid 5880 (right: 3-layer filter left: 5-layer filter) shown in Figure 4.21 and Figure 4.22. Center frequency, bandwidth and ripple level for these filters as obtained from EM simulations and measurements are shown in Table 4.7. A good agreement with the desired values verifies the design procedure proposed here. We note th at results from the design calcu lation (SBEM) and the EM simulation are in close agreement. However, S21 values at frequency above the pass-band as obtained from the EM simulation show a slight deviation. The main reason for this behavior is the discontinuity reactances between the two different coupled sections (other than open-ends) which were not taken into account in the design process. Approximations used in the equations concerning the two different phase velocities in inhomogeneous dielectrics as described in Section 4.1 can cause the deviation from the desired filter specifications as shown in Figure 4.21 and Figure 4.22. Center frequency Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 64 0.0 dB tow -10.0 dB -20.0 dB -30.0 dB IS111(Momentum) IS211 (Momentum) IS111 (Ideal) IS21I (Ideal) IS111(Measured) IS211 (Measured) -40.0 dB -50.0 dB • 1.0 Li 2.0 i i 3.0 i i 4.0 i lL LI i dJ . 5.0 6.0 7.0 frequency (GHz) i 8.0 i i 9.0 i l! 10.0 11.0 Figure 4.21. The performance of an inhomogeneous 3-layer parallel coupledline band-pass filter shift is also perhaps caused by other discontinuity reactances. Also, the op timization process used in determining physical dimensions from [L] and [C] matrices is not perfect. Experimental results are also included for comparison. It is noted that the measured results are slightly more deviated to higher frequency side than the EM simulation results. It is mainly because of an alignment problem for several layers, finite ground planes and possible air gaps between substrates. These imperfections in the fabrication process can cause such deviation. These measurements were carried out by a full 2-port calibration (S-O -L-T cali bration [64]). W ith a TRL calibration [64], better measured results could be Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 65 O.OdB Ooooo ------ IS11 ------ IS21 ------IS11 ------ IS21 ° IS11 • IS21 -10.0dB -20.0dB , (Momentum) (Momentum) (Ideal) (Ideal) (Measured) (Measured) -30.0dB -40.0dB -50.0dB 1.0 2.0 3.0 4.0 5.0 6.0 7.0 frequency (GHz) 8.0 9.0 10.0 11.0 Figure 4.22. The performance of an inhomogeneous 5-layer parallel coupledline band-pass filters Table 4.7. Center frequency, bandwidth and ripple for inhomogeneous parallel coupled-line band-pass filters Ideal response SBEM 3-layer filter 5-layer filter M om entum 3-layer filter 5-layer filter Measured 3-layer filter 5-layer filter Center Frequency (GHz) 6 3 dB Bandwidth (%) 50 Ripple Level (dB) 0.5 5.79 5.96 49.7 49.1 < 0.42 < 0.39 5.86 6.00 48.5 43.7 < 1.25 < 0.85 6.00 6.15 41.3 43.1 < 2.68 < 2.88 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 66 Table 4.8. The specifications used for multilayer CPW parallel coupled-line band-pass filters Topology A Center frequency Bandwidth Ripple Number of resonators £t3 Zr2 £rl h3 h2 hi 4 GHz 30 % 0.5 dB 2 10.2 10.2 10.2 25 mil 10 mil 25 mil Topology B 4 GHz 30 % 0.5 dB 2 10.2 10.2 10.2 25 mil 10 mil 25 mil obtained. 4.3.3 C P W F ilte rs Very few designs of multilayer CPW filters have been reported so far [32, 34, 36, 39]. In this thesis, the methodology developed has been used for designing CPW filters in multilayer configura tions. In this design, coplanar lines are combined with asymmetric microstrip lines, thereby combining the advantage of CPW with the design flexibility of multilayer configurations. Two examples of multilayer CPW filters are shown in Figure 4.23. In these layouts, air bridges are not needed at the end of CPW coupled sections where the ground planes are connected on CPW layer. This is an advantage of using multiple substrates. EM simulations with air-bridges incorporated at the input and output ports showed th at performance changes are not significant. Filter specifications selected for CPW configurations are shown in Table 4.8. An optimization process for evaluating physical dimensions has also been carried out using the ‘Simple^ algorithm [61] as in multilayer microstrip Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 67 (a) (b) Figure 4.23. The layout of 3-layer CPW parallel coupled-line band-pass filter configuration for (a) Topology A, (b) Topology B Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 68 Table 4.9. Physical dimensions for 3-layer CPW parallel coupled-line band pass filters, (a) Topology A (b) Topology B Section # W\ (mm) W2(mm) S(m m ) g(mm) Z qh(SI) input 1.104 — — 0.674 50 1 0.504 2.027 -1.161 0.974 18 2 1.26 1.241 -0.39 — 18 3 2.1 0.502 -1.285 0.944 output — 1.084 — 0.653 50 2 0.287 0.277 -0.058 — 40 3 0.674 0.521 -0.377 0.604 output — 0.948 — 0.39 50 (a) Section # W\ (mm) W2(mm) S(m m ) g(mm) Z qn(Q) input 0.951 — — 0.391 50 1 0.521 0.674 -0.374 0.606 40 (b) filters, and the line impedances and three target parameters as explained in Section 4.1.4 are also optimized together with the physical dimensions. Mak ing iterations with SBEM leads to the physical dimensions for the two filter examples as shown in Table 4.9. Wi, W2, S and additional physical dimension g (the distance between the conducing strip and the ground layer as shown in Figure 4.23) are layout dimensions. The length of each coupled section is again taken as the quarter-wavelength (at the center frequency) based on the arith metic mean of the phase velocities for the two modes in the coupled section. Also, the length of each line in all coupled sections is made shorter to take into account open end fringing capacitances. Using the physical layouts, filter circuits are simulated on a full-wave Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 69 0.0 dB — — -— -10.0 dB IS111 (Momentum) IS211 (Momentum) IS111 (Ideal) IS21I (Ideal) -20.0 dB -30.0 dB -40.0 dB -50.0 dB 1.0 2.0 3.0 4.0 5.0 frequency (GHz) 6.0 7.0 Figure 4.24. The performance of a 3-layer CPW parallel coupled-line band pass filter for topology A EM simulator. The performances of two different CPW filters in multilayer configurations are shown in Figure 4.24 and Figure 4.25. Center frequency, bandwidth and ripple level for these filters as obtained from the design cal culation (based on SBEM and MDS) and EM simulations are shown in Ta ble 4.10. Here we have compared these simulation results. A good agreement to the desired values verifies the design procedure proposed here. However, deviations at the higher frequencies may be related to the loss of accuracy of quasi-TEM approximation. The results from the EM simulation show a fairly good agreement to our design based on SBEM analysis. As in the cases of in homogeneous microstrip filters, the shift of center frequency and the deviation Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 70 0.0 dB — — -— -10.0 dB IS111(Momentum) IS211 (Momentum) IS111 (Ideal) IS211 (Ideal) -20.0 dB -30.0 dB -40.0 dB -50.0 dB 1.0 2.0 3.0 4.0 5.0 frequency (GHz) 6.0 7.0 Figure 4.25. The performance of a 3-layer CPW parallel coupled-line band pass filter for topology B from the desired filter response are attributed to the effect of other disconti nuity reactances. Taking the arithmetic mean of two different phase velocities for the calculation of the length of the coupled lines may also be a reason for the deviation from the desired specifications. 4.4 Discussion Systematic design procedures for asymmetric parallel coupled-line mi crostrip filters in a homogeneous and an inhomogeneous multilayer substrate environment and for CPW filters have been presented. The necessary design equations have been formulated and lead to the implementation of various Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 71 Table 4.10. Center frequency, bandwidth and ripple for 3-layer CPW parallel coupled-line band-pass filter designs Ideal response SBEM Topology A Topology B M omentum Topology A Topology B Center Frequency (GHz) 4 3 dB Bandwidth (%) 30 Ripple Level (dB) 0.5 3.69 3.69 38.21 38.48 < 0.66 < 0.65 3.73 3.72 38.61 34.41 < 1.41 < 1.55 parts in the design procedure. The design procedure of homogeneous multi layer filters is used as the starting point for the development of the design for inhomogeneous coupled line microstrip filters. An optimization procedure combined with SBEM analysis is used to arrive at the physical dimensions of the filter starting from filter specifications. The critical part of the design is the optimization process used in finding the physical dimensions. Other meth ods such as Artificial Neural Network modeling discussed in Chapter 5 may be used to accelerate the optimization process substantially. S-parameters for each coupled section are calculated separately and then combined to provide the performance of the whole circuit. Since the calculation using NMPs from SBEM is based on a quasi-static analysis, it does not take into account the existing fringing field around the open-end lines. However, it provides an approximate but a fast way to verify the design. A full-wave EM simulation using the method of moments has been used to verify the design procedure. Finally experimental measurements have been performed to verify these designs. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 72 The determination of line impedances affects the width of each cou pled section. In some cases, these impedances can play a significant role in deciding the corresponding physical geometry. For the procedure described here, we used values between 10 Q and 80 f2 for the line impedances. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. CHAPTER 5 DESIGN OF END-COUPLED BAND-PASS FILTERS IN MULTILAYER CONFIGURATIONS Another kind of filter configuration studied in this project is endcoupled band-pass filters. This configuration results in a simple physical struc ture containing gap coupled sections between half-wavelength resonators. No discontinuities, other than capacitively coupled gaps, occur in this circuit. Con ventionally, these filters have been utilized in single layer configurations and designed based on the method available in the literature [7, 54]. This method, however, is suitable for a single-layer filter structure only. The single layer restricts the bandwidth less than 15 % [7]. In this Chapter, multilayer end-coupled band-pass filters are dis cussed. The key motivation has been overcoming the narrow band restriction existing in single-layer configurations. A design procedure has been developed using a full-wave simulation program (HP-Momentum). Besides, an ANN model has been developed successfully for reducing the design time. 5.1 Derivation of Design Procedure The general configuration of an end-coupled band-pass filter realized in two-layer structure is shown in Figure 5.1. Each resonator is half-wavelength long at the design frequency, and can be placed at different layers depending Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 74 on the design topology. Cross-section at xx’ Figure 5.1: The layout of a multilayer end-coupled band-pass filter Single-layer end-coupled band-pass filters using the equal widths of resonators have been designed following the design procedure available in the literature [7, 54]. Because the tight coupling between the resonators is needed for wideband filters, multilayer configurations are employed in this thesis. To derive design equations, the general end-coupled band-pass filter in Figure 5.1 is redrawn as a transmission line circuit shown in Figure 5.2. The gaps between the resonators are modeled by 7r-network of capacitances [7,65]. For these endcoupled band-pass filters, the characteristic impedances for each resonator can be different and the resonators can be placed at different layers. i. M)N Figure 5.2. An equivalent transmission line circuit for end-coupled band-pass filters This transmission line circuit in Figure 5.2 can be rewritten as shown in Figure 5.3 when dN = 4>+—-+^*+‘ . An equivalent circuit shown in Figure 5.4 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 75 using admittance inverters and half-wavelength resonators is then employed to eventually rewrite transmission line circuit shown in Figure 5.2 using the net work equivalence shown in Figure 5.5. Figure 5.4 shows that this equivalent circuit is now identical in form with the parallel coupled-line filter equivalent circuit shown in Figure 4.4. In Figure 5.4, J-param eters are determined from the characteristic impedances (Z0, Z 0j , . . . , Z on), low pass filter prototype el ements and the bandwidth as derived in Eq. (4.4). <j>is 180° at the design frequency. For the circuits in Figure 5.2 and Figure 5.4 to be equivalent, the admittance inverters must be equivalent to the capacitors and the transmission lines combination as shown in Figure 5.5. fti.i 3 L = = » H l-iC ± 3 C ------ ------- Figure 5.3. A modified transmission line model for end-coupled band-pass filters -90 -90 -90 Figure 5.4. An equivalent circuit using admittance inverters and A/2 resonators {<f>= 180°) Equating ABCD matrices of the two circuits in Figure 5.5, the fol lowing relations are derived. B pon + B.S N B p \n + B sn _ Z q (N -I) Z qn Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. (5.1) 76 J®SN • -------- • -------- A -------- • JN - 90 ° j^ P lN ,^ jfi>2N ZpN --------• Figure 5.5. The relation between an admittance inverter and a gap expressed by susceptances and transmission lines BpiN + Bp2N + B p i n B p 2n + 1 / ( Z q(n - i ) Z q n ) Bsn J n Z o(n - \ ) Z qn — JN = K 2 (5.2) Then, <f>N and On are then determined as: (j>N ~ tan_1[____________________ 2(Bsn + Bp 2n)_____________________j Z o(n - i ){B p \ n B p 2n + B p2n B s n + BSNB P1N — 1 /(Z o(n - i )Z qn) (5.3) On — 180° + <t>N + <t>N+ 1 (5.4) For a simple case of single layer filters using the same characteristic impedances (Z q) and ignoring shunt susceptances (B p i n etc.), we get B sn = Jn 1 - ( J n Z q )2 0jv = —tan 1(2Z qB s n )These relations are exactly same as those available in the literature [7, 54] Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 77 The two equations (5.1) and (5.2) are used for finding the values of the shunt and series susceptances needed for the filter design. Once the values of these susceptances are determined, the electrical lengths to be used are calculated through the values of <j>^ s in Eq. (5.3). Since the gap between the two resonators determines the susceptances (Bpin, Bp 2 n and B Sn) in Eq. (5.1) and Eq. (5.2), the design of the gap geometry plays a crucial role in the design of end-coupled band-pass filters. A full-wave simulation program has been used for calculating these susceptances and optimizing the geometries for the gap to yield the desired parameters (K i and K 2)- In most cases, it takes a long time to optimize this gap geometry using a full-wave simulator. Therefore, an ANN model has been developed as an alternative method (discussed in Section 5.4) to reduce the optimization and design time. 5.2 Description of Design Procedure The overall design procedure developed for multilayer end-coupled band-pass filters is summarized in Figure 5.6. This procedure can be divided into three parts: (1) Evaluation of two design parameters (K \ and K 2) as derived in Eq. (5.1) and Eq. (5.2), (2) Determination of physical dimensions (widths and gap spacings) that yield the design parameters (K \ and K 2) as evaluated in Part (1), and (3) EM simulation and experimental measurement based on the physical geometry obtained in Part (2) to validate the design. For P art (1), desired design parameters (K i and K 2) for each gap are evaluated using filter specifications (bandwidth, the number of resonators, Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 78 .Ran.I Filter specifications Initial guess for w j'w2 and g for each gap C h a n g e ^ ’s Change wj ,v^ ,g Momentum Bad 2 design parameters (K, , K , ) for each gap Calculate Compare (Kj . K j ) Good Part 2 Calculate Calculate Length of sections Part 3 EM simulation/ Measurement Comparison Final design Figure 5.6: A design procedure for multilayer end-coupled band-pass filters Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 79 ripple level and characteristic impedances of transmission lines) as derived in Eq. (5.1) and Eq. (5.2). Since the widths of half-wavelength transmission line resonators can be selected by the design, the characteristic impedances (Z0/v’s) can be chosen independently. The values of impedances (Z0N’s) affect the values of design parameters ( K\ and K 2). For Part (2), design parameters (Ki and K 2), determined in Part (1) for each gap, are used to find the physical geometry for each gap coupled section. In order to find physical dimensions for each gap, HP-Momentum was used to calculate the series and shunt capacitances. These capacitances determine the values of the left hand sides of Eq. (5.1) and Eq. (5.2) (i.e. K \ and K 2). EM simulations are carried out iteratively for each gap until correct values of the desired design parameters (K\ and K 2) are obtained. The characteristic impedances (Zo/v’s) are also optimized for appropriate physical geometry of each gap coupled section leading to the desired K\ and K 2. For P art (3) of the design procedure, the susceptances for each gap de termine the electrical lengths of transmission line resonators given by Eq. (5.4). Using the physical dimensions (widths, gap spacings and lengths), the com plete circuit is simulated on HP-Momentum. For better performance, some adjustment may be performed for the gap spacing after EM simulations of the complete circuit. Eventually, the results of this simulation are compared to the experimental measurements to verify the design. 5.3 Design Examples Two design examples of two-layer end-coupled band-pass filters (A and B) correspond to the filter specifications shown in Table 5.1. Because these Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 80 Table 5.1: Specifications for multilayer end-coupled band-pass filters Design frequency Bandwidth Ripple Number of resonators Sr2 £rl h2 h .L Design A 3 GHz 30 % 0.5 dB 5 2.2 2.2 10 mil 10 mil Design B 4 GHz 35 % 0.5 dB 5 2.2 2.2 10 mil 10 mil filters are implemented in two layer structures, adjacent transmission line res onators are placed at different levels. A gap geometry consists of two different widths at the two sides and an overlapping section as shown in Figure 5.1. All the 3 dimensions {W\, W2 and g) for each of the gaps are optimized using HP-Momentum by adjusting the spacing and the characteristic impedances of transmission lines. The optimized values of gaps’ dimensions are listed in Table 5.2 and Table 5.3. Electromagnetic simulations were carried out for the physical geome tries of the two filters shown in Figure 5.7 and Figure 5.10. Figure 5.8 and Table 5.2. Physical dimensions of a two-layer end-coupled band-pass filter (units in mm) for Design A. Dimensions Wi, W 2, g and I are shown in Figure 5.1 Section # W! w2 9 I 1 1.6004 1.991 4.7 28.7251 2 1.991 1.6004 3.12 32.2453 3 1.6004 1.991 2.5 30.8652 4 1.991 1.6004 2.5 32.2373 5 1.6004 1.991 3.12 28.7837 6 1.991 1.6004 4.7 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. - 81 Figure 5.7. The physical layout for a two-layer end-coupled band-pass filter (Design A) O.OdB IS111(Momentum) IS211 (Momentum) o IS111(Measured) • IS211 (Measured) -1 O.OdB -20.0dB -30.0dB -40.0dB -50.0dB 1.5 2.0 2.5 3.0 3.5 frequency (GHz) 4.0 4.5 Figure 5.8. The performance of a two-layer end-coupled band-pass filter (De sign A) Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 82 Table 5.3. Physical dimensions of a two-layer end-coupled band-pass filter (units in mm) for Design B. Dimensions W\, g and I are shown in Figure 5.1 Section # Wx W2 9 I 1 1.6004 1.991 3.73 21.172 2 1.991 1.8054 2.58 23.5294 3 1.8054 1.895 2.16 22.588 4 1.895 1.8054 2.16 23.5237 5 1.8054 1.991 2.58 21.1621 6 1.991 1.6004 3.73 - Figure 5.9. The photograph of two-layer end-coupled band-pass filters fabri cated on RT/duroid 5880 (bottom: Design A, top: Design B) Figure 5.10. The physical layout for a two-layer end-coupled band-pass filter (Design B) Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 83 O.OdB OOOOOOO^OOOOOOOf OOOOfrOOfT ^rooooooo^oooooo o<> Oo I -1 O.OdB -20.0dB -30.0dB ____ 2>l____ IS111(Momentum) IS211 (Momentum) IS111(Measured) IS211 (Measured) -40.0dB -50.0dB 2.0 2.5 3.0 3.5 4.0 4.5 frequency (GHz) 5.0 5.5 6.0 Figure 5.11. The performance of a two-layer end-coupled band-pass filter (Design B) Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 84 Table 5.4. Center frequency, bandwidth and ripple level for multilayer endcoupled band-pass filters Specification Design A Design A Momentum simulation Design A Design B Measured Design A Design B Center Frequency (GHz) 3 dB Bandwidth (%) Ripple Level (dB) 3 4 30 35 0.5 0.5 3.071 4.071 27.65 33.65 <1.017 <1.317 3.2 4.2 20.31 25.95 <1.75 <1.71 Figure 5.11 show the performances obtained from full-wave simulations and experimental measurements. Two filters have been fabricated on RT/duroid 5880 for experiment as shown in Figure 5.9. Gap spacings can be adjustable for better performance. A good agreement between the filter specifications and the simulated performance is shown in Table 5.4 in terms of three important parameters. The center frequency shifted slightly higher and the 3-dB band width is smaller than what was expected. Furthermore, the pass-band ripple level is greater than the desired 0.5 dB. This may have been caused by ignoring the real part in the determination of capacitances of gap coupled sections as only the imaginary parts of Y-parameters have been used for calculating [C] matrix. Dielectric loss and conductor loss also affect the pass-band ripple. Less accurate calculation of the lengths of gaps and transmission lines may yield a frequency shift. Measured results show a slight deviation from the specifications and Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 85 simulation results. This may be caused by imperfect alignment of two substrate layers, finite ground plane and possible air gaps between two layers. Since an air gap makes the height of the bottom substrate higher and the effective dielectric constant lower than the nominal values, the center frequency shifted to higher and the insertion loss was worsened. This air gap will cause the simulation results to change by including this effect into the simulation process. Specially, the decrease of 3-dB bandwidth arises from the dielectric, conductor and radiation losses that worsen the magnitude response of the insertion loss. 5.4 D esign o f E n d -C o u p le d F ilte rs w ith A N N M odels A long computer time is required to optimize various gap dimensions because repeated full-wave simulations need to be carried out. This kind of time consuming optimization process does not lead to a fast and convenient design for end-coupled band-pass filters. The use of ANN models can reduce considerably the required CPU time to optimize gap dimensions. The method ology used for developing accurate and efficient ANN models has been well discussed and demonstrated in [66]. Some basic concepts of ANN modeling are reviewed here. The use of ANN models for design of end-coupled filters is demonstrated. 5.4.1 A N N M odeling The ANN architecture used in model ing end-coupled filters is shown in Figure 5.12 and consists of an input layer, an output layer, and one hidden layer. It is a multilayer, feed-forward ANN, utilizing the error-backpropagation learning algorithm [67]. The hidden layer, which incorporates nonlinear activation functions, allows modeling of complex Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 86 input/ output relationships between multiple inputs and multiple outputs. In puts are connected to the hidden layer by a set of weights. The input Uj of the j - th neuron in the hidden layer is obtained by the summation of the weighted input variables and an additional bias term. Thus the input Uj can be represented as: % = E w* x ‘ <5-5) x=0 where X 0 = 1 and WjP is the corresponding connection weight between the input layer and the hidden layer. The output of the neuron in the hidden layer is obtained as: Zj = g{uj) (5.6) where g(u) is the activation function of the neuron. The activation function of the input layer is the identity the hidden layer. function since the inputs are directly passed to Betweenthe hidden layer and the output layer, a sigmoidal function is used for the activation function as: = <5-7> The hidden layer is connected to the output layer by another set of weights. The outputs of the output layer are obtained in a manner similar to the ones of the hidden layer. By combining all these steps one can obtain the input/output relation of the ANN as: Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 87 u «>> es 00 3 B* O 3 o o o N 2e ■ •oo X 00 oo 3Q. C Figure 5.12. The architecture of typical single hidden layer artificial neural network Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 88 Yk = g{vk) = « ( £ < ’» ( £ " # ’*)) j= 0 (5-8) i= 0 Training of the ANN model is accomplished by adjusting these weights to give the desired response. The ANN learns relationships among sets of in pu t/output d ata which are characteristic of the component under considera tion. First, the input vectors of the training dataset are presented to the input neurons and output vectors are computed. ANN outputs are then compared to the known outputs (of the training dataset) and errors are computed. Error derivatives are then calculated and summed up for each weight until all the training examples have been presented to the network. These error derivatives are then used to update the weights for neurons in the model. Training pro ceeds until errors become lower than prescribed values. Details of the training algorithm are given in [68, 69]. 5.4.2 C o u p led F ilte rs A N N M o d elin g M eth o d o lo g y for M u ltila y e r E n d In order to shorten the optimization time, ANN models may be employed. In this thesis, CU-ANN® has been used for this purpose. ANN models can be used to effectively determine physical values for gap cou pled sections from given desired parameters (synthesis). ANN models have also been developed providing the correct Y - or S-parameters based upon the physical geometry (analysis) to be used in commercial microwave circuit sim ulators. Simulations using HP-Momentum are used to provide a training data for both the synthesis and analysis ANN models. Training data is obtained by specifying the design frequency, the physical dimensions and their ranges for Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 89 the gap coupled sections under consideration. Y - or S-parameters obtained from EM simulations are used for training the ANN models. / Analysis model W1 for a coupling gap g Figure 5.13: Analysis ANN model for gap coupled sections / Synthesis model K 1 for a coupling gap K„ Figure 5.14: Synthesis ANN model for gap coupled sections For analysis model, the design frequency and physical dimensions such as widths and gap spacing are used as inputs to ANN models as shown in Figure 5.13. The outputs are the elements of the Y-parameters. Once the Y-parameters of a given gap coupled section have been obtained, they can be used to determine 2 design parameters (K i and K 2) in Eq. (5.1) and Eq. (5.2), and then <f>s s in Eq. (5.3). Transmission lines in the multilayer structure are also modeled using ANNs to yield the characteristic impedances Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 90 and propagation constants as outputs. Since these two parameters determine S-parameters consequently, analysis models of the gap and the transmission line models are linked to commercial microwave circuit simulators as shown in Figure 5.15 for circuit analysis and optimization. This simulator passes the input variables to the user defined linear model subroutine, which is used to integrate the model into the circuit simulator [70]. For synthesis model, two design parameters ( K i , K 2) and the design frequency are used as inputs, and the desired physical parameters are used as the outputs as shown in Figure 5.14. This is an inverse modeling problem because the inputs and outputs are interchanged. This mapping can often cause multi-valued outputs with respect to the one input. In addition, since the input space is (most likely) not characterized fully, the ANN model can produce incorrect results due to the absence of training data for particular regions of input data. In order to overcome this problem associated with the inverse mapping, the outputs of the synthesis ANN model are reconnected to the inputs of the analysis model as shown in Fig 5.16. K \ and K 2 calculated from the outputs of the analysis model are then compared to those obtained from the circuit specifications which have been used as inputs to the synthesis model. In this way, a determination can be made as to the accuracy of the synthesis model for a given region of input space. If the model is not accurate for a given set of K \ and K 2, they are altered by selecting different set of Z 0N's. 5.4.3 A N N M odels The Design of Multilayer End-Coupled Filters Using Both synthesis and analysis models for a gap coupled sec tion have been developed using 875 simulations performed on HP-Momentum which have been used for training/testing data for ANN models. W\, W2, g and Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 91 Commercial microwave circuit simulator Model input variables User-defined linear model subroutine EM-ANN EM-ANN model inputs model outputs Feed-forward ANN subroutine EM-ANN model data EM-ANN model file Figure 5.15. Flow of data for linking EM-ANN models to commercial mi crowave circuit simulators Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 92 Circuit specifications J-parameters Change Z ^ s No Design parameters (K p iq ) Synthesis ANN Compare Acceptable, W , , W2 and g Analysis ANN Figure 5.16. A synthesis procedure for gap coupled sections using ANN models frequency have been repeatedly altered using a uniform grid. One end-coupled band-pass filter has been developed using ANN models in two layer structure. For comparison, the specifications used in Section 5.3 are again selected for the design example. Starting with these circuit specifications, physical param eters obtained using synthesis and analysis models for gap coupled sections are shown in Table 5.5. Using these physical dimensions, this filter is analyzed on a circuit simulator which incorporates the analysis ANN models of gap and transmission lines. Figure 5.17 illustrates filter performance of this filter. Simulation results from Momentum using the physical geometry without ANNs are repeated here for comparison with these performances. Table 5.6 gives the center frequency, Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 93 Table 5.5. Physical dimensions of a two-layer end-coupled band-pass filter (units in mm) with ANNs (Design A) Section # Wi W2 9 I 1 1.6212 1.8035 4.88 28.854 2 1.8035 1.6212 3.35 32.2224 3 1.6212 1.8035 2.89 30.8876 4 1.8035 1.6212 2.89 32.2224 5 1.6212 1.8035 3.35 28.854 6 1.8035 1.6212 4.88 - 0 dB — — -— -10 dB IS111(Momentum) IS211 (Momentum) IS111(ANN) IS211 (ANN) -20 dB -30 dB - -40 dB -50 dB 1.5 2.5 3.5 4.5 frequency (GHz) Figure 5.17: Performance of a two-layer end-coupled filter using ANNs Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 94 Table 5.6. Center frequency, bandwidth and ripple for a two-layer end-coupled band-pass filter with ANNs Specification M om entum simulation ANN analysis Center Frequency (GHz) 3 3.07 3.08 3 dB Bandwidth (%) 30 27.65 28.90 Ripple Level (dB) 0.5 < 1.017 <1.084 bandwidth and ripple level of the designed filter with ANNs. The filters de signed with ANNs and without ANNs are comparable. The ripple level for the ANN design is slightly larger than desired. Besides, overall shapes are slightly deviated from the filter designed without ANNs. However, the advantage of using ANN models for filter design is a large savings in required CPU time as shown in Table 5.7. In this table, the CPU time on an HP700 workstation and the number of altering physical geometry is compared. The optimization time without ANNs is also presented for comparison. The optimization time of the complete circuit using the linked analysis ANN models on HP-MDS [71] shows an efficiency in the filter design. 5.5 Discussion Two examples of end-coupled band-pass filters in a two-layer con figuration have been designed using the design procedure developed in this Chapter. Overlapping gaps between resonators make it possible to design wideband filters, and these overlapping gaps can only be realized in multi layer configurations. In addition to wide bandwidth, more design flexibility Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 95 Table 5.7. Design times and required iterations for end-coupled filters with ANN modeling and without ANNs Section ANN # iterations 1 2 3 ANN optimization using HP-MDS W ithout ANN 1 2 3 6 4 4 CPU 0.83 0.55 0.55 time sec. sec. sec. 6 58 sec. 84 64 52 84 min. 25 sec. 50 min. 04 sec. 45 min. 12 sec. has been obtained with multilayer structure. Taking the shunt capacitances of gap coupled sections into account, we characterize the gap geometry bet ter than the conventional method which does not consider those capacitances. Newly derived design parameters have been used as criteria for optimization of gap geometry. Due to the huge amount of time for optimization process, ANN mod els have been developed. The ANN models reduce the required CPU time drastically in comparison with the way used earlier in this Chapter. Once the ANN models are set up, new designs with different circuit specifications can easily be carried out in a very small fraction of the time. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. CHAPTER 6 MODELING FOR THREE-LINE BALUNS IN MULTILAYER CONFIGURATIONS 6.1 Introduction Many microwave applications need the balun which transforms a bal anced transmission signal to an unbalanced transmission signal and vice versa. These include double balanced mixers [72-78], push-pull amplifiers [79-81], antenna feed networks [82-90], frequency doublers [91-93] and etc. A large number of balun configurations have been reported in literature. Among them a planar version of Marchand balun has been adapted for a long time by using microstrip lines [8 , 20, 40-42], and applications of planar Marchand baluns have steadily increased in microwave integrated circuits (MIC) and microwave monolithic integrated circuits (MMIC). For use in MIC and MMIC, wide bandwidth and compactness of baluns are of high interest. Multilayer configurations make MIC/MMIC more compact and can exhibit wide bandwidths due to inherent tight coupling in coupled-line compensated baluns. Besides, flexible design can be realized by using multilayer configurations. A compact configuration of 3-line balun reported recently in litera ture [43] is shown in Figure 6.1. This 3-line balun has more compactness than Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 97 planar Marchand baluns which combine two identical coupled lines with differ ent termination. However, a design procedure for implementing 3-line baluns in single layer or two-layer geometry has not been available. In this Chapter, we describe a generic approach [94] suitable for de signing this 3-line balun configuration for single-layer and two-layer structure. We show that this 3-line balun configuration can be represented as a combi nation of two identical directional couplers each consisting of a 2 -coupled line section. This representation is a key step in the design procedure developed. The procedure has been used for designing single-layer and two-layer 3-line baluns. The approach is verified by comparing the results with full-wave sim ulation results. In addition, a two-layer 3-line balun has been fabricated and measured to verify the design procedure developed. Zout Z in • • z out I = A/4 Figure 6 .1 : The general configuration of a 3-line balun 6.2 Description of Design Procedure 6.2.1 Couplers Representation of a Balun by Two Coupled-Line When the two balanced terminations of a balun are considered as Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 98 two ports, a balun circuit can be considered as a 3-port network as shown in Figure 6.2. The characteristics of baluns can generally be expressed in terms of the reflection coefficient (Su = 0 ), and the sum of £>21 and S 31 (S2i + S 3 1 = 0 ). 3-port S-parameters of an ideal balun are given by: 0 - e ~ i 9/y/2 e~ie/y/2 - e~ i29/2 -e ~ i29l2 - e~ i29/2 —e~i29/2 [*5] Balun — e~i9/ y/2 The 3-port block diagram (Figure 6.2) of a balun can be divided into two separate blocks as shown in Figure 6.3 where the S-parameters of the two sub-circuits are: ,-jO —e~j9 [5] CircuitA —e~i9 IN (i) ( 6.2) CircuitB — — 0 i~>9 0 (2) OUT+ (3) OUT- Balun Figure 6.2: The block diagram of baluns One of the possible methods of realizing circuits A and B is by use of appropriately terminated coupled-line directional couplers as shown in Fig ure 6.4. This configuration can behave like a balun when: Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 99 IN Circuit A OUT+ Circuit B OUT- (1) Figure 6.3: The bifurcated block diagram of baluns CIRCUIT A CIRCUIT B Figure 6.4: A 3-line balun composed of two 2-line couplers Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 100 3 0 [S]cir«.«A(0 = 90°) = 0 ~3 -3 0 >[S']CircuitB^ = 90°) = 3 0 (6.3) when 9 is the electrical length of the two couplers. The combination of these two 2-line coupler circuits yields the fol lowing S-parameters and functions as a balun: 0 j / V 2 -j/y /2 j/y /2 1/2 1/2 -j/y /2 1 /2 1 /2 • (6.4) To use the design procedure for asymmetric directional couplers re ported earlier [9, 10, 20], [Y] matrices for the circuit A and the circuit B need to be represented in terms of the coupling factor (/?) and the coupler port admittances (Yen, Y02) where Y01 = 1/Z0i ,Y 02 = l / % 2, as: 0 [y\ CircuitA — -3 ~3 PVYqiYqi (6.5) 0y/Yp i Yqz 0 yfiHP and ~3 CircuitB — Vqi —0y/Yp 1Yot (6.6) : Yo1 —0VY q1 Vq2 ~3 0 The corresponding [S] matrices with the input impedance (2Zin) and the output impedance (Zout) are calculated using [Y] matrices obtained in Eq. (6.5) and Eq. (6 .6 ) as: Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 101 Table 6.1. Some choices of Zoi, Z$2 for balun input/output impedances Zin = Z ^ = 50Q Z q2(£1) 20.42 40.825 100 Zoi(fi) 38 40.825 50 /?(Coupling factor) 0.367 0.5 0.707 I | 2(1—P) [•S']C ircuitA 1 T — j 2 0 y /2 ( 1- P )y01Y o iZ in Zout X (6.7) j 2 0 ^ 2 ( l - P 2 )Yol Yo2Z in Z out X [<5] Circuits — y ^ l - 0 2 + * 0 Y Oiy / Y 5 i Y m Z i n Z o . t - 2Ym lY 0i + 0 2 YO2 ) Z i n Z ou, >2^1 - 0 2i-Yoi + SV Y ^Y m )V *Z inZ °~■ > 2 ^ 1 - /9=(—Vbi + 0 v 'V o iV O2 )v '2 Z i n Z (>u , 1 - /32 + 4 ^ y o iv ^ i'V o :Z ,„ Z 0„. - 2y0i(Voi + tfaVo2)^i« ( 6 .8 ) where X — l+/?2(—l+2Yoi5'o2^in^out) and ^ — 1—/22—4/?Yol^/^ol^o2^m^out^■ 2yo1(Kol + / ^ ^ o u t Equating [S]circmM in Eq. (6.3) to [S]c«r««M in Eq. (6.7), and [S ]cw :ts in Eq. (6.3) to [5]CircuttB in Eq. (6.8), H t /S ( 6 -9 ) and Z02 = 4Z01 - ^01 (6.10) We note th at for a given set of balun impedances at input and output ports Zin and Zmt, the values of coupled line parameters Z qi and Z 02 are not Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 102 unique. For example when Zin = Zmt = 50ft, any of the combinations shown in Table 6.1 will satisfy Eq. (6.9) and Eq. (6.10). It is found that different choices for the values of coupler impedances (ZqX and Z02) lead to different bandwidths for the balun. Network simulations were carried out for two baluns, one using symmetrical directional coupler with Z Qi = Z 02 = 40.825ft, and the other with Z 0i = 38Q and Z Q2 = 20.42ft. For the symmetrical case, S u bandwidth (1‘S'nl < -10 dB) is 48.4 %, the amplitude imbalance is within 0.91 dB, and phase error is 0°. For the non-symmetrical case, S n bandwidth is 20.9 %, the amplitude imbalance is less than 1.68 dB, and phase error is 0°. Thus we note th at among the cases studied, the symmetrical case yields better performance. For this design, Z 0 1 = Z 02 = Z 0, then /? = 0.5 and Z 0 = yj2ZinZmit/Z. 6.2.2 D esign o f 3 -L in e B alu n s Design of the 3-line balun shown in Figure 6.1 is based on finding an equivalence between a 6-port section of 3 coupled lines (shown in Figure 6.5 (a)) and a 6-port combination of two couplers as shown in Figure 6.5 (b). The normal mode parameters of the 3coupled lines shown in Figure 6.5 (a) can be found by equating 6-port [Y] m atrix of these 3-coupled lines to the [Y] matrix of the 6-port circuit shown in Figure 6.5 (b). For the circuit shown in Figure 6.5 (b), the two sets of identical 2-coupled lines shown enclosed by the dotted lines are perfectly isolated. For finding out this equivalence, three different phase velocities of the coupled line in Figure 6.5 (a) are assumed to be equal. This approximation is similar to that commonly used for design of microstrip directional coupler. Our experience in this research project shows that good balun designs can be arrived at even when using this approximation. This procedure leads to the following four relations among the normal mode parameters of the structure in Figure 6.5 (a) Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 103 • 4 • 6 (a) 1 • 3 » (b) Figure 6.5. Equivalence between (a) a section of 3-coupled lines and (b) a 6-port network combination of two couplers Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 104 and the c - and 7r-mode parameters of two identical couplers in Figure 6.5 (b). ml R irY c 1 — R cY ttI p itrr ( 6 . 11 ) -q lie Yp, - ¥„, _ ¥ c l - ¥ , : R v 1 - R v2 Rts (6.12) Rc Rv2Yp\ —Ry\Yn\ _ RcYcl — R^Yni RviRv2{Ypl - Ynl) ~ R cR„(Yci - ywl) (6.13) (6.14) where R y 1, R v 2 are the voltage ratios and Ym1, ynl, Ypi are the admittances of 3 normal modes (m ,n ,p modes) for 3-coupled lines [95], and R c, R n,Yci, Y^i are c- and 7r-mode voltage ratios and admittances for 2-line couplers [57]. It may be noted th at we have only 4 equations (6.11-6.14) for 5 independent values (i?vi, R vi, F'mi, F„i and Ypl) of NMPs of 3-coupled lines. Thus one of these parameters needs to be selected independently and this choice leads to different designs for the balun. These NMPs for the 3-line structure are used to find the geometry of the 3-line balun. 6.2.3 P h y sical G e o m e try for th e 3 -L in e B a lu n geometry is determined by an optimization process. This process compares iteratively the desired NMPs for 3-coupled lines (evaluated as indicated in Section 6.2.2) with NMPs calculated from selected dimensions for 3-coupled lines. A quasi-static field analysis program SBEM [9, 10] has also been used to calculate inductance and capacitance matrices for specific geometries. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Physical 105 Balun specifications Initial guess for W! ,W2 and s (^ in ’ ^om ’ 5) ) SB E M f Coupler specifications (13=0.5,2^) o r (p, , 7q2) Calculate [L] & [C] NM P for the coupler Calculate NM P SBEM RVi chosen NM P for the 3-line balun (Ryi’Kyz’ %ii ■Y m» Ypi) Electrical Design Change RVI, Change ,V£ ,S Bad Compare Good Final ^ ^ ,S for the 3-line balun Design of Physical Dimensions Figure 6.6: A design procedure for 3-line baluns The design procedure discussed in this section is summarized in the flow diagram of Figure 6.6. The electrical design part in the left hand column yields NMPs for 3-coupled lines, and the physical design part in the right hand column leads to the physical dimensions appropriate for realizing the NMPs calculated in the electrical design part. For the physical design part, physical parameters (Wi, W2 and S) are altered iteratively for optimization. In addition, an intermediate parameter (‘a’) used in the design of 2-line couplers (explained in Section 4.1.3) can be altered, and R v i can also be altered for optimization of the physical parameters. The design is verified by simulating the optimized geometry on a fullwave electromagnetic simulator and measuring the performance of a two-layer Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 106 Table 6.2: Parameters for the design example of a single-layer 3-line balun Inputs h 15 mil 10 Zin 50 ft Zout 50 ft Outputs Z qi Z 02 Coupling factor(/?) Wx W2 S 40.825 ft 40.825 ft -6.0 dB 0.348 mm 1.086 mm 0.018 mm 3-line balun designed and fabricated using the design procedure reported here. 6.3 D esig n E x am p les We illustrate the procedure developed by an example of a single-layer 3-line balun shown in Figure 6.7 and two examples of two-layer 3-line baluns shown in Figure 6.8 and Figure 6.9. OUT(3) OUT(2) I N(l) Figure 6.7: The physical layout of a single-layer 3-line balun 6.3.1 S in g le-L ay er 3 -L in e B aiu n s Input parameters and op timized output parameters for the single-layer design example axe shown in Table 6.2. In this case, the spacings between the adjacent lines are so narrow Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 107 Table 6.3. Parameters for the design example of a two-layer 3-line balun (Topology A) Inputs 20 mil hi h2 20 mil 2.2 ^rl 2.2 Cr2 Zin 50 ft Zaut 50 ft Outputs Zoi Zo2 Coupling factor(/3) Wi W2 S Length(at 3 GHz) 40 ft 35 ft -6.6 dB 4.280 mm 3.643 mm 1.710 mm 17.749 mm (0.018 mm in this example) that it is difficult to fabricate this design. Therefore we need to use two-layer circuits for this purpose. OUT(3) OUT(2) IN(1) Figure 6.8: The physical layout of a two-layer 3-line balun (Topology A) 6.3.2 T w o -L ay er B aiu n s Input parameters and optimized out put parameters for the two-layer design examples are shown in Table 6.3 and Table 6.4, respectively. For the 3-line structure used for the balun, the wave length is taken as the arithmetic mean of phase velocities of 3 normal modes divided by the design frequency. Using the physical geometry obtained, the two-layer 3-line balun Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 108 OUT(3) OUT(2) IN(1) Figure 6.9: The physical layout of a two-layer 3-line balun (Topology B) Table 6.4. Parameters for the design example of a two-layer 3-line balun (Topology B) Inputs 20 mil hi 20 mil h2 2.2 frl 2.2 Cr2 Zin 50 ft Zout 50 ft Outputs Zoi Zo2 Coupling factor (/?) W1 W2 S Length (at 3 GHz) 43 ft 55.7 ft -4.9 dB 1.343 mm 5.771 mm 0.506 mm 17.243 mm Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 109 0.0 dB -10.0 dB -20.0 dB IS111(Momentum) IS211 (Momentum) IS311 (Momentum) IS111 (ideal) IS21I (ideal) IS31I (ideal) -30.0 dB -40.0 dB 1.0 1.5 2.0 2.5 3.0 3.5 frequency (GHz) 4.0 4.5 Figure 6.10. The performance of two-layer 3-line balun (Topology A) designed by the procedure developed and comparison with an ‘ideal’ balun Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 110 0.0 dB -10.0 dB -20.0 dB IS111(Momentum) IS211 (Momentum) IS311 (Momentum) IS111 (ideal) IS21I (ideal) IS311 (ideal) -30.0 dB -40.0 dB 1.0 1.5 2.0 2.5 3.0 3.5 frequency (GHz) 4.0 4.5 5.0 Figure 6.11. The performance of two-layer 3-line balun (Topology B) designed by the procedure developed and comparison with an ‘ideal’ balun Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Ill 210.0 205.0 Momentum, topology A Momentum, topology B 200.0 195.0 6> 190.0 0} 2- 185.0 co, 180.0 175.0 170.0 165.0 160.0 155.0 150.0 1.0 1.5 2.0 2.5 3.0 3.5 frequency (GHz) 4.0 4.5 5.0 Figure 6.12. The phase imbalances of two-layer 3-line baluns designed by the procedure developed Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 112 Vias to ground <i ----------X __ . .... — ..........\ IX. .. V Via to upper layer (a) (b) Figure 6.13. (a) The layout of a two-layer 3-line balun fabricated on Duroid RT5880, (b) the photograph of a two-layer 3-line balun fabricated on Duroid RT5880 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 113 0.0 dB -10.0 dB -20.0 dB — IS111(Momentum) — IS21I (Momentum) — IS311 (Momentum) — e !S111(measured) — * |S211 (measured) — « IS311 (measured) -30.0 dB - -40.0 dB 2.5 3.0 3.5 frequency (GHz) 4.5 5.0 Figure 6.14. The measured performance of a two-layer 3-line balun (Topol ogy B) designed by the procedure developed and comparison with a full-wave simulation Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 114 210.0 205.0 Measured, topology B 200.0 195.0 (•6sp) 10S /-I-3S / 190.0 185.0 180.0 170.0 165.0 160.0 155.0 150.0 1.0 1.5 2.0 3.5 2.5 3.0 frequency (GHz) 4.0 4.5 5.0 Figure 6.15. The measured phase imbalance of a two-layer 3-line balun de signed by the procedure developed Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 115 Table 6.5: Summary of a two-layer 3-line balun performance (Topology A) Ideal M om entum Center frequency (GHz) 3 2.86 n \s u \ < -10 dB) (GHz) 2.67~3.33 2.26~3.45 IS21ICO 1^311(/) I S 21 — z s 31 (dB) -3.45~-3.01 -3.22~-2.48 (dB) -3.45~-3.01 -4.44~-3.48 180° 169.6° ~ 173.5° structures have been simulated on a full-wave EM simulator (Momentum). S-parameters obtained from an EM simulation are compared with those for an ‘ideal’ balun in Figure 6.10 and Figure 6.11. The performance of the ‘ideal’ balun is calculated using the desired NMPs and the phase velocities for the three modes assumed to be equal. The phase imbalance (ZS2i — ZS31) is plot ted in Figure 6.12. The performances of simulation and measurement are summarized along with an ideal response in Table 6.5 and Table 6 .6 . We note th at for topology A, the center frequency is shifted to 2.86 GHz, the actual transmission coefficients are in -4.44 - -2.48 dB range, the amplitude imbalance at the balanced output ports is within 1.96 dB and the phase error is less than 10.4° over the frequency range of 2.26 - 3.45 GHz where |5 u | < -10 dB. For topology B, the center frequency is shifted to 2.98 GHz, the actual transmis sion coefficients are in -4.44 - -2.56 dB range, the amplitude imbalance at the balanced output ports is within 1.88 dB and phase error is only 0.2° over 2.14 - 3.78 GHz where |S n | < -10 dB. Thus we note that the topology B yields simulated performance close to the ideal performance. Moreover, through sev eral simulations we find that the topology B allows 0.5 mm misalignment in the metallizations on the two layers. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 116 Table 6.6: Summary of a two-layer 3-line balun performance (Topology B) Ideal M om entum M easured Center frequency (GHz) 3 2.98 3.08 f{\S n \ < -10 dB) (GHz) 2.33~3.67 2.01~3.81 2.14~3.78 l& iK /) \SM ) ZS21 —lS z\ (dB) -3.46~-3.01 -3.78~-2.56 -4.31~-2.87 (dB) -3.46~-3.01 -4.44~_2.98 -4.99~-2.69 180° 180° ~ 180.2° 180.3° ~ 184.1° It may be noted that, as in other synthesis procedures at microwave frequencies, procedure developed here does not take into account via induc tances, discontinuity reactances, difference in the phase velocities of 3 normal modes, and dispersion in coupled lines. One needs to compensate for these effects by an optimization of the initial design obtained. However, the method developed provides an efficient tool for initial design. A balun using topology B was fabricated on the Duroid RT5880 sub strate. The layout is shown in Figure 6.13 where the lines to the input and the output ports are extended to locate connectors easily. Its performance is measured and plotted in Figure 6.14 and Figure 6.15. As shown in Figure 6.14 and Figure 6.15, the design frequency is shifted to 3.10 GHz, |S n | is less than -10 dB over 2.13 - 3.78 GHz. In this frequency range, the actual transmission coefficients varies from -4.99 dB to -2.2 dB, the amplitude imbalance is within 2.12 dB and the phase error is less than 4.51°. These measurement results agree fairly well with the simulation results. Some of the possible reasons for lack of better agreement are : the air gap between two layers, the lead in ductance of vias used to connect ground and two layers, non-identical physical lengths of the two extended output ports, misalignment between two substrates Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 117 and inaccurate calibration process (because of input and output connections at different levels). 6.4 Discussion A design procedure for the three-line balun (using the design of two- line couplers) has been presented. The analytical procedure yields normal mode parameters for the coupled lines. Physical dimensions are obtained by optimization using a quasi-static analysis program. Alternatively an EM-ANN (Electromagnetic Artificial Neural Network) model could be developed for this procedure. This method was verified by designing single-layer and two-layer 3line baluns. The single-layer version produces very narrow spacing between three strips, therefore, two-layer versions (that provide more design flexibility) have been implemented. A two-layer 3-line balun was fabricated and mea sured to verify the design procedure. Experimental results are compared to those obtained from a full-wave EM simulation. This kind of balun showed a good performance in spite of the use of imperfect fabrication facilities leading to a misalignment between the two substrates. Thus, this design allows a con siderable flexibility in the design procedure and yields reasonable tolerances for fabrication. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. CHAPTER 7 SUMMARY AND FUTURE WORK 7.1 Multilayer Microwave Circuit Design M ethodology A systematic approach for establishing efficient design methodologies of multilayer passive microwave circuits such as filters and baluns has been presented in this thesis. The determination of design parameters, the synthesis process, and the verification of the design comprise three parts for designing these multilayer circuits. Various equivalent networks have been utilized to derive the design equations for filters and baluns. Admittance inverter models and transmission line models play a key role in building the design equations for filters. Balun circuits have employed a design method used earlier for twocoupled line directional couplers for deriving the design equations. A multilayer multi-conductor transmission line model provides a comer stone for analyzing two-coupled lines and three-coupled lines to be used in setting up desired normal mode parameters. An analysis from the circuit configurations to net work parameters (i.e. S-, Y -, Z - or ABCD-parameters) makes it possible to establish these desired NMPs. These NMPs are then used as parameters to be optimized in the synthesis process part. The synthesis process finds phys ical dimensions for circuits using an optimization algorithm. A quasi-static field analysis program, (SBEM), has widely been used together with Simplex method, a commonly used optimization algorithm, for parallel coupled-line Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 119 filters and three-line baluns. End-coupled filters employed an ANN model for optimizing physical geometry. Once the ANN models have been developed, a large amount of time can be saved in finding physical parameters and in simulating circuits on a commercial microwave simulator. For the third part of the design methodology, a verification is needed using physical parameters obtained from the synthesis process. A network simulation and a full-wave electromagnetic simulation are available tools in computers for verifying the developed design procedures. Experimental measurements have also been per formed to confirm these design procedures. An important part of a whole design process is the optimization of physical geometry. Two main potential problems in the optimization process are: a possibility of stalling into local minima and a considerably large amount of required CPU time. As shown in the design of end-coupled band-pass filters, ANN models shorten the CPU time requirement and possibly avoid the local minima which can arise with conventional optimization algorithms. In summary, the general methodology th at have been developed generically in this thesis can be applicable to any circuits/components th at make use of multilayer multiconductor transmission lines. For instance, directional couplers, filters, planar baluns, spiral inductors and capacitors can be designed using this methodology. However, as we examined in this thesis, every circuit has its special features th at translate to specific design steps that are not con tained in the generic methodology. For parallel coupled-line filters, a special procedure to obtain the desired NMPs from the filter specifications is needed. Well known g - and J-param eters are used for this special purpose. For endcoupled band-pass filters, two design parameters other than NMPs are used Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 120 for the desired design values to be optimized. For 3-line baluns, the design of coupled-line couplers as an intermediate step to obtain the desired NMPs is utilized. Research reported in this thesis brings out these specific design details for these circuits. 7.2 M u ltila y e r M icrow ave C irc u it E x am p les 7.2.1 P a ra lle l C o u p le d -L in e B a n d -P a s s F ilte rs A design methodology has been developed to design multilayer parallel coupled-line band-pass filters. The main purpose of using multilayer structure in this fil ter is to design filters with a wide bandwidth. Since tightly coupled lines are necessary for a wide bandwidth, multilayer structure facilitate the physical lay out. Asymmetrical geometries for coupled lines are also employed to provide a design flexibility in multilayer configurations. Three different physical environments have been explored to realize this class of filters. Those are homogeneous (stripline), inhomogeneous(microstrip line), and CPW configurations. Because the homogeneous medium results in equal phase velocities for all normal modes, explicit expressions have been de rived for the desired NMPs. In inhomogeneous media, phase velocities are different for the different normal modes. In this case, one additional design freedom for optimizing the physical geometry exists. The CPW configurations can be implemented using design procedures for homogeneous and inhomoge neous cases. Two design examples have been carried out for homogeneous filters using 3 layers and 4 layers, respectively. For these filters (using 20 mil sub strates with er = 2.2), a 40 % bandwidth, 3 resonator configuration and 0.5 dB Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 121 pass-band ripple level have been realized at the center frequency of 10 GHz. A full-wave EM simulation has been performed over 2 - 1 8 GHz frequency range. Both of these examples show a close agreement with the circuit specifications. Also, two design examples have been carried out for inhomogeneous filters using 3 layers and 5 layers, respectively. 50 % bandwidth, 3 resonators and 0.5 dB pass-band ripple level were used as the specifications for 6 GHz center frequency filters. The substrates used in homogeneous filters were also utilized for inhomogeneous configurations. Designs were verified with full-wave EM simulations and experimental measurements. The results over 1 - 1 1 GHz frequency range have been shown to yield a good agreement with the filter specifications. The CPW configurations have also been used to create two different topologies of filters. Both of examples have been performed using 3 layers to realize 30 % bandwidth, 2 resonators, 0.5 dB pass-band ripple and 4 GHz center frequency. These designs were verified by full-wave EM simulations performed over 1 - 7 GHz range. These design examples implemented in the three different environ ments for multilayer parallel coupled-line band-pass filters show th at the de sign methodologies developed axe valid for any kind of different physical config urations and those can be applied to other circuits employing parallel coupled lines. 7.2.2 E n d -C o u p le d B a n d -P a s s F ilte rs A systematic design methodology has been developed to design multilayer end-coupled band-pass filters. Since the single-layer end-coupled filters are not suitable for obtain ing a wide bandwidth, multilayer structures were employed to overcome this Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 122 restriction in the bandwidth. These filters consist of gap coupled sections and the half-wavelength transmission lines. A full-wave simulator has been used to optimize the gap coupled section placed through multiple substrates. Since this approach requires a large amount of CPU time to optimize physical ge ometry for each gap coupled section, an ANN model has been developed to reduce the required CPU time. Once the ANN models are derived using the simulation data from an EM simulator, the optimization of each gap coupled section and even of the complete circuit is much faster than that performed directly on an EM simulator. Only a small fraction of CPU time is necessary to design this filter with ANN models. Two design examples have been created using two substrate layers. One is realized for 30 % bandwidth, 0.5 dB pass-band ripple level, 5 resonators, and 3 GHz center frequency. The other is for 35 % bandwidth, 0.5 dB passband ripple level, 4 GHz center frequency, and 5 resonators. Both designs have been carried out using 10 mil substrates with er = 2.2. Full-wave simulations and measurements show a good agreement to the circuit specifications for both cases. One of two designs has been carried out by using ANN models de veloped. The simulation results from ANN models also show an agreement to those designed using full-wave EM simulations without ANN models. The ANN models can be applied to any other circuit designs that require a huge amount of CPU time. 7.2.3 T h re e -L in e B alu n s A methodology for designing two- layer three-line baluns has been developed. This class of baluns are more com pact than the planar Marchand balun developed earlier. Single-layer three-line Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 123 baluns presented a difficulty in obtaining reasonable spacing dimensions. The two-layer three-line baluns developed here provide physically realizable geom etry and a design flexibility. Characterization of three-coupled lines are based upon an analysis of two-coupled line directional couplers. Since 4 equations are established for the 5 desired NMPs, an enhanced freedom in obtaining the physical parameters is available. Two design examples have been carried out using two layer substrates of 20 mil and e = 2.2. Two different topologies have been investigated by plac ing the conducting strips differently. Full-wave simulations and measurements were presented over 1.5 - 4.5 GHz frequency range. One design shows a better performance than the other design. Thus, one can choose a topology leading to a better design performance. 7.3 F u tu re W o rk 7.3.1 C o m p a c tio n o f F ilte rs Various parallel coupled sections in multilayer structures have been connected together in a straight forward direction to implement circuit specifications. This kind of layout topology does not provide compactness in comparison to the single-layer coupled-line filters. More compaction could be obtained if the coupled sections on two adjacent layers are connected bent at an angle as shown in Figure 7.1. Many possibilities of selecting physical topology exist. The characterization of each coupled section used in this thesis may be used for establishing the design procedure for this circuit. A full-wave field analysis program needs to used for analyzing modified parallel coupled sections. Also, end-coupled filters can be made more compact by bending the Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 124 OUT layer 1 Figure 7.1. A possible layout of a more compact parallel coupled-line band pass filter half-wavelength transmission lines or placing the gap coupled section at some angle. For this circuit to work, a different characterization of bent transmission lines and/or gap coupled sections with some angle needs to be performed. More compact end-coupled band-pass filters could be obtained with this kind of physical layout as shown in Figure 7.2. ANN models could alleviate the complexity of designing modified physical layout. m out layer 1 layer 4 layer 2 layer 3 Figure 7.2. A possible layout of a more compact end-coupled band-pass filter Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 125 7.3.2 B alu n s B a n d w id th C o n sid era tio n s in D esigning T h re e -L in e Although two-layer three-line baluns provide more compact and flexible design topology than the planar Marchand balun and single-layer three-line baluns, one aspect that was not taken into account in developing the design procedure is the bandwidth consideration. Since the bandwidth is an important factor for balun design, a procedure for designing baluns with a specified bandwidth needs to be investigated. In addition, cascaded three-line baluns as shown in Figure 7.3 could be explored to see if these can yield a wider bandwidth. Figure 7.3: A possible layout of a cascaded three-line balun 7.3.3 O th e r M u ltilay er C irc u its In this thesis, a methodol ogy has been developed for filters and balun circuits. In addition to filters and baluns, many other potential applications of this methodology needs to be explored for other multilayer circuits such as spiral inductors, capacitors and couplers. Continued investigations of these circuits will be helpful in develop ment of systematic design procedures for multilayer circuit designs. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. BIBLIOGRAPHY [1] T. Tokumitsu, K. Nishikawa, K. Kamogawa, I. Toyoda, and M. Aikawa, “Three-Dimensional MMIC Technology for Multifunction Integration and Its Possible Application to Masterslice MMIC,” IEEE Microwave and Millimeter-wave Monolithic Circuits Symposium, pp. 85-88, 1996. [2] I. Toyoda, T. Tokumitsu, and M. Aikawa, “Highly Integrated ThreeDimensional MMIC Single-Chip Receiver and Transmitter,” IEEE M T T S International Microwave Symposium, pp. 1209-1212, 1996. [3] R. H. Jansen, J. Jotzo, and M. 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Streit, “A Novel 12-24 GHz Broadband HBT Distributed Active Balanced Mixer,” IEEE Radio Frequency Integrated Circuits Symposium, pp. 75-78, 1997. [78] K. Kamozaki, N. Kurita, T. Tanimoto, H. Ohta, T. Nakamura, and H. Kondoh, “50-100 GHz Octave Band MMIC Mixers,” IEE E Radio Frequency Integrated Circuits Symposium, pp. 95-98, 1997. [79] K. Nishikawa, I. Toyoda, and T. Tokumitsu, “Miniaturized ThreeDimensional MMIC K-Band Upconverter,” IEEE Microwave and Guided Wave Letters, Vol. 7, No. 8, pp. 230-232, Aug. 1997. [80] R-C. Hsu, C. Nguyen, and M. Kintis, “Uniplanar Broad-Band Push-Pull FET Amplifiers,” IEEE Transactions on Microwave Theory and Tech niques, Vol. 45, No. 12, pp. 2150-2152, Dec. 1997. [81] W. Bischof, W. Ehrlinger, K. Haug, M. Berroth, and M. Schlechtweg, “An Extremely Wide Band Balanced Amplitude Controller in Coplanar Waveguide Technology,” Proceedings o f 25th European Microwave Confer ence, pp. 921-925, 1995. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 136 [82] G. S. Hilton, C. J. Railton, C. J. Ball, M. Dean, and A. L. Hume, “Mod eling a Three-Element Printed Dipole Antenna Array Using the FDTD Technique,” IEEE Antennas and Propagation Society International Sym posium, pp. 1062-1065, 1997. [83] Y.-D. Lin and S.-N. Tsai, “Coplanar Waveguide-fed Uniplanar Bow-Tie Antenna,” IEEE Transactions on Antennas and Propagation, Vol. 45, No. 2, pp. 305-306, Feb. 1997. [84] A. Nesic and S. Dragas, “Frequency Scanning Printed Array Antenna,” IEEE Antennas and Propagation Society International Symposium, pp. 950-953, 1995. [85] N. I. Dib, R. N. Simons, and L. P. B. Katehi, “New Uniplanar Transitions for Circuit and Antenna,” IEEE Transactions on Microwave Theory and Techniques, Vol. 43, No. 12, pp. 2868-2873, Dec. 1995. [86] M. W. Numberger and J. L. Volakis, “A New Planar Feed for Slot Spiral Antennas,” IEEE Transactions on Antennas and Propagation, Vol. 44, No. 1, pp. 130-131, Jan. 1996. [87] J. J. Van Tonder and J. K. Cloete, “A Study of an Archimedes Spiral Antenna,” IEEE Antennas and Propagation Society International Sympo sium, pp. 1302-1305,1994. [88] K. Tilley, X.-D. Wu, and K. Chang, “Dual Frequency Coplanar Strip Dipole Antenna,” IEEE Antennas and Propagation Society International Symposium, pp. 928-931, 1994. [89] D. Hofer and V. K. Tripp, “A Low-Profiie, Broadband Baiun Feed,” IEEE Antennas and Propagation Society International Symposium, pp. 458-461, 1993. 1 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 137 [90] M.-Y. Li, K. Tilley, J. McCleary, and K. Chang, “Broadband Coplanar Waveguide-Coplanar Strip-Fed Spiral Antenna,” Electronics Letters, Vol. 31, No. 1, pp. 4-5, Jan. 1995. [91] S. A. Maas and Y. Ryu, “A Broadband, Planar, Monolithic Resistive Frequency Doubler,” IEEE M T T -S International Microwave Symposium, pp. 443-446, 1994. [92] D. F. Filipovic, R. F. Bradley, and G. M. Rebeiz, “A Planar Broadband MIC Balanced Varactor Doubler Using a Novel Grounded-CPW to Slotline Transition,” IEEE M T T -S International Microwave Symposium, pp. 1633-1636, 1994. [93] R. Bitzer, “Planar Broadband MIC Balanced Frequency Doubler,” IEEE M T T -S International Microwave Symposium, pp. 273-276, 1991. [94] C. Cho and K. C. Gupta, “A New Design Procedure for Single-Layer and Two-Layer 3-Line baluns,” IEEE M T T -S International Microwave Symposium, pp. 777-780, June 1998. [95] V. K. Tripathi, “On the Analysis of Symmetrical Three-Line Microstrip Circuits,” IEEE Transactions on Microwave Theory and Techniques, Vol. 25, No. 9, pp. 726-7292, Sept. 1977. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. APPENDIX A AN OPTIMIZATION OF PHYSICAL GEOMETRY USING “SIMPLEX” ALGORITHM A .l Main function This main function provides input/output interface for necessary pa rameters to optimize physical dimensions, and calls “Simplex” algorithm. ^************************************************************* * Finding optimized values for w l, w2 and s * * until the error function gets a minimum value * * using an optimization or a minimization algorithm * * (Amoeba) along with ”SBEM” software * *************************************************************j #inciude <stdio.h> #include <stdlib.h> #include <math.h> #include <time.h> #include ”nr.h” #include ”nrutil.h” #include ”sbem.h” #define sqr(x) ((x)*(x)) #define LP 10 #define MP 4 #define NP 3 #define N 500 #define FTOL 1.0e-6 #define PI 3.141592654 int k=0; char rs; double func(double *); double Rc, Rp, Zcl, Zpl, vpc, vpp; double w l, w2, s; Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 139 double k id , k2d, k3d; /* ------------- (BEGIN MAIN)---------------------------------- */ int main (void) { int i, nfunc, j, ndim=NP; int Ns, Ni; double J, zOl, z02, bw, zOi, zOo, zOlp, z02p; double *x, *y, **p; double fO, lambda; double initl, init2, init3; FILE *fpo; char *foname = "soptd.out”; double g[13][13] = { { 0, 0, 0, 0, 0 }, { 0, 0.6986, 1.0000 }, { 0, 1.4029, 0.7071, 1.9841 }, { 0, 1.5963, 1.0967, 1.5963,1.0000 }, { 0, 1.6703, 1.1926, 2.3661, 0.8419, 1.9841 }, { 0, 1.7058, 1.2296, 2.5408, 1.2296, 1.7058, 1.0000 }, { 0, 1.7254, 1.2479, 2.6064,1.3137, 2.4758, 0.8696, 1.9841 }, { 0, 1.7372, 1.2583, 2.6381,1.3444, 2.6381, 1.2583, 1.7372, 1.0000 }, {0, 1.7451, 1.2647, 2.6564, 1.3590, 2.6964, 1.3389, 2.5093, 0.8796, 1.9841 }, {0, 1.7504, 1.2690, 2.6678, 1.3673, 2.7239, 1.3673, 2.6678, 1.2690, 1.7504, 1.0000 }, {0, 1.7543, 1.2721, 2.6754, 1.3725, 2.7392, 1.3806, 2.7231, 1 3485, 2.5239, 0.8842,1.9841} }; printf(”*****************************************************\n”)' printf(”* Finding the optimized values *\n”); printf(”* of w l, w2 and s for Rc, Rp, Zcl and Zpl *\n”); print.f(w******************************* do { printf(”N = ”); scanf(”%i”, &Ns); } while(Ns < = 0); do { printf(”Which coupled section = ”); scanf(”%i”, &Ni); } while(Ni < = 0 || Ni > Ns+1); do { printf(”Band width = ”); scanf(”%lF, &bw); } while(bw < = 0); do { printf(”Z01 = ”); scanf(”%lF, &z01); } while(z01 < 10 || zOl > 100); do { printf(”Z02 = ”); scanf(”%lF, &z02); } while(z02 < 10 || z02 > 100); do { printf(”Is the actual geometry same as that of ‘sbem’?(y/n) ”); scanf(”%s”, &rs); } while(!(rs==’n’ || rs= = ’N’ || rs= = ’y’ || rs= = ’Y’)); if((fpo=fopen(foname, ”w”))==NULL) { printf(”Unable to open %s for writing\n”, foname); Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. exit(l); } x = dvector(l,NP); y = dvector(l,MP); p = dmatrix(l,MP,l,NP); if(N i==l) zOi = zOl; if(Ni==Ns+l) zOo = z02; zOlp = 2/z02; z02p = 2/z01; if(N i==l) J = z0i/sqr(z01) *sqrt(PI*z01p*bw*z0i/(4*g[Ns][Ni])); else if(Ni==Ns+l) J = l/z02*sqrt(PI*bw*z0o*z02p/(4*g[Ns][Ni-l] *g[Ns][Ni])); else J = PI*bw/4 *sqrt(z02p*z01p/(g[Ns][Ni-l]*g[Ns][Ni])); kid = J*z01+l/(J*z02); k2d = J*z01*z02; k3d = J*z02+l/(J*z01); f0 = 6e9; do { printf(”Initial values for (wl,w2,s) = ”); scanf(”%lf %lf %lf”, &initl, &init2, &init3); } while(initl <=0.0 || init2 <=0.0); for(i=l; i<=MP; i+ + ) { for(j=l; j<=NP; j+ + ) { if (i= = l || i==j) p[i][j] = initl; if (i= = (j+ l)) p[i][j] = fabs(init3); if (i!=l && i==(j-l)) p[i][j] = init2; if (i==0+2)) p[i][j] = init2; if (i==(j+3)) p[i][j] = initl; p[MP][NP] = init3; x[j] = p[i][j];} y[i] = func(x); } amoeba(p, y, ndim, FTOL, func, &nfunc); printf(”Outputs: w l w2 s Rc Rp Zcl Zpl Error\n”); printf(”%14.6f %8.6f %8.6f %8.6e %8.6f %8.6e %8.6f %8.6f %%\n”, wl,w2,s,Rc,Rp,Zcl,Zpl,y[MP]*100); fprintf(fpo fprintf(fpo,”* Inputs *\n”); fprintf(fpo,”N = %i\n”, Ns); fprintf(fpo,”Coupled section %i\n”, Ni); fprintf(fpo,”J = %f\n”, J); fprintf(fpo,”ZOl = %.2f\n”, zOl); fprintf(fpo”Z02 = %.2f\n”, z02); fprintf(fpo,”BW = %.2f %%\n”, bw*100); fprintf(fpo ft)rintf(fpo,”* Results *\n”); Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 141 fprintf(fpo ”* * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * ) * fprintf(fpo,”wl = %.6f\n”, wl); fprintf(fpo,”w2 = %.6f\n”, w2); fprintf(fpo,”s = %.6f\n”, s); fprintf(fpo,"shift = %.6f\n”, wl/2+s-w2/2); fprintf(fpo,”Rc = %.6e\n”, Rc); fprintf(fpo,”Rp = %.6e\n”, Rp); fprintf(fpo,”Zcl = %.6e\n”, Zcl); fprintf(fpo,”Zpl = %.6e\n”, Zpl); fprintf(fpo,”vpc = %e\n”, vpc); fprintf(fpo,”vpp = %e\n”, vpp); lambda = (vpc+vpp)/(2*f0); fprintf(fpo,”Iambda/4 at %.0f GHz = %f mm\n”, f0/le9, lambda/4* le3); fprintf(fpo,”Function value at the minimum point: %f %%\n”,y[MP]*100); free.dmatrix(p, 1,MP, 1,NP); free.dvector(y,l ,MP); free.dvector (x, 1,NP); printf(”Output written to %s\n”, foname); fclose(fpo); return 0; } A.2 Link to SBEM This function computes the normal mode parameters using [C] matrix returned by “SBEM” function. / * ------------- (func)--------------------------------- */ double func(double *x) { double val; double LI, L2, Lm; double Cl, C2, Cm; double D, D l, D2; double **C, **L; double ms; double kl, k2, k3; C = dmatrix(l,MP,l,MP); L = dmatrix(l,MP,l,MP); w l = x[l]; w2 = x[2]; s = x[3]; if(wl<=0.0 || w2<=0.0 || s<0) { w l = fabs(wl); Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 142 w2 = fabs(w2); s = fabs(s); } k++; sbem(&wl, &w2, &s, C, L); Cm = (C[l][2]+C[2][l])/2.0*le-12; Lm = (L[l][2]+L[2][l])/2.0*le-9; if(rs==’n’ || rs= = ’N’) { C2 = C[l][l]*le-12; Cl = C[2][2]*le-12; L2 = L[l][l]*le-9; LI = L[2][2]*le-9; } else { Cl = C[l][l]*le-12; C2 = C[2][2]*le-12; LI = L[l][l]*le-9; L2 = L[2][2]*le-9; } D = sqr(L2*C2-Ll*Cl) + 4*(Lm*Cl+L2*Cm)*(Lm*C2+Ll*Cm); D1 = Ll*Cl+L2*C2+2*Lm*CnH-sqrt(D); D2 = Ll*Cl+L2*C2+2*Lm*Cm-sqrt(D); if(D<0 || D 1<=0 || D2<=0) { printf(”Error in D, D1 or D2\n”); val = k*10; goto L20; } Rc = (L2*C2-Ll*Cl+sqrt(D))/(2*(Lm*C2+Ll*Cm)); Rp = (L2*C2-Ll*Cl-sqrt(D))/(2*(Lm*C2+Ll*Cm)); vpc = sqrt(2)/sqrt(Ll*Cl+L2,,tC2+2*Lm*Cm+sqrt(D)); vpp = sqrt(2)/sqrt(Ll*Cl+L2*C2+2*Lm*Cm-sqrt(D)); Zcl = vpc*(Ll-Lm/Rp); Zpl = vpp*(Ll-Lm/Rc); kl = (Rp*Zcl-Rc*Zpl)/(Rc*Rp*(Zcl-Zpl)); k2 = Rc*Rp*(Zcl-Zpl)/(Rp-Rc); k3 = (Rc*Zcl-Rp*Zpl)/(Zcl-Zpl); veil = sqrt(sqr((kl-kld)/kld)+sqr((k2-k2d)/k2d)+sqr((k3-k3d)/k3d)); free_dmatrix(C,l,MP,l,MP); free.dmatrix(L,l,MP,l,MP); L20: printf(”w l = %6.5f w2 = %6.5f s = %6.5f vpc = %4.2f vpp = %4.2f Err = %6.7f %% N = %i\n”, wl,w2,s,vpc/le8, vpp/le8, val* 100, k); return val; } Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 143 A.3 “Simplex” function This C code finds a minimization function based on “Simplex” algo rithm using the physical parameters passed from the Main function. / * ------------------ (Simplex Function)-------------------------*/ #include <math.h> #define NMAX 5000 #define ALPHA 1.0 #define BETA 0.5 #define GAMMA 2.0 #define GET.PSUM for (j=ly<=ndimj+-l-) { for (i=l,sum=0.0;i<=mpts;i++) sum + = p[i][j]; psum[j]=sum;} void amoeba(p,y,ndim,ftol,funk,nfunk) double **p,y[],ftol,(*funk)(); int ndim,*nfunk; { int ij,ilo,ihi,inhi,mpts=ndim-l-l; double ytry,ysave,sum,rtol,tol, amotry(),*psum,*dvector(); void nrerror(),ffee.dvector(); psum=dvector( 1,ndim); *nfiink=0; GETJPSUM for (;;) { ilo=l; ihi = y[l]>y[2] ? (inhi=2,l) : (inhi=l,2); for (i=l;i<=m pts;i++) { if (y[i] < y[ilo]) ilo=i; if (y[i] > y[ihi]) { inhi=ihi; ihi=i; } else if (y[i] > y[inhi]) if (i != ihi) inhi=i; } tol = fabs(y[ihi])<fabs(y[ilo])? fabs(y[ihi]):fabs(y[ilo]); rtol=2.0*fabs(y[ihi]-y[ilo])/(fabs(y[ihi])+fabs(y[ilo])); if (rtol < ftol || tol<ftol) break; if (*nfunk > = NMAX) nrerror(”Too many iterations in AMOEBA”); ytry=amotry(p,y,psum,ndim,funk,ihi,nfunk,-ALPHA); if (ytry < = y[ilo]) ytry=amotry(p,y,psum,ndim,funk,ihi,nfunk,GAMMA); else if (ytry > = y[inhi]) { ysave=y[ihi]; ytry=amotry(p,y,psum,ndim,funk,ihi,nfunk,BETA); if (ytry > = ysave) { for (i=l;i<=m pts;i++) { Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. if (i != ilo) { for (j=lj<=ndim ;j++) { psum[j]=0.5*(p[i][j]+p[ilo][j]); p[i][j]=psum[j]; } y[i]=(*funk)(psum); } } *nfunk + = ndim; GET_PSUM } } } free_dvector(psum, 1,ndim); } double amotry(p,y,psum,ndim,funk,ihi,nfunk,fac) double **p,*y,*psum,(*funk)(),fac; int ndim,ihi,*nfunk; { int j; double facl,fac2,ytry,*ptry,*dvector(); void nrerrorQ ,free.dvector(); ptry=dvector (1 ,ndim); facl=(1.0-fac)/ndim; fac2=facl-fac; for (j=ly<=ndim y++) ptry[j]=psum[j]*facl-p[ihi]p]*fac2; ytry=(*funk)(ptry); ++(*nfunk); if (ytry < y[ihi]) { y[ihi]=ytry; for (j=ly<=ndima+4-) { psump] + = ptry [j]-p[ihi] [j]; P[ihi][j]=ptry[j]; } } free_dvector(ptry, 1,ndim); return ytry, } #undef ALPHA #undef BETA #undef GAMMA #undef NMAX Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. APPENDIX B DATA FLOW FROM EM-ANN MODELS TO HP-MDS B .l User-defined linear m odel Instructions of how to integrate an EM-ANN model into HP-MDS is given to help one create his or her own EM-ANN model library. This library is linked to HP-MDS whenever it calls the user-defined model. B.1.1 Creating and preparing a directory The purpose of this step is to create and prepare a directory to copy necessary files onto for user-compiled linear model development. Example : mkdir models cd models run /usr/...{system dependent path}.../hp85150/lib/mnsmodels/modelprepare B .l. 2 Run the “makemod” This program will create a Ccode template for user’s own model. Several questions will be given to user about the model to be developed. B.1.3 Editing the C-code tem plate file The only function to be modified is the “u_mode/name_eval()” . In this function, S- or Y-parameters are calculated. In the following example, the “u_modeiname_eval” function calls the feed-forward ANN function which is linked to the weight values from the file “endgap_dat”. J% ************************************************************************ * File: endgap.c * Description: Model code for the user-compiled linear model: "enddgap” * Created: 08 Oct 1998 11:37:59 * RCS: H ea d er: ************************************************************************ * The function ”ujendgap_eval()” is the function that * calculates Y-parameters. * * The function ”u_endgap_query()” returns the value for * ”read-only” parameters. (Non-read-only parameters are handled elsewhere.) * If you do not have any "read-only” parameters, you do not need to modify * this procedure. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 146 * * The function ”u,endgap-dispose()” frees any memory * allocated by u_endgap-eval(). * ************************************************************************ 7 #define DEBUG 1 /* Define this to be zero to turn off debugging. */ /* * usermodel.h includes stdio.h, math.h, string(s).h, ctype.h, sys/types.h, * and malloc.h */ #include "usermodel.h” #include <stdlib.h> #include ”nnjsub-gap” ^*********************************************************************** * Here is a list of preprocessor macros which are used to access the * parameters of this device: */ #define PARAM.wl 0 #define PARAM_w2 1 #define PARAM_g 2 #define PARAM_endgap_dat 3 static int u.endgap_eval(); static int u_endgap.query(); static void u_endgap_dispose(); ^*********************************************************************** * The USER_PARAM data structure describes the parameters used by this * device. */ static USER-PARAM u.endgap_params[| = { { "wl”, /* name */ NULL, NULL, DP-READABLE—IP-DIFFERENTIABLE—IP.SETTABLE—IP-MODIFIABLE— IP-REQUIRED, REAL-TYPE, 0 .001 , 0, /* default value if real or integer */ 0, /* default imag value if complex */ /* default string if string (next line) */ NULL }, { ”w2”, /* name */ NULL, Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 147 NULL, IP .READABLE—IP .DIFFERENTIABLE—IP .SETTABLE—IP .MODIFIABLE— IP-REQUIRED, REAL.TYPE, 0 . 001 , 0, /* default value if real or integer */ 0, /* default imag value if complex */ /* default string if string (next line) */ NULL }, { ”g”, /* name */ NULL, NULL, IP .READ ABLE—IP_DIFFERENTLABLE—IP.SETTABLE—IP-MODIFIABLE— IPJREQUIRED, REAL.TYPE, 0 . 001 , 0, /* default value if real or integer */ 0, /* default imag value if complex */ /* default string if string (next line) */ NULL }, { ”endgap-dat”, /* name */ NULL, NULL, IP .READABLE—IP .SETTABLE—IP-MODIFIABLE—IPJREQUIRED, STRING-TYPE, 0, 0, I* default value if real or integer */ 0, /* default imag value if complex */ /* default string if string (next line) */ NULL } }; ^*********************************************************************** * The USER_MODEL data structure describes the device, and any parameters * used by it. */ USER-MODEL u.endgap = { 1, ”endgap”, NULL, 2, u-endgap.params, sizeof(u.endgap.params) / sizeof(USER_PARAM), MODEL-EVALUATES.Y, u-endgapjeval, Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. u.endgap.query, u-endgap.dispose }; ^*********************************************************************** * u.endgap.eval() calculates Y-parameters. This is the * main model evaluation routine. */ static int u.endgap_eval(Name, Flags, Omega, Matrix, NumberOfPorts, Parameters, Substrate, SavedData) char *Name; int Flags; RealNumber Omega; ComplexNumber *Matrix; int NumberOfPorts; USERJDATA *Parameters; struct SubstrateModelData *Substrate; void **SavedData; | y ******************************************************************J * Add code to calculate Y-parameters here. y****************************************************************** J double I[10],O[10],pi,wl, w2, g,freq; ComplexNumber param; char ctmp[50]; pi=3.14159265358973; wl=UGETJlEAL-VALUE(Parameters[PARAM-wl]); w2=UGETJREAL_VALUE(Parameters[PARAM.w2]); g=UGET_REAL_VALUE(Parameters[PARAM.g]); freq=Omega/ (2.0*pi*1.0e9); l[0]=wl; I[l]=w2; I[2]=g; I[3]=freq; strcpy(ctmp,UGET^TRING-VALUE(ParametersfPARAMjendgap.dat])); neuraljiet_gap(l,0,ctmp); /* param.Real=50.0; param.lmag=0.0; CMPLX_ASSIGN(MATRIXl_Z(Matrix, NumberOfPorts, 1), param); CMPLX_ASSIGN(MATRIXl_Z(Matrix, NumberOfPorts, 2), param);*/ param.Real=O[0]; param.lmag=0[l]; CMPLX_ASSIGN(MATRIXl_ELEMENT(Matrix, NumberOfPorts, 1,1), param); Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. param.Real=0 [2]; param.Imag=0[3]; CMPLX.ASSIGN(MATRIXl_ELEMENT(Matrix, NumberOfPorts, 1,2), param); CMPLX-ASSIGN(MATRIXl_ELEMENT(Matrix, NumberOfPorts, 2,1), param); param.Real=0 [4]; param.Imag=0[5]; CMPLX_ASSIGN(MATRIXlJELEMENT(Matrbc, NumberOfPorts, 2,2), param); return (YES); } ^*********************************************************************** * u.endgap_query() is used only if "read-only” parameters exist. If this * model does not have any ’’read-only” parameters, this routine does not have * to be modified. If there are "read-only” parameters, you must modify this * procedure to return the value of the "read-only” parameter. */ static int u_endgap.query(ParameterID, NumberOfPorts, Parameters, Substrate, SavedData, Value) int ParameterID; int NumberOfPorts; USERJDATA *Parameters; struct SubstrateModelData ^Substrate; void **SavedData; USERJDATA *Value; { /* Initialization */ USETJDATA_TYPE(* Value, UNKNOWN.TYPE); /* leave this alone! */ /* * To the following switch statement, add case statements to extract * the value of read-only parameters (if any - if there aren’t any, * just leave this procedure alone). */ switch (Parameter®) { default: /* * If this is parameter is not handled by this routine, just * exit. */ break; } return (YES); } * u.endgap.dispose() is used to free memory that was allocated and stored * on the "saved.data” parameter of the u_endgapjeval() function. * If you do not use the ”saved.data” parameter of u_endgap.eval(), you * do not need to modify this routine. * */ static void u.endgap.dispose(SavedData) Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. void **SavedData; { if (*SavedData) { /* * Free any additional data here. */ free(*SavedData); } } /* * Local Variables: * c-indent-level: 4 * c-continued-statement-offset: 4 * c-brace-offset: -4 * c-argdecl-indent: 0 * c-label-offset: -4 * End: */ B.2 The feed-forward A N N function neural .net.gap (1,0 ,ctmp) double I[10],0[10]; char ctmp[50]; { int ij,k,r,c,l; double minmax[21][2], wl[50][ll],w2[10][51],IN[ll]; double sum, net[50],f[51],net2[10],ON[10]; float x; FILE *fpt; /* Read input file*/ fpt=fopen(ctmp,”r”); fscanf(fpt,” %d%d%d:’,&i,&k,&j); for(r=0;r<i+k;++r) { for(c=0;c<2;-f+c){ fscanf(fpt,” %e”,&x); minmax[r] [c]=x;}} for(r=0;r<j;+-i-r){ for(c=0;c<=i;++c){ fscanf(fpt,”%e”,&x); wl[r][c]=x;}} for(r=0;r<k;-t-+r) { for(c=0;c<=j;++c){ fscanf(fpt,”%e”,&x); w2[r][c]=x;}} fclose(fpt); /* Normalize Inputs between 0 and 1 */ IN[0]=1.0; for(r=k;r<i-t-k;++r){ IN[r-k+1]=(I[r-k]-minmax[r] [0]) / (minmax[r] [l]-minmax[r] [0]);} Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. /* Multiply normalized inputs by first set of weights and sigmoid*/ f[0]=1.0; for(r=0;r<j;++r){ sum=0.0; for(c=0;c<=i;++c){ sum=sum+wl[r][c]*IN[c];} net[r]=sum; f[r+1]=1.0/ (1.0+exp(-net [r]));} /* Multiply by second set of weights, Sigmoid, denormalize */ for(r=0;r<k;++r){ sum=0.0; for(c=0;c< =j;++c) { sum=sum+w2[r] [c]*f[c];} net2[r]=sum; ON[r]=1.0/(1.0+exp(-net2[r])); 0[r]=((ON[r]-0.2)*(minmax[r][l]-minmax[r][0])/0.6)+minmax[r][0];} } B.3 An EM -A N N weight file 4 /* number of inputs */ 6 /* number of outputs */ 12 /* number of neurons in the hidden layer */ /* Max and Min values for the outputs */ 7.974182e-07 3.704246e-04 8.132715e-04 4.239201e-02 -2.674593e-04 -7.694745e-07 4.384907e-04 3.057494e-02 8.945518e-07 2.607813e-04 9.052016e-04 5.294224e-02 8.000000e-014.200000e+00 4.000000e-01 2.000000e+00 1.000000e+00 4.000000e+00 1.500000e+00 4.500000e+00 /* The weights between the input and the hidden layer */ -2.936455e+00 3.038668e-01 7.041506e-01 1.238946e+00 6.709919e-01 -3.292541e-01 -1.433612e-01 -2.736312e-02 -9.260146e-01 -2.899395e-01 -2.886026e+00 5.198771e-01 -2.793950e-02 1.342801e+00 -4.452597e-01 -7.513946e+00 -4.724797e+00 2.844372e+00 1.828593e+00 2.468859e+00 -2.738880e+00 -4.925343e-02 -2.290847e-01 -3.586707e-01 -4.73001 le-01 -4.998860e+00 8.719739e-01 9.786560e-01 -1.240659e-01 2.165266e+00 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 152 1.173558e+01 9.464445e-02 -2.368811e+00 -3.73115tJe+00 -5.036164e+00 -5.500352e+00 1.296099e+00 -2.421762e-01 1.393999e+00 2.269715e+00 -2.895616e+00-3.112258e-01 5.363251e-01 1.253820e+00 -7.669684e-01 -3.455950e+00-9.192074e-01 1.131245e-01 9.544331e-01 1.661224e+00 -3.356013e+00 5.031830e-02 -1.454407e+00 1.159295e+00 1.390404e+00 4.017048e+00 -2.575329e-01 -8.039668e-01 -2.025872e+00 -2.201498e+00 /* The weights between the hidden and the output layer */ 3.859342e+00 -2.745112e+00 -1.360446e+00 -1.746495e+00 -1.639044e+00 -1.552682e+00 1.312729e+00 -3.075470e+00 4.647749e+00 1.823731e+00 -1.892173e+00 -9.283437e-01 -1.331090e+00 3.851617e+00 1.410064e+00 -2.662861e+00 -7.582046e-01 -2.033446e+00 -2.386133e+00 -2.099265e+00 -2.327482e+00 2.026903e+00 -3.300690e+00 -3.055536e+00 -7.966869e-01 -1.451613e+00 -5.967424e+00 1.318110e+00 8.776059e-01 1.013951e+00 2.540218e+00 1.592350e+00 -9.007094e-01 4.992166e+00 -3.339734e-01 5.225501e-02 1.123291e+00 1.209594e+00 1.739809e+00 6.247129e+00 1.108459e+00 -1.782773e+00 -1.905597e+00 -3.701628e+00 -1.621191e-l-00 -1.998428e+00 -4.297600e+00 -1.419235e+00 -1.271881e+00 -1.145129e+00 -2.169320e+00 -2.319211e+00 7.034432e+00 -1.498197e+00 -1.378570e+00 -8.561791e-01 -1.333040e+00 -7.732884e-01 1.596873e-01 -5.521996e+00 -1.639091e+00 -4.638169e-01 -7.809489e-01 -1.365040e+00 -2.112312e+00 5.269771e+00 1.695510e+00 -2.380372e+00 -2.916158e+00 -1.494385e+00 -1.817080e+00 -2.322940e+00 -3.380170e+00 -8.619703e-01 -8.335024e-01 -7.763543e-01 -2.818443e+00 -1.993454e+00 B.4 Compiling and linking the model Now add the name of the model file after “CFILES = ” in the Makefile and run “make”. A new simulator file “mns” is created. Obtain the permission from user’s system administrator to move the file “mns” into .../mns800. B.5 Read design icons file into MDS To use the newly installed models, the design icons file must be read into MDS. One way to do this is to copy an existing design icon and to modify it for user’s needs. The symbol and the scion page are mainly modified based on the user’s intention. Finally execute “perform/add to menu” and one can use his or her own model as other MDS model to create circuits by executing “insert/component/u ser modeV. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. B.6 N otes on m odel usage Within MDS model : (1) All inputs for W \, W 2 , G, I are in mm. (2) Input correct path to ANN model file names. (Ex. ‘usr/ferrari2/student/ choc/annmodel/ endgap_dat’) Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.

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