# Artificial neural network modeling for computer-aided design of microwave and millimeter-wave circuits

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ARTIFICIAL NEURAL NETWORK M ODELING FOR COMPUTER-AIDED DESIGN O F MICROWAVE AND M ILLIM ETER-W AVE CIRCUITS by PAUL MARTIN W ATSON B.S., University o f Utah, 1991 M.Eng., University o f Utah, 1993 A thesis subm itted to the Faculty of the Graduate School o f the University of Colorado in partial fulfillment o f the requirements for the degree of Doctor of Philosophy Department of Electrical and Com puter Engineering 1998 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. UMI Number: 9827794 UMI Microform 9827794 Copyright 1998, by UMI Company. All rights reserved. This microform edition is protected against unauthorized copying under Title 17, United States Code. UMI 300 North Zeeb Road Ann Arbor, MI 48103 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. This thesis for the Doctor o f Philosophy degree by Paul Martin W atson has been approved for the Department o f Electrical and Computer Engineering By K.C. Gupta regory L. Creech Date O & .-0 2. The final copy of this thesis has been exam ined by the signators, and we find that both the content and the form meet acceptable presentation standards o f scholarly work in the above mentioned discipline. | Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Watson, Paul M artin (Ph.D. Electrical Engineering) Artificial N eural Network Modeling for Computer-Aided Design o f Microwave and M illimeter-W ave Circuits Thesis directed by Professor K.C. Gupta A novel approach for accurate and efficient modeling of passive microwave/mm-wave components by using electromagnetically-trained artificial neural netw ork (EM-ANN) software modules is presented. Artificial neural networks are employed to model complex relationships between physical parameters of a component and the corresponding electrical response. Full-wave EM analysis is employed to characterize passive components. Structures for simulation are chosen using design o f experiments (DOE) methodology. Analysis EM-ANN models are then trained using physical parameters as inputs and component response (i.e. Sparameters) as outputs. In addition, synthesis models can be developed by interchanging the inputs and outputs used for component characterization. Methods for incorporation o f prior knowledge (existing models) for model development have been explored. It has been dem onstrated that use of prior knowledge (when it exists) reduces the num ber of EM simulations that are needed to characterize the component to be modeled. Once trained, the EM -ANN models can be inserted into a commercial microwave circuit simulator where they provide results approaching the accuracy of the EM simulation tool used for characterization of the microwave/mm-wave components without increasing the analysis time significantly. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. The proposed iv technique is capable of providing models for simulation and optimization o f microwave/mm-wave components where models do not exist or are not accurate over the desired region o f operation. EM-ANN modeling o f microstrip vias and multilayer interconnects is demonstrated. An example of using EM-ANN models to optimize component geometry is included for a stripline-to-stripline multilayer interconnect. A methodology for the synthesis (leading to physical dimensions) of multilayer asymmetric coupled microstrip lines using ANN models is presented. Both synthesis and analysis models have been developed. Models are appropriate for synthesis o f multilayer structures like filters, baluns, and directional couplers. EM-ANN modeling has also been used for generating a library of component models for CPW circuit design. Design and optimization o f a CPW folded double stub filter and a 50 Q, 3 dB power divider circuit, using the developed CPW EM-ANN models, has been demonstrated. Research has also been conducted on novel CPW patch antennas. Using EM-ANN modeling techniques, a wide bandwidth CPW patch antenna has been designed and validated by both EM simulation and measurements. A discussion of these results and ideas for future research are presented. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. V ACKNOWLEGEMENT I would like to thank all o f those individuals who helped to make this dissertation possible. I wish to thank Dr. K.C. Gupta, the dissertation advisor, for his continued support, encouragement, and guidance. Also, I thank Dr. Roop L. Mahajan, Dr. Gregory L. Creech, and Manish Marwah for many helpful discussions on artificial neural network techniques. I am grateful for the assistance provided by Dr. Tom Jones, Mark Calcaterra, and Alan Tewksbury o f W right-Patterson Air Force base in dealing with the Palace Knight program. I thank Dr. Melinda Piket-May and Dr. Zoya Popovic for serving on my committee. I wish to express my deepest gratitude to my wife, Mamie, for her continuing love, support, and devotion without which none o f this work would have been possible. Finally, I thank my children, Shea, Keegan, and Cloe for making my life brighter when I get home. ii Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. TABLE OF CONTENTS CHAPTER 1 INTRODUCTION...................................................................................................... 1 1.1 1.2 2 M otivation....................................................................................................... 1 1.1.1 M odeling for C A D ...........................................................................1 1.1.2 Artificial Neural Network M odels................................................4 Organization o f the T h esis...........................................................................5 INTRODUCTION TO MULTILAYER, FEED-FORWARD ARTIFICIAL NEURAL N ETW O R K S.......................................................................................8 2 .1 ANN T opology................................................................................................9 2.2 ANN M odel Development (Training)........................................................12 2.2.1 Data Preprocessing........................................................................ 14 2.2.2 Error Back-Propagation.................................................................14 2.2.3 Error Functions...............................................................................16 2.2.4 2.3 3 2.2.3.1 Absolute Error............................................................. 16 2.2.3.2 Relative Error.............................................................. 17 Learning R u le s...............................................................................18 Model Generalization and O verfitting...................................................... 19 MODELING M E T H O D O LO G Y ......................................................................... 20 3.1 Selection o f Training Data by Design of Experiments (DOE) T echniques................................................................................................. 20 3.2 ANN Training M ethodology......................................................................25 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. v ii 3.3 4 5 6 3.2.1 Data P re-Processing.......................................................................25 3.2.2 Simultaneous Training and Testing.............................................. 26 Use o f Prior K now ledge.............................................................................. 27 ANN M ODELS FOR MICROWAVE/MILLIMETER-WAVE DESIGN.... 32 4.1 Selection o f Model Inputs and Outputs......................................................32 4.2 Training Data G eneration............................................................................ 33 4.3 Error M easures.............................................................................................. 34 4.4 Integration o f EM -ANN Models with CircuitS im ulators.......................35 4.5 Design and Optimization Using EM-ANN M odels................................ 37 EM-ANN M ODELS FOR VIAS AND MULTILAYER IN TER C O N N EC TS............................................................................................... 38 5 .1 M icrostrip Transmission Line Model......................................................... 39 5.2 Broadband GaAs 1-port Microstrip V ia.................................................... 42 5.3 Broadband GaAs 2-port Microstrip V ia.................................................... 43 5.4 Stripline-to-Stripline Multilayer Interconnect...........................................45 5.5 M icrostrip-to-M icrostrip Multilayer Interconnect.................................. 47 5.6 Model Development Using Prior Knowledge...........................................49 5.6.1 Two-Port Broadband GaAs Microstrip Ground V ia .................49 5.6.2 Stripline-to-Stripline Multilayer Interconnect: Frequency Range Extension............................................................................. 53 5.7 Integration o f EM -ANN Models with a Network Sim ulator.................57 5.8 Optimization o f Component Structure.......................................................59 M ULTICONDUCTOR MULTILAYER COUPLED TRANSM ISSION LINE DESIGN USING ANN MODELS ...........................................................60 6.1 Synthesis of Asymmetrical Multilayer Coupled Line Sections............ 62 t t Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. v iii 6.2 6.3 6.4 7 ANN Modeling Methodology for M ultilayer Asymmetric Coupled Lines ........................................................................................................... 64 6 .2 .1 Analysis Model............................................................................... 65 6.2.2 Synthesis M odel.............................................................................67 M ultilayer Filter Design using ANN M odels...........................................70 6.3.1 ANN Model Development for Coupled Line S ectio n s............71 6.3.2 Design Example: 2-Layer Coupled Line Filter........................ 74 6.3.3 Comparison o f 2-Layer Filter Design Using ANN M ethod and Optimization M ethod.............................................................. 78 D iscussion..................................................................................................... 80 DESIGN AND OPTIMIZATION OF CPW CIRCUITS USING EM ANN MODELS FOR CPW CO M PO N EN TS.............................................................. 82 7.1 EM-ANN Modeling of Chamfered CPW 90° Bends.............................. 84 7.1.1 Optimally Chamfered Conventional CPW B end......................86 7.1.2 Novel Compensated CPW B en d ................................................. 88 7.1.3 CPW Bend Comparisons.............................................................. 89 7.1.4 CPW 90° Bend with Air-Bridge Height as an Input Parameter ........................................................................................91 7.2 EM-ANN Modeling o f CPW Transmission Lines.................................. 94 7.3 EM-ANN Models for CPW Opens and S h o rts....................................... 95 7.4 EM-ANN Modeling o f CPW Step-in-W idth...........................................97 7.5 EM-ANN Modeling of CPW Symmetric T-junctions.......................... 100 7.6 CPW Circuit Design Exam ples................................................................ 102 7.7 7.6.1 CPW Folded Double-Stub F ilter............................................... 102 7.6.2 CPW 50 Q, 3 dB Power D ivider............................................... 106 D iscussion................................................................................................... 110 j i Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. ix 8 EM-ANN MODELS FOR DESIGN OF CPW PATCH A N TEN N A S 8.1 8.2 8.3 8.4 9 112 Radiation Characteristics o f CPW Line and Open E n d ....................... 113 8.1.1 Radiation from a Wide CPW L in e.............................................. 113 8.1.2 Radiation from CPW O pen-Ends................................................ 113 Transmission Line Equivalent o f a Rectangular CPW Patch............... 119 8.2.1 Transmission Line Model for CPW Antennas......................... 119 8.2.2 EM-ANN Model for CPW Transmission L in e..........................120 8.2.3 EM-ANN Model for CPW Open-End E ffects.......................... 122 8.2.4 CPW Patch Antenna Design Without Including Feed Effects ......................................................................................127 CPW Patch Antenna Design Including Feed Discontinuities.............. 128 8.3.1 EM-ANN Model for Feed Discontinuities................................129 8.3.2 CPW Patch Antenna Design Using EM-ANN M o d els.......... 130 8.3.3 CPW Patch Antenna Design Optimization Using EM -ANN Models ......................................................................................134 D iscussion.................................................................................................... 139 SUMMARY AND FUTURE W O R K .................................................................140 9.1 EM-ANN Modeling Methodology............................................................140 9.2 EM-ANN Modeling Examples.................................................................. 142 9.3 9.2.1 Microstrip Vias and Multilayer Interconnects.......................... 142 9.2.2 Multiconductor Multilayer Coupled Transmission Line Models ......................................................................................143 9.2.3 EM-ANN Models for CPW Com ponents................................. 144 9.2.4 EM-ANN Models for Design o f CPW Patch A ntennas 145 Future W o rk ................................................................................................145 9.3.1 Nonlinear Active Device M odeling.......................................... 145 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 9.3.2 ANN Model Development for Passive Components using Measured Data................................................................................146 9.3.3 CPW Patch Antenna....................................................................... 146 9.3.4 ANN o f Complete Circuit M o d u les............................................146 9.3.5 Synthesis o f Com ponents.............................................................. 147 BIBLIOGRAPHY.................................................................................................................148 APPENDIX A ........................................................................................................................159 A. 1 User-Defined Linear Model Subroutine...................................................159 A.2 Feed-Forward ANN Subroutine................................................................ 165 A.3 Sample EM-ANN Model Input F ile ......................................................... 167 APPENDIX B USER-DEFINED LINEAR M ODEL LIBRARY FOR CPW COMPONENTS.............................................................................168 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. LIST OF FIGURES FIGURE 2.1 Artificial neural network architecture........................................................ 10 2.2 Logistic activation function used in hidden layer and output layer neurons............................................................................................................13 3.1 DOE 2k factorial design............................................................................... 23 3.2 DOE central composite design................................................................... 24 3.3 Modified DOE central composite design..................................................24 3.4 Modified DOE central composite design with additional interior points.............................................................................................................. 25 3.5 Schemes for using prior knowledge (existing models) for artificial neural network training, (a) difference method and (b) PKI method. 31 4.1 R ow of data for linking EM-ANN models to commercial microwave circuit simulators..........................................................................................36 5.1 Cross-section o f microstrip transmission line geometry where W) is the width o f the microstrip line, Hsub is the substrate height, and er is the relative dielectric constant o f the substrate................................40 5.2 GaAs microstrip ground via geometry. Substrate thickness = 4 mil, £t=12.9, tan5=0.002, crmetai=4.1xl07, and tmetai=0.1 mil.................42 5.3 Two-port GaAs microstrip grounding via. Substrate thickness = 4 mil, £r=12.9, tan8=0.002, CmetaF^-lxlO7, and tmemi = 0.1 m il............... 44 5.4 Stripline-to-stripline interconnect structure with W|ine= 13.675 mil, Zo = 50 ohms, £,= 2.94, tanS = 0.0012, tmetai= 1.4 mil, cy^ai = 5.7xl07, and H = 20 mil.............................................................................. 46 j Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. x ii 5.5 Microstrip-to-Microstrip interconnect with Zo = 50 ohms, Wbol = 23 mil, W Iop = 125 mil, grl = 10.2, er2 = 2.2, tan5 = 0.0012, tmetal = 1.4 mil, CTmetai = 5.7x 107, and H = 25 mil...............................................47 5.6 Comparison o f EM-ANN model (NET1), HP-Momentum (HPMOM), HP-MDS via elem ent (msvia), and MSVIA with added components (msvia + comp). GaAs via with er= 12.9, HSUb= 4 mil, tmeupo.l mil, a metai=4.lx 107, tan5 = 0.002, W|/Wp= 0.3875, Dvia/Wp =0.4, and W,/Hsllb = 0.3375.......................................................... 58 6.1 Example of a multiconductor multilayer coupled line geometries in an inhomogeneous medium. Both layer-to-layer and same layer coupling sections are shown...................................................................... 63 6.2 Procedure for the design o f asymmetric multilayer coupled line sections using optimization [80]............................................................... 63 6.3 Analysis ANN model for asymmetric multilayer coupled line sections.......................................................................................................... 66 6.4 Synthesis ANN model for asymmetric multilayer coupled line sections.......................................................................................................... 66 6.5 Modified synthesis procedure for asymmetric multilayer coupled line sections using ANN models in place o f optimization.................... 69 6.6 Top view of a 2-layer coupled line filter consisting of 3 coupled line sections. Sections I and 3 couple from layer 1 to layer 2 and section 2 couples from layer 1 to layer 1. Input and output ports are on the top o f layer 2.............................................................................. 70 6.7 Two-layer filter response. Both ANN modeled (light solid lines) and SBEM (dark dashed lines) results are shown...................................76 6.8 Two-layer filter response. Both ANN modeled (light solid lines) and SBEM (dark dashed lines) results are shown...................................78 7.1 CPW 90° bend structures with Wa = 40 pm, Ha = 3pm, Hsub = 625 pm, £r = 12.9, and tanS = 0.0005. (a) Conventional chamfered bend and (b) novel compensated bend (Ha is height o f air-bridge above the substrate, Wa is the width of the air-bridge, and Hsub is the substrate thickness.).............................................................................. 85 7.2 Optimal chamfer for return loss versus W/G for the conventional CPW 90° bend. (Fig. 7. la .) ....................................................................... 88 i i i ! Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. x iii 7.3 Com parison o f unchamfered (Comer), conventional (Opt. Chamf.), and novel (Comp. Bend) CPW bends. W = 70 pm, G=20 pm, 8r=12.9, and Hsub=625 pm ...........................................................................90 7.4 CPW short circuit geometry........................................................................ 95 7.5 CPW open circuit geometry.........................................................................96 7.6 S-param eter response for CPW open and short circuits. W = 70 pm, G = 60 pm, and reference planes at the discontinuities................. 96 7.7 CPW step-in-width geometry....................................................................... 98 7.8 S-param eter response for a 71 Q. to 50 O CPW step-in-width transition. W[ = 20 pm, W2 = 70 pm , G = 60 pm, and reference planes at the discontinuity........................................................................... 99 7.9 CPW symmetric T-junction geom etry..................................................... 100 7.10 S-param eter response for a typical CPW symmetric T-junction. W in = W out = 70 pm, Gin = Gout = 60 pm , and reference planes at the air-bridge locations.......................................................................... 101 7.11 CPW folded double-stub filter geom etry................................................ 103 7.12(a) Sii for CPW folded double-stub filter for the optimized EM-ANN circuit (EM -ANN Opt.), the original EM -ANN circuit (EM-ANN Org.), and EM simulation (EM sim .).......................................................104 7.12(b) S 21 for CPW folded double-stub filter for the optimized EM-ANN circuit (EM-ANN Opt.), the original EM -ANN circuit (EM-ANN Org.), and EM simulation (EM sim .).......................................................105 7.13 CPW pow er divider geometry.................................................................... 107 7 .14(a) S 11 for C PW power divider for the optimized EM-ANN circuit (EM -ANN Opt.), the original EM -ANN circuit (EM-ANN Org.), and EM simulation (EM sim.).................................................................. 108 7 .14(b) S 21 for CPW power divider for the optim ized EM-ANN circuit (EM -ANN Opt.), the original EM -ANN circuit (EM-ANN Org.), and EM simulation (EM sim.).................................................................. 109 8.1 Open-end CPW geometry........................................................................... 114 8.2 Sim ulated radiation patterns (Ee and E^) o f a CPW line (W=1.5 cm, G=0.01 cm, L=3 cm and f = 5 GHz) without an open end. The plane o f the pattern is perpendicular to the gaps (<J>= 90°)..................114 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. x iv 8.3 Far-Field radiation patterns (Ee and E^) at 5 GHz for two openended CPW s with W = 1.5 cm, L=3 cm , Gend = 0.85 cm, and different gap widths (<j) = 90°). (a) G = 0.5 cm and (b) G = 0.01 cm...................................................................................................................115 8.4 Far-Field radiation patterns (<j> = 90°) at 5 G H z for two open-ended CPW s with G = 0.05 cm, Gend = 0.85 cm , L=3 cm, and different conductor widths (W). (a) W = 1.5 cm and (b) W = 2.0 cm............ 117 8.5 M agnetic current distributions for two CPW open-ends with W = 1.5 cm , Gend = 0.85 cm, L=3 cm, and different gap widths at 5 GHz. (a) G = 0.5 cm and (b) G = 0.1 cm ............................................. 118 8.6 Ideal C PW patch antenna geometry and corresponding transmission line equivalent circuit m odel............................................. 119 8.7 Typical trends for Zo and p (phase constant) with (a) f = 5 GHz, G = 0.05 cm , and W variable, (b) f = 5 G Hz, W = 1.5 cm, and G variable, and (c ) W = 1.5 cm, G = 0.05 cm, and frequency variable......................................................................................................... 121 8.8 Trends o f the radiation conductance, G r, and capacitance, C, for a CPW open-end with Gend=0.85 cm at 5 GHz. (a) G variable and W=1.5 cm . (b) W variable and G=0.05 cm ..........................................125 8.9 Trends o f the radiation conductance, G r, and capacitance, C, for a CPW open-end with Gend=0.8 cm versus frequency, (a)W=1.5 cm and G=0.05 cm. (b) W =i cm and G =0.05 cm ................................126 8.10 CPW patch fed on the radiating edge and its corresponding transm ission line model............................................................................. 129 8.11 Layout o f CPW patch antenna design. Electrical parameters referenced to the resonant frequency o f 4.99 G H z............................... 131 8.12 Comparison o f return loss for the CPW patch antenna shown in Fig. 8.11........................................................................................................132 8.13 Far field radiation patterns for the antenna shown in Fig. 8.11. (a) E-plane (<|) = 0°) and (b) H-plane (<|> = 90°)............................................. 133 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. XV 8.14 Effects of radiating edge feed section and line on CPW patch antenna (W=1.5 cm G=0.1 cm and Gend=0-85 cm) S 1 1 response. (Al) Ideal patch with no feed (Lpaich= 1-6465 cm). (Bl) Addition o f feed section. (Cl) Addition o f incoming feed line..........................135 8.15 Effects of increasing the patch length (Lpa(ch=1.937 cm). (Al: La=0 cm and B 1: La=3.4 c m .)......................................................................... 135 8.16 Layout for CPW patch antenna with longer than ideal patch length. All dimensions are in cm. Electrical parameters referenced to the resonant frequency of 5.56 GHz.............................................................. 137 8.17 Comparison o f return loss for the longer than ideal patch length CPW patch antenna....................................................................................137 8.18 Far field radiation patterns, measured and EM simulation, (a) Eplane (tj) = 0°). Only E_theta is shown due to antenna damage during measurement, (b) H-plane (<j> =90°)...........................................138 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. LIST OF TABLES TABLE 5.1 Variable input parameters for microstrip transmission line model.............. 40 5.2 Error results (average and standard deviation) between the EM-ANN model and linecalc for the m icrostrip transmission line for absolute error training.....................................................................................................41 5.3 Error results (average and standard deviation) between the EM-ANN model and linecalc for the m icrostrip transmission line for relative error training.....................................................................................................41 5.4 Variable input parameters for GaAs microstrip ground via modeling........ 42 5.5 Error results (average and standard deviation) between the EM-ANN model and EM simulation for the 1-port microstrip via............................... 43 5.6 Error results (average and standard deviation) between the EM-ANN model and EM simulation for the 2-port microstrip via............................... 44 5.7 Variable parameters for stripline-to-stripline multilayer interconnect m odel....................................................................................................................46 5.8 Error results (average and standard deviation) between the EM-ANN model and EM simulation for the stripline-to-stripline multilayer interconnect......................................................................................................... 46 5.9 Variable parameters for microstrip-to-microstrip interconnect m odel........ 48 5.10 Error results (average and standard deviation) between the EM-ANN model and EM simulation for the microstrip-to-microstrip multilayer interconnect......................................................................................................... 48 1 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. x v ii 5.11 Error results for the 2-port microstrip via using regular training. (7 train structures, 4 inputs, 4 outputs, 5 hidden neurons, 49.w eights).......... 51 5.12 Error results for the 2-port microstrip via, difference method. (7 train structures, 4 inputs, 4 outputs, 8 hidden neurons, 76.w eights).......... 51 5.13 Error results for the 2-port microstrip via, PKI method. (7 train structures, 8 inputs, 4 outputs, 5 hidden neurons, 69 w eights)...................51 5.14 Error results for the 2-port microstrip via, regular training. (15 train structures, 4 inputs, 4 outputs, 13 hidden neurons, 121 w eights)...............52 5.15 Error results for the2-port microstrip via, difference method. (15 train structures, 4 inputs, 4 outputs, 12 hidden neurons, 112 weights) 53 5.16 Error results for the 2-port microstrip via, PKI method. (15 train structures, 8 inputs, 4 outputs, 11 hidden neurons, 147 w eights).............. 53 5.17 Error results for the stripline-to-stripline interconnect frequency extension model, regular training. (5 train structures, 3 inputs, 4 outputs, 10 hidden neurons, 84 weights).........................................................55 5.18 Error results for the stripline-to-stripline interconnect frequency extension model, difference method. (5 train structures, 3 inputs, 4 outputs, 13 hidden neurons, 108 weights)...................................................... 55 5.19 Error results for the stripline-to-stripline interconnect frequency extension model, PKI method. (5 train structures, 7 inputs, 4 outputs, 8 hidden neurons, 102 weights)........................................................................55 5.20 Error results for the stripline-to-stripline interconnect frequency extension model, regular training. (9 train structures, 3 inputs, 4 outputs, 11 hidden neurons, 92 weights).........................................................56 5.21 Error results for the stripline-to-stripline interconnect frequency extension model, difference method. (9 train structures, 3 inputs, 4 outputs, 13 hidden neurons, 108 weights)...................................................... 56 5.22 Error results for the stripline-to-stripline interconnect frequency extension model, PKI method. (9 train structures, 7 inputs, 4 outputs, 10 hidden neurons, 124 weights)......................................................................56 5.23 Comparison of simulation times for the GaAs via described in Fig. 5.6. The tim es for MSVIA and NET1 are averaged over 100 frequency points. HP-M omentum results are for 1 frequency point............................57 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. x v iii 6.1 Variable input parameters and corresponding ranges for the layer 1 to layer 2 coupling section model........................................................................ 7 1 6.2 Variable input parameters and corresponding ranges for the layer 1 to layer 1 coupling section m odel......................................................................... 71 6.3 Error results for the layer 1 to layer 2 coupling line section analysis model. (725 train/test examples, 25 verify; 3 inputs, 6 outputs, 15 hidden neurons, 156 weights)........................................................................... 72 6.4 Error results for the layer 1 to layer 1 coupling line section analysis model. (645 train/test structures, 25 verify; 3 inputs, 6 outputs, 15 hidden neurons, 156 weights)........................................................................... 72 6.5 Error results for the layer I to layer 2 coupling line section synthesis model. (725 train/test examples, 25 verify; 4 inputs, 3 outputs, 13 hidden neurons, 107 weights)........................................................................... 73 6.6 Error results for the layer I to layer 1 coupling line section synthesis model. (645 train/test examples, 25 verify; 4 inputs, 3 outputs, 14 hidden neurons, 115 weights)........................................................................... 73 6.7 Filter specifications used for the design o f a 2-layer asymmetric coupled line filter................................................................................................ 74 6.8 Physical dimensions obtained from ANN models for the 2-layer Filter example. Filter specifications are given in Table 6.7.................................. 75 6.9 Comparison o f two-layer filter responses........................................................76 6.10 Optimized physical dimensions obtained from ANN models for the 2layer filter example. Filter specifications are given in Table 6.7............... 77 6.11 Comparison o f optimized two-layer filter responses..................................... 77 6.12 Physical dimensions obtained from optimization method for the 2layer filter example. Filter specifications are given in Table 6.7............... 79 6.13 Center frequency and bandwidth parameters for the 2-layer filter designed using the optimization method. Also, the response of the filter using A NN modeling is repeated here for comparison purposes 79 6.14 Two-layer filter design times and required iterations for ANN modeling and the optimization method of [80]............................................. 80 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. x ix 7.1 Variable param eter ranges for CPW components............................................87 7.2 Error results (average and standard deviation) between the EM-ANN model and full-wave simulation for the optimally cham fered CPW bend....................................................................................................................... 87 7.3 Error results (average and standard deviation) between the EM-ANN model and full-wave simulation for the compensated bend.........................89 7.4 Comparison of return loss for the conventional optimally chamfered bend and the novel compensated bend for several structures. (Frequency = 50 G H z)....................................................................................... 91 7.5 Variable input param eter ranges for the CPW 90° bend................................ 92 7.6 Error results for the variable air-bridge height CPW bend model, regular training. (5 train structures, 4 inputs, 4 outputs, 14 hidden neurons, 130 w e ig h ts)....................................................................................... 93 7.7 Error results for the variable air-bridge height CPW bend model, difference method. (5 train structures, 4 inputs, 4 outputs, 15 hidden neurons, 139 w e ig h ts)....................................................................................... 93 7.8 Error results for the variable air-bridge height CPW bend model, PKI method. (5 train structures, 8 inputs, 4 outputs, 13 hidden neurons, 179 w eights)........................................................................................................ 93 7.9 Error results (average and standard deviation) between the EM-ANN model and EM sim ulation for the CPW transmission line........................... 94 7.10 Error results (average and standard deviation) between the EM-ANN model and full-wave simulation for the CPW short circuit..........................97 7.11 Error results (average and standard deviation) between the EM-ANN model and full-wave simulation for the CPW open circuit..........................97 7.12 Error results (average and standard deviation) between the EM-ANN model and full-wave simulation for the step-in-width.................................. 98 7.13 Error results between the EM-ANN model and EM sim ulation for the CPW symmetric T-junction (average and standard deviation). Input branchline port is Port 1, and the output ports on the main line are Ports 2 and 3....................................................................................................... 102 8.1 Input variables and ranges for CPW transmission line m odel.....................120 8.2 Error results (average and standard deviation) for the CPW line model. 120 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. XX 8.3 Error values (average and standard deviation) for the C PW open-end m odel...................................................................................................................123 8.4 Ideal CPW patch antenna designs.................................................................... 128 8.5 Error results (average and standard deviation) for the CPW feed discontinuity model........................................................................................... 130 8.6 Comparison of resonant frequency and bandwidth for EM-ANN modeling, EM simulation, and measurement................................................131 8.7 Comparison of resonant frequency and bandwidth for EM-ANN modeling, EM simulation, and measurement. CPW patch antenna with longer than ideal patch length..........................................................................137 | t Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. CHAPTER 1 INTRODUCTION 1.1 Motivation 1.1.1 Modeling for CAD Computer-aided design (CAD) of microwave/mm-wave integrated circuits and monolithic microwave/mm-wave integrated circuits relies heavily upon models developed for passive circuit components. Accurate characterization and modeling o f passive circuit com ponents and discontinuities is vital for accurate circuit simulation and increased first-pass design success. The degree o f accuracy to which the performance o f a microwave/mm-wave circuit can be predicted by CAD depends on the accuracy o f characterization and modeling o f components. Passive components can be categorized as either lumped or distributed in nature. Lumped elements (via holes, discontinuities, spiral inductors, etc.) are considered small with respect to the operating wavelength, w hile distributed elem ents (microstrip transmission lines, coplanar waveguide transmission lines, coupled lines, etc.) have sizes comparable to the wavelength. G enerally, microwave circuit design requires both lumped and distributed elements. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 2 Distributed elements are modeled using sections o f transmission lines [1-4]. As an example, transmission lines can be described by their characteristic impedance, Zo, and complex propagation constant, y. Discontinuities associated with distributed elements (bends, steps-in-width, open and shorted stubs, junctions etc.) and lumped elements are generally modeled by networks o f equivalent circuit parameters (ECPs), consisting of resistors, inductors, and capacitors [1-5]. Models can be developed using analytical, electromagnetic (EM) and measurement based techniques [5]. Analytical models, when they exist, are generally based on assumptions that are valid only over a certain limited range o f operation. Also, analytical models require a high level o f expertise and a long development time. Electromagnetic simulation can provide accurate responses. However, the computational expense required does not make practical interactive circuit design using EM simulations feasible, especially when the circuit response must be optimized. Measurement-based models are developed by measuring the S-parameter characteristics of the element, requiring costly mask designs, fabrication, and testing. Although this method can be accurate, it is generally limited to the specific structures that are fabricated and measured. Since analytical models require prohibitive assumptions to be made and require a high level of expertise and knowledge to develop, empirical modeling techniques are attractive alternatives. Empirical models for passive circuit components may be developed by using EM simulation or measured data. Even when accurate numerical data is available, efficient use o f these results for CAD is not straightforward. Empirical models for distributed components (microstrip lines, Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 3 CPW lines, etc.) have generally been developed by curve-fitting responses to specialized functions [1]. The choice o f function requires some degree of expertise about the data to be modeled. This expertise may be lacking for novel components. The most common method for developing empirical models for lumped components has been using equivalent circuit parameter (ECP) models [1-6]. Equivalent circuit models are developed by first extracting ECP values from numerical data for different component geometries and at different operating points, if needed. These results can then be stored in look-up tables [7] or used for obtaining empirical expressions for each ECP based on curve-fitting [2]. However, accurate results are dependent on having adequate equivalent circuit representations, extraction routines, and fitting functions. This approach may be adequate for previously explored structures, which are well understood, but may not be adequate for novel structures for which limited knowledge is available. Therefore, common modeling techniques suffer from the necessity o f having to choose an appropriate function or equivalent circuit to fit the numerical data. As an alternative to the above mentioned modeling techniques, it may be desirable to directly model (or map) the input/output relationships that exist between characteristic parameters (input variables) o f a component and the corresponding response (output variables). Conventional methods used for this purpose are polynomial regression, for exam ple [8, 9], and look-up table models, for example [7]. With these methods, separate models are required for each output variable. Also, prior knowledge about the input/output mapping, which may not be available, is needed in order to select the order o f the model for polynomial regression and the Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 4 interpolating functions for look-up table models. Therefore, a more general modeling technique is necessary, capable o f modeling nonlinear and linear mappings between multiple input variables and multiple output variables. Artificial neural networks (ANNs) offer such an alternative. 1.1.2 Artificial Neural Network Models Artificial neural networks (ANNs) have emerged as a powerful technique for modeling general input/output relationships. In the past, ANNs have been used for many complex tasks. Applications have been reported in areas such as control [10], telecommunications [11], biomedical [12], remote sensing [13], pattern recognition [14], and manufacturing [15], just to name a few. However, until recently, ANNs have been used only to a very limited extent in the area o f microwave/mm-wave design. Applications reported in literature include: automatic impedance matching [16], microstrip circuit design [17], microwave circuit analysis and optimization [18, 19], active device modeling [20-22], and modeling of passive components [23-31], Note that a majority o f the papers on passive component modeling are a result of the research reported in this thesis. Artificial neural network models can be more accurate than polynomial regression models [32-37], allow more dimensions than look-up table models [37], and allow multiple outputs for a single model. Models using ANNs are developed by providing sufficient training data (i.e. EM simulation or measured data) from which it learns the underlying input/output mapping. Several valuable characteristics are offered by ANNs [38]. First, no prior knowledge about the input/output mapping is required for model development. Unknown relationships are inferred from the data Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 5 provided for training. Therefore, with an ANN, the fitted function is represented by the network and does not have to be explicitly defined. Second, ANNs can generalize, meaning they can respond correctly to new data that has not been used for model development. Third, ANNs have the ability to model highly nonlinear, as well as linear input/output mappings. In fact, it has been shown that ANNs are capable of forming an arbitrarily close approximation to any continuous nonlinear mapping [39]. The prim ary objective o f this research is to demonstrate the feasibility o f and provide a general methodology for the developm ent o f accurate and efficient electromagnetically-trained ANN (EM-ANN) models for use in CAD of microwave/mm-wave circuits. These models are capable o f providing EM simulation accuracy within a microwave circuit simulator environment and thus lead to an accurate and efficient CAD. 1.2 Organization o f the Thesis This thesis begins with an overview o f the methodology used for developing EM-ANN models for microwave/mm-wave circuit components. general concepts concerning ANNs are discussed. In Chapter 2, The ANN architecture, training algorithm, data pre-processing, and error formulation are reviewed. presents the specific methodology used throughout this thesis. Chapter 3 Attention is paid to the selection of ANN training data and the methods used for obtaining optimal ANN architecture for a given component to be modeled. Also, methods for simplifying the input/output mapping that needs to be learned by the ANN, through incorporation o f prior knowledge (existing models), are discussed [31]. Specific issues related to the Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 6 development of EM -ANN models for microwave components are covered in Chapter 4. Selection of model inputs and outputs and generation o f training data for microwave components are discussed. Also, methods for linking EM-ANN models to commercial microwave circuit simulators are detailed. The remaining chapters of this thesis contain various examples and uses of EM-ANN models for the CAD of microwave/mm-wave circuits. EM-ANN modeling o f microstrip vias and multilayer interconnects is considered in Chapter 5 [25,26]. Models are developed for microstrip line characteristic impedance, one- and two-port microstrip vias, a stripline-to-stripline multilayer interconnect, a microstrip-tomicrostrip multilayer interconnect, and a microstrip-to-CPW multilayer interconnect. An example of using EM-ANN models to optimize the component geometry is included. Use of prior knowledge (existing models) for model development is also demostrated in Chapter 5. Chapter 6 presents a methodology for the synthesis (leading to physical dimensions) of multilayer asymmetric coupled microstrip lines using artificial neural ANN models [27]. Both synthesis and analysis models are developed. Models are appropriate for synthesis of multilayer structures like filters, baluns, and directional couplers. Accuracy comparable to other optimization methods for multilayer filter design is achieved, but in a small fraction o f the time. The proposed methodology is demonstrated by the design of a 2-layer coupled line filter. Chapter 7 is concerned with generating a library o f EM-ANN models for CPW circuit design [28,29]. M odeled components include: CPW transmission lines (frequency dependent Zo and ere), 90° bends, short circuit stubs, open circuit stubs, step-in-width discontinuities, and symmetric T-junctions. Design and optimization o f a CPW Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 7 folded double stub filter and a 50 Q , 3 dB power divider circuit, using the developed CPW EM-ANN models, are demonstrated. Chapter 8 deals with developing EMANN models for novel CPW patch antenna design [30]. Models are developed for wide strip CPW lines, CPW open-end effects including radiation conductance, and feed interactions. Since this is a novel antenna, no design information was available in the literature. However, using EM-ANN modeling techniques, a couple of wide bandwidth CPW patch antennas have been designed and validated by both EM simulation and measurements. The thesis concludes with a discussion o f results and directions for future research in Chapter 9. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. CHAPTER 2 INTRODUCTION TO MULTILAYER, FEED-FORWARD ARTIFICIAL NEURAL NETWORKS Multilayer, feed-forward artificial neural networks consist of parallel, highly interconnected layers o f computational nodes termed neurons. These networks can be viewed as providing a general framework for representing nonlinear functional mappings between a set o f input variables and a set of output variables. Mapping is achieved by representing the nonlinear function of many variables in terms of compositions of nonlinear functions o f a single variable, called activation functions. In a related matter, Kolmogorov [40] has shown that every continuous function of several variables can be represented as the superposition o f a small num ber o f functions of one variable. Supervised training o f the ANN is provided by adjusting adaptive weights which provide connections between neurons, using the error backpropagation algorithm. Two-layer networks, containing one hidden layer and an output layer of neurons are the most popular. Both layers have sigmoidal activation functions for the neurons. It has been shown that two-layer networks of this form can arbitrarily approximate any continuous mapping from one finite-dimensional space to another, provided the num ber of hidden layer neurons is sufficiently large [39]. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 9 This chapter reviews the architecture and corresponding equations for twolayer ANNs using error back-propagation training. Issues related to ANN training, including data selection and pre-processing, error formulation, the error backpropagation algorithm, and generalization are discussed. For a more detailed discussion of ANN concepts refer to [38]. 2.1 ANN Topology The topology o f the ANN used for this work is shown in Fig. 2.1. It is a two- layer network, consisting o f an input (non-computing) layer, a hidden layer of neurons, and an output layer o f neurons. It is fully connected, which means that each neuron is connected to every neuron in the next layer. All connections have an adjustable weight associated with them. Each com puting neuron has, associated with it, a nonlinear activation function. The number o f neurons in each layer is problem dependent and is decided upon during training. One can write down the analytical function corresponding to the network of Fig. 2.1 as follows. The input, Uj, of the y'th hidden neuron is obtained by forming a weighted linear combination o f the / input variables, ,v„ and the corresponding connection weight, , to give i=i Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 10 Input Layer Hidden Layer Output Layer w1<5 -yi j1 wj0 r k l wk0 -yk -►yK i=1,2....1 j=1,2 J k=1,2 K Fig. 2.1 Artificial neural network architecture. where is the additional bias input to the jth neuron. This input, Uj, can be written as t (i) Uj = Z W j i X , ( 2 .2 ) i= 0 where jc0=1 . The output, Zj, of hidden neuron j is then obtained by transforming the linear sum of (2.2) using the activation function o f the neuron g(») to give Z j = S(U j )- Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. (2.3) 11 The network outputs are obtained by transforming the outputs o f the hidden layer neurons in a sim ilar manner. Thus, for each output unit k, a weighted linear combination o f the outputs of the hidden layer neurons is formed to give v k = 'LJj=0w ^ z J <2 -4 ) where the bias weight has again been absorbed into the sum by setting z0= 1. The output of the network is then obtained by transforming (2.4) by the activation function of the output layer neurons to give (2-5) y k= s(vk) Combining (2.2), (2.3), (2.4), and (2.5) one obtains the output o f the network shown in Fig. 2.1 as y k= • ( 2 -6 ) Equation (8.6) can be written in vector-matrix form as Y = i ( w 2-«(w,*x)) Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. (2.7) where X is the input vector, Y is the output vector, and W j and W 2 are the weight connection matrices between the input and hidden layer and between the hidden layer and output layer, respectively. The activation functions, for both the hidden layer neurons and the output layer neurons, are sigmoidal. The specific sigmoidal function used for this work is the logistic function given by g(u) = -tit- (2.8) l +e Sigmoidal activation functions have several desirable properties. First, a sigmoid function is bounded. Second, the value o f a sigmoid function is monotonic. Third, a sigmoid function is continuous and smooth and is therefore differentiable anywhere. The logistic activation function o f (2.8) is shown in Fig. 2.2 and varies from 0 to 1 as u varies from -oo to +oo. The values o f the weights determine the slope and shift o f the logistic function. 2.2 ANN M odel Developm ent (Training) Network training (or learning) is accomplished by adjusting the weights o f the network based upon some error criteria between the actual outputs o f the network, _v’k, and the target output values, tk- To start with, the weights are initialized to small random values. Then input vectors are passed forward through the neural network I Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 13 0.75 -- 0.5 0 . 2< 10 -7.5 -5 -2.5 0 2.5 5 7.5 10 u Fig. 2.2 Logistic activation function used in hidden layer and output layer neurons. and the corresponding outputs are computed. In the beginning, the actual outputs will not be close to the target outputs. Actual network outputs are then compared to target output values and the derivative o f the error between them with respect to each o f the weights, is calculated. Error derivatives with respect to each weight are summed for all input/output vectors, which is termed batch processing. Weights are then adjusted based upon their contribution to the error such that overall network error decreases. These steps of calculating the error derivatives for all the training data and then updating the weights is termed an epoch. This “gradient descent” procedure continues in an iterative manner until overall error is reduced to an acceptable level. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 14 2.2.1 Data Preprocessing Data selection is crucial for the development o f ANN models. Data must be selected to capture important input/output mapping relationships. Once data has been selected, it is generally separated into training, testing, and independent verification datasets. Training data is used for model development while testing data is used to determine when training should halt. Verification data is used for final model validation. An important form o f data preprocessing consists o f a simple linear rescaling of the input/output data. This is useful when different variables have typical values which differ significantly. Data is generally scaled from 0 to 1 or from -1 to 1 depending upon the activation function used. With linear rescaling, each variable is assigned the same importance (errors are o f the same magnitude) for model development and determined weights should not be markedly different. Another form of data preprocessing is the use of prior knowledge. Prior knowledge about the mapping to be learned can be incorporated into network training by altering the input/output data. This alteration can reduce the complexity of the mapping and therefore require less training data to capture. This is discussed in more detail in Chapter 3. 2.2.2 Error Back-Propagation Error back-propagation refers to the propagation o f errors backward through the network to find the error derivatives with respect to each weight. Once the error derivatives are determined, they can be used in conjunction with a method such as gradient descent to update the network weights. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 15 Using differential calculus the derivatives of the error, £", with respect to each weight for a single input vector, n, can be found as dw .dE n -m > — '/ <2-9 > for the second layer of weights between the hidden layer and the output layer, and where Sk = g (vv) <?E (2.10) for the first layer of weights between the input layer and the hidden layer. Note that when multiple network outputs are present, EP, is the combination of the errors from all the outputs so that r = r ( y , y K)- ( 2 - 11 ) Error derivatives are then summed for all input vectors and used to update the weights of the network. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 16 2.2.3 Error Functions 2.2.3.1 Absolute Error Training to reduce the absolute error from the network is accomplished by using the condition of least squared error between the target output, tk, and the network output, yk. The error function for a single input vector is given by ( 2 . 12 ) This choice of error function is convenient since it is differentiable and provides a positive error surface which is used in conjunction with gradient search techniques. As one can see from (2.12), this choice o f error function is aimed at reducing the absolute error from the network, placing em phasis on reducing the largest errors. Using this error measure, the error back-propagation equations become (2.13) for the second layer o f weights , and <3En - — • ri = 8 (Uj)2^wk A xi where 4 = g (vk )(yk - t k ) for the first layer of weights. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. (2.14) 17 2.2.3.2 Relative Error Many times the absolute error is not as important as the relative error. For example, when creating a model for the characteristic impedance of a microstrip line, the output values may range from 10 Q to 100 Cl. A 1 f i absolute error corresponds to a 10% error at 10 Q but only a 1% error at 100 Q . In this situation it would be beneficial to put more emphasis on reducing the relative error. To perform network training on relative error, we have modified the error function o f (2.12) as follows (2.15) Using this error measure, the error back-propagation equations become (2.16) for the second layer o f weights , and Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 18 / where Sk = g \ v k ) — L r { tl (2.17) J for the first layer o f weights. An example o f training on relative error is given in Chapter 5 for the characteristic impedance o f microstrip lines. 2.2.4 Learning Rules The most common learning rule used to update the weights of the network is the steepest gradient descent method and is used extensively in this work. The name “steepest descent” implies that weight changes move the weights in a direction in which the error declines most quickly. The weight update rule is given below as •+i t (2.18) where t is the epoch number, r\ is the learning rate, and p. is the momentum. Error derivatives given in the previous section may be used in conjunction with (8.18) for network training. Other error minimization algorithms may be used for learning such as adaptive steepest gradient and conjugate gradient methods. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 19 2.3 M odel Generalization and Overfitting The goal o f neural network modeling is to produce a model that is valid not only for the training data but for data (within the range o f the input variables) that the network has never seen before. This is referred to as the generalization capability o f the network. It is possible for the network to fit the training data too closely or even exactly. This is termed overfitting and occurs when the network learns the noise in the data in addition to the underlying function to be modeled. In this case, the models generalization capabilities will be poor. The number of neurons in the hidden layer is crucial to the ANNs ability to generalize. Too many neurons in the hidden layer tend to lead to overfitting, while a network with too few hidden layer neurons may not be able to learn the desired input/output mapping. Therefore, one needs a method to monitor whether overtraining has occurred and to determine the optimal number o f neurons in the hidden layer for a given problem. Methods used for this work are discussed in detail in Chapter 3. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. CHAPTER 3 MODELING METHODOLOGY This chapter reviews the methodology used for development of ANN models throughout this work. Attention is paid to selection o f training data and methods for obtaining the optimal ANN model for a given component. Also, methods for simplifying the input/output mapping that needs to be learned by the ANN through incorporation o f existing knowledge are demonstrated. 3.1 Selection of Training Data by Design o f Experiments (DOE) Techniques In order to train the ANN models, input/output relationship data (termed examples) needs to be collected. In many situations, this data is not readily available and can be very time-consuming to obtain. In these cases, a minimum number of training points need to be chosen so that important input/output relationships are presented to and learned by the ANN model. Simple models require less training data, while highly nonlinear models require an increased number o f training data points. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 21 For some components, analytical models are possible and input/output relationships may be expressed in closed forms. W hen the input/output relationships are too complex, experimental data may need to be obtained to characterize the component. For many complex relationships, design o f experiments (DOE) methodology is used to systematically study the input/output relationships o f a component or process [41]. A designed experiment is a test or a series of tests in which purposeful changes are made to the input variables of a process or system so that the causes of changes in the output response can be observed and identified. Experimental results are then used to build the model of the input/output relationship using response surface methodology (RSM). In RSM problems, the input/output relationships are unknown. The first step is to approximate the input/output relationships. This is usually done using low-order polynomials or other fitting technique over a small portion o f the input variables’ ranges. However, when the process is influenced by a large number of input variables, is highly nonlinear, has more than one output variable, or when a global fit to the response surface is needed, these conventional fitting methods are limited [19,42], An alternative approach for modeling o f the response surface is the use of ANNs [42], ANNs are able to deal with highly nonlinear and multiple input/output variables effectively, providing excellent interpolative capabilities [38]. This allows development of a global model representing a component. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 22 Although response surface methods have been developed for regression analysis, they can be used to determine simulation points which effectively cover the region of interest. W hen building a model, one would like to reduce the training time by providing as little training data as necessary, for achieving a desired accuracy. This implies starting w ith a low-order experimental design and sequentially building up to higher-order designs by adding additional training data. The simplest experimental designs for fitting first-order response surfaces are 2k factorial designs, where k is the number o f input variables as shown in Fig. 3.1 [41] for a two variable case. For the design, only minimum and maximum values of each input parameter are used. Minimum and maximum input parameter values are represented as -1 and +1, respectively. This design requires 2k comer points. Because there are only two levels for each input variable, this design is useful for characterizing output responses that are approximately linear over the range o f the input variables. If a first-order design is not sufficient for capturing the input/output relationships of the component, then additional simulation points are added to capture the higher-order nonlinearities. The most widely used experimental design for fitting second-order response surfaces is the central composite design [41]. Central composite designs are advantageous in that they can be built up from 2k factorial designs by adding axial points and a center point as shown in Fig. 3.2. The axial points are positioned to provide a circular pattern. Minimum and maximum parameter values are represented by -1 and +1, respectively. One may also use a modified central composite design as shown in Fig. 3.3. For this design, all points are l| i Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 23 shifted inward so that there are no simulation points outside the input variable space. Central composite designs require 2k com er points, 1 center point, and 2(k) axial points, where k is the num ber o f variable parameters. If the nonlinear input/output relationships have still not been sufficiently captured, simulation points spaced midway between the central com posite points, as shown in Fig. 3.4, are then added to capture higher-order nonlinearities. In this manner, design of experim ents is built up sequentially, adding more sim ulation points if increased model accuracy is desired. 0 d.D H.i) 0 0 (1.-D Fig. 3.1 DOE 2k factorial design. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. (0. t.4 ) ( 1. 1) > 1 . 1) (0 . 0 ) (-1 .4 . 0) (1.4. 0) (-1.-D (0.-1.4) Fig. 3.2 DOE central composite design. ( 0 . 1) (0.7.0.7) £ (0 .0 ) ( - 1 .0 ) Q ( 1 .0 ) (0.7.-0.7) Q (-0.7.-0.7) (0 .- 1) Fig. 3.3 Modified DOE central composite design. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 25 i *2 (0.1) Q (0.7.0.7) ^ 00.7.0.7) • • II • A W ------9 X1 | • • 0 0 .0 ) (0.0) (0.7.-O.7) £ (-0.7.-0.7) (0.-1) ' Fig. 3.4 Modified DOE central composite design with additional interior points. 3.2 ANN Training Methodology Training o f the ANNs for this work has been accomplished using CU-ANN*, a user-friendly software developed at the University o f Colorado at Boulder by Marwah et al. [43]. This section briefly describes the methodology used and its advantages. 3.2.1 Data Pre-Processing To begin with, training data is separated into two datasets, one for training and one for testing. Model validation data is kept separate and is not used in any capacity for training the ANN. The inputs are linearly normalized between 0 and 1. Outputs are linearly normalized between 0.2 and 0.8 so that output neurons operate in the Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 26 relatively linear portion of the logistic function. If the range o f any o f the inputs or outputs is large, they can be logarithmically normalized before training. 3.2.2 Sim ultaneous Training and Testing One advantage of using the methodology o f [43] is the ability to perform simultaneous training and testing. Testing dataset errors can be monitored as training progresses to avoid overfitting o f the training data. In this way, a model with good generalization capabilities is developed. Before training begins, all network weights are randomly initialized to small values near zero. After each pass through the training data, or epoch, the correlation coefficient, R 2, and the normalized mean-squared error, £ Ms e are calculated for the training dataset and for the testing dataset after R 2 reaches 0.8 [43]. £m se is a measure of the absolute error while R2 is a relative measure ranging from 0 to 1. The two error measures together give an indication of the quality of the model and are given below (3.1) R- = l n=U =l and (3.2) w here N is the number of input/output examples, K is the number o f output variables, y nt is the predicted output of the model, Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 27 is the target output, and t is the target output mean. W henever E mseuu decreases, the weights are stored. Therefore, the model with the lowest testing dataset errors is saved, providing a model with the best generalization capabilities. Another feature o f CU-ANN is the ‘simple to complex’ procedure used to determine the neural network architecture. A network with too few neurons will not be able to map complex input/output relationships, while a network with too many neurons tends to overfitt the training data [38]. First, a simple network architecture is chosen, usually containing one hidden layer with a small number o f neurons. If learning is slow or desired accuracy is not achieved, additional neurons are added to the hidden layer. In the CU-ANN software, the process o f changing the network architecture has been automated. The best network architecture is saved, identifying the optimal network. 3.3 Use o f Prior Knowledge A potential drawback o f ANN modeling is the amount o f training data that needs to be provided in order to obtain an accurate model. Training data must be provided to characterize the component to be modeled over a desired range of operation and for different combinations o f geometrical and physical model inputs. The difficulty arises when training data is expensive or difficult to obtain. The amount of data needed to train an ANN model can be reduced by using design of Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 28 experiment (DOE) techniques. However, even with the use o f DOE techniques, the required amount of data needed for model development can still be too large. An approach to reducing this data is through reducing the complexity o f the input/output mapping that must be learned by the ANN. To this end we propose using prior knowledge (existing models) about the component to be modeled. Prior knowledge, for example, can be in the form o f analytical equations, empirical models, already trained ANN models, or some available experimentally measured data. These existing models are models which contain information about the component to be modeled but do not give the required accuracy over the desired range o f operation. Use o f prior knowledge for microwave design has been shown to be an effective means of reducing the amount o f training data needed to obtain desired model accuracy [26, 44]. In [44], prior knowledge is incorporated into a knowledge based neural network structure, consisting o f 7 layers, in the form of empirical functions or analytical approximations as activation functions in “ knowledge layers”. Drawbacks of this approach are the more complicated structure o f the network for which conventional error backpropagation training is not applicable, the restriction o f having prior knowledge in equation form, and the possible restriction of only having one network output. For a chemical vapor deposition in a horizontal reactor, Marwah [45] and M arwah and Mahajan [46] propose using different model transfer techniques to convert a previously trained physical neural network model (called the source model) to an equivalent model (called the target model). Three different techniques, namely Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 29 difference method, source weights method, and prior knowledge input method (PKI) are evaluated. The PKI method was shown to out perform the other two methods. To get better insight into the dynamics of the above mentioned model modifier techniques, the output/input behavior was monitored during the training process. It was noted that in the difference method, the difference between the source and the target was not a simpler function of the inputs as compared to the target. As a result, no benefit was expected to result from this modifier approach. This was supported by the training results, which showed that the percent relative error on the target points was the same as that obtained by training the target model without the help o f the source model. The source weight technique resulted in a similar performance. With the PKI method, on the other hand, the source function converged towards the target function continuously as the training proceeded. Trained on one-fourth of the points used for the source model, the target model achieved the same accuracy as the source model. These techniques have not been investigated thoroughly for their performance in modeling of microwave components. In this section, we present two of the three techniques mentioned above for incorporating prior knowledge (or existing models) into ANN model development using EM simulation. These are the difference method and the PKI method. In the difference method, the ANN is trained on the difference between the target model output and the existing model (source model) output, shown in Fig. 3.4a. This method is expected to give good results when the difference has a simpler input/output mapping as a function of the inputs than the target data. A simpler input/output mapping requires less training data to characterize. An example o f the Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 30 use o f the difference method has previously been reported in [26]. In the PKI method, the source model outputs are used as inputs for the ANN model in addition to the other inputs, shown in Fig. 3.4b. In this case, the input/output mapping that m ust be learned by the ANN is that between the output response o f the existing model and that of the target model. For the case when the target outputs are the same as the existing model outputs, the learning problem is reduced to a one-to-one mapping. Note that conventional two-layer neural networks along with error backpropagation training are used with both the difference and PKI methods, which is advantageous for a user. Applications o f the difference m ethod and the PKI method for developing electromagnetically-trained ANN (EM -ANN) models for microwave design encompass new ANN model development, range extension of existing ANN models, and the addition o f input parameters to existing ANN models. Examples o f using prior knowledge for ANN model developm ent are presented in following chapters. A 2-port microstrip via model is developed in Section 5.7.1 with the aide o f an analytical expression for inductance o f the via. In Section 5.7.2. the frequency range of a stripline-to-stripline multilayer interconnect model is extended using an already developed ANN model as prior knowledge. As a final example, in Section 7.1.4, an input parameter (air-bridge height) is added to an existing ANN model (CPW 90° bend), again using an existing ANN model as prior knowledge. I Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 31 Existing Prior Knowledge Physical Param eters Frequency ■AS EM Simulation T raining Signal Physical Param eters Frequency ANN M odel Error (a) Existing M odel Outputs Physical Param eters Frequency Existing Prior EM Simulation K n o w le d g e EM O utput A N N O utput ANN Model Physical Parameters Frequency Error ( Training l Signal (b) Fig. 3.5 Schemes for using prior knowledge (existing models) for artificial neural network training, (a) difference method and (b) PKI method. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. CHAPTER 4 ANN MODELS FOR MICROWAVE/MILLIMETER-WAVE DESIGN This chapter discusses some general issues related to the developm ent of ANN models for passive microwave/mm-wave components. model developed are given in the following chapters. Specifics for each In this chapter, selection of model inputs and outputs, as well as generation of training data are discussed. Also, error measures for model validation are given. After the ANN models are developed, they are linked to a commercial microwave simulator where they can be used for circuit design and optimization. 4.1 Selection of Model Inputs and Outputs Selection of input parameters for microwave/mm-wave passive components is relatively straight-forward. Inputs are generally important physical (geometrical) parameters of the component, which one would like to vary, and frequency. Input variables’ ranges are determined by desired model usage requirements. In the design of microwave/mm-wave circuits, it is often desirable to interconnect many active and passive elements together. This can be accomplished by representing model outputs in the form o f S-parameters, which are related to the Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 33 power reflected and transmitted by a given component. S-parameters are also a convenient way to link developed models with commercial microwave simulators for design and optimization. For this work, most ANN model outputs are given as Sparameters. The magnitude and phase o f each S-parameter is a separate output. Therefore, if the component to be modeled is a one-port device, the output parameters would be ISnI and Z S n . For a more detailed discussion of S-parameter theory and applications refer to [47]. For transmission line models, the outputs o f the ANN model are the characteristic impedance, Z„, and the propagation constant, p. Knowing these two parameters, and the length o f the line, the S-parameters o f a section o f the line can be found. In this way, the length o f the line is not included as a variable input parameter for the ANN model. 4.2 Training Data Generation Training data for passive microwave/mm-wave component models generally comes from measurements o f actual components or from electromagnetic (EM) simulation. Using actual measurements can be costly since it requires design and fabrication of many components for characterization. However, by using actual measurement data, one may obtain a model that is valid for their specific fabrication process, which may be desirable. EM simulation is the alternative to using measured data for model development and is used throughout this work. The EM simulator used for this purpose is HP-Momentum [48], except for the development of models for multilayer Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 34 coupled line design which are discussed in detail in Chapter 6. The EM sim ulator yields S-parameters for given com ponent geometries, which are then used to train ANN models. These models trained by EM simulations are therefore term ed electromagnetically-trained artificial neural network (EM-ANN) models. One drawback of using EM simulation for the generation o f training data is that EM simulation can be very time-consuming. Therefore, DOE techniques and prior knowledge, as discussed in the previous chapter, should be used in order to reduce the number of EM simulations necessary for model development. 4.3 Error Measures Error measures can either be absolute or relative in nature. The choice o f w hich error measure to use is determ ined by the type of accuracy desired and model usage requirements. Most EM-ANN model errors reported in this work are presented as the absolute average and the standard deviation of error for each output. For S- parameters, this is useful since it allows a designer to determine the amount o f signal reflection and/or transmission o f the model on average and to estimate some useful error bounds. In some cases, relative errors are important, as with the characteristic impedance, Zq, of a transmission line. W hen Zq is small, a small absolute error can produce large mismatch errors w hen impedance matching is carried out. However, a larger absolute error is allowable for higher Zo values. Therefore, relative errors are considered in this case. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. ! 35 4.4 Integration of EM-ANN Models with Circuit Simulators Once the EM-ANN models have been trained and their accuracy determined, they can either be used in stand-alone mode or they can be integrated with a commercial microwave circuit simulator depending on the type and desired usage o f the model. These models then provide accuracy approaching that o f the EM simulator used for generating the training data. As shown in Fig. 4.1, EM-ANN models have been integrated into HP-MDS [49], a commercially available microwave circuit simulator. Models can be inserted into other circuit simulators in a similar manner. During simulation, HP-MDS passes input variables, such as frequency and the physical parameters of a component, to the user-defined linear model subroutine used for linking models to the circuit simulator. This subroutine is then responsible for returning S-parameters of the component back to HP-MDS for further processing. The input variables are passed to a feed-forward ANN subroutine, by the user-defined linear model subroutine, for computation of model S-parameters or the data required for com puting them. The feed-forward ANN subroutine implements the algorithm o f Section 2.1 for finding the output o f a 2-layer ANN. EM-ANN models are stored as files, w hich are read by the feed-forward ANN subroutine. Each model file contains the num ber o f input parameters, the number of output parameters, the number of neurons in the hidden layer, the maximum and minimum values (used for normalization) for each o f the input and output parameters, and the weight connection matrices. An exam ple of a user-defined linear model subroutine, the feed-forward ANN subroutine, and an EM-ANN model input file are given in Appendix A. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 36 Models can also be grouped into libraries. A library is a collection o f models that can be linked to HP-MDS as a group. This offers a convenient way to create and distribute models for use by others. An example o f a library o f coplanar waveguide (CPW) components, created for model distribution, is given in Appendix B. Commercial microwave circuit simulator Model S-param eters Model input variables User-defined linear model subroutine EM-ANN model outputs EM-ANN model inputs Feed-forward ANN subroutine EM-ANN model data EM-ANN model file Fig. 4.1 Flow of data for linking EM-ANN models to commercial microwave circuit simulators. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 37 4.5 Design and Optimization Using EM -ANN Models Once EM-ANN models have been linked to the circuit simulator, they can be used in the design and optimization o f microwave/mm-wave circuits. EM-ANN models are used just as any other m odel available within HP-MDS (or similar network simulator). The models can be simulated alone or combined w ith many other models to form a complete circuit. Circuit and/or component optimization, where the gradient o f a function is needed, can also be performed using the routines available within the circuit simulator. Two-layer networks with sigmoidal hidden units have the ability to simultaneously approximate both a function and its derivative [50]. This is due to having continuous hidden layer and output layer neuron activation functions (sigmoids), which are differentiable everywhere. Examples of design and optimization o f microwave/mm-wave circuits and components are presented in following chapters. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. CHAPTER 5 EM-ANN MODELS FOR VIAS AND MULTILAYER INTERCONNECTS Efforts to lower the cost and reduce the weight/volume of microwave circuits have resulted in high-density and multilayer circuits where a large number of via interconnects are used. W ith this increased complexity and higher operating frequencies, accurate and efficient characterizations o f via interconnect discontinuities and single-layer ground vias m ust be carried out in order to achieve accurate simulation results [51]. Several recent efforts have focused on the analytical and numerical evaluation of via discontinuities using quasi-static and full wave techniques [51-67], Quasi-static models are valid only at lower frequencies. Full-wave EM simulation and characterization can lead to accurate results, but at much higher computational expense which prevents their use in practical interactive CAD. Applications of the EM -ANN methodology for modeling via elements in microstrip circuits and multilayer via interconnects are presented in this chapter. Modeling examples include, m icrostrip transmission line, one- and two-port microstrip vias, a stripline-to-stripline multilayer interconnect, a microstrip-to- Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 39 microstrip multilayer interconnect, and a microstrip-to-CPW multilayer interconnect. As a demonstration, use of prior knowledge, as discussed in Chapter 3, has been used to develop models for a 2-port microstrip via and to extend the frequency range o f the stripline-to-stripline multilayer interconnect model. Results are compared with normal training methods (no use of existing knowledge). The developed EM-ANN models have been linked to HP-MDS [49] (a commercial microwave circuit simulator) where they can be used for circuit simulation and optimization. An example comparing the 1-port microstrip via model, available in HP-MDS, to the EM-ANN 1-port microstrip via model is presented. Also, component optimization, using the stripline-to-stripline multilayer interconnect model, is demonstrated. 5.1 Microstrip Transmission Line Model Many times a model for a microstrip transmission line is needed either as a element or to provide useful data for a circuit designer. Therefore, an ANN model has been created to provide the characteristic impedance dielectric constant (e Cfr) for microstrip transmission lines. (Z q ) and the effective Another reason for this modeling example is to demonstrate a situation where it is better to train on relative error rather than on absolute error as discussed in Chapter 2. For example, when creating a model for the characteristic impedance of a microstrip line, the output values may range from 10 Q to 100 Q. A 1 Q absolute error corresponds to a 10% error at 10 Q but only a 1% error at 100 Q. In this situation it would be beneficial to put more emphasis on reducing the relative error. The goal for this model was to ! j Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 40 have the sum o f the average and standard deviation o f the residual errors for Zq be less than 1%. Figure 5.1 shows the geometry of the microstrip line to be modeled. Variable input parameters and corresponding ranges are given in Table 5.1. Output parameters Training data has been provided using linecalc [68]. are Zo and 8eff. Since the training data was not time-consuming to obtain, DOE techniques were not used. Instead, a uniform grid of points was simulated to provide the training data. The training/test dataset consisted of 155 examples while the verification dataset contained 100 examples. Models were trained using both absolute and relative error criteria for comparison. The final models were trained using all 155 training/test examples and both required 10 hidden layer neurons. Table 5.1 Variable input parameters for microstrip transmission line model. Input Parameter Minimum Value Maximum Value Frequency 1 GHz -1 2 18 GHz 1 13 Iogio(W|/HSUb) er W Hs u b | I £r ground /////////////////////? // Fig. 5.1 Cross-section of microstrip transmission line geometry where W] is the width of the microstrip line, HSUb is the substrate height, and Sr is the relative dielectric constant of the substrate. i Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 41 The residual error results for both absolute error training and relative error training are given in Table 5.2 and in Table 5.3, respectively. Looking at the Zo results, notice that the training on absolute error provides lower absolute error, but higher relative (percentage) error. The highest relative errors are at low Z q values as expected and do not meet the goal o f having the average and standard deviation results sum to less than 1%. W hen using relative error measures during training, lower relative errors are obained and our accuracy goal is achieved. Table 5.2 Error results (average and standard deviation) between the EM-ANN model and linecalc for the microstrip transmission line for a bsolute e rro r training. Train/test dataset Average error Standard dev. Verification dataset Average error Standard dev. Zo(tt) Zo (%) S e fT £ e ff ( % ) 0.206 0.205 1.161 1.157 0.012 0.012 0.377 0.376 0.338 0.520 0.774 0.875 0.015 0.013 0.293 0.223 Table 5.3 Error results (average and standard deviation) between the EM-ANN model and linecalc for the microstrip transmission line for relativ e e rro r training. Train/test dataset Average error Standard dev. Verification dataset Average error Standard dev. Zo(Q) Zo (%) S e rf S e ff ( % ) 0.300 0.344 0.456 0.334 0.014 0.015 0.244 0.186 0.399 0.679 0.518 0.464 0.011 0.011 0.186 0.150 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 42 5.2 Broadband GaAs 1-port M icrostrip Via Figure 5.2 shows the structure and some parameters o f the one-port via under consideration. The height of the substrate (HSUb). the dielectric constant (£r). and all loss parameters are considered constant for this example. The width o f the incoming microstrip line. Wi, the side o f the square shaped via pad. W p. and the diameter of the via hole. D via. are the three variable design parameters. Input variables for the EMANN model and their ranges are given in Table 5.4. Output variables aie the magnitude and phase of Sn referenced to 50 Q port termination. REFERENCE PLANE via Fig. 5.2 GaAs microstrip ground via geometry. Substrate thickness = 4 mil, 8r=12.9, tan5=0.002, crm«ai=4-l.x.l07, and 1 mil. Table 5.4 Variable input parameters for GaAs m icrostrip ground via modeling. Input Parameter Frequency W,/WD DviaAVp W|/Hsub M inimum Value 5 GHz 0.3 0.2 0.1 M axim um Value 55 GHz 1.0 0.8 2.0 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 43 EM simulations were performed from 5 to 55 GHz in 10 GHz steps using a commercially available full-wave electromagnetic simulator (HP-Momentum [48]). Via structures for 15 DOE central composite points, as well as for 14 additional training/testing points spaced midway between the previous points, were simulated. In addition, 16 structures were simulated for independent verification o f the model after com pletion o f the training. Best results were obtained by using 10 neurons in the hidden layer and the 15 central composite points, as well as the 14 interior points for training the network. Residual error results for the EM-ANN model are given in Table 5.5. We note that an excellent accuracy has been achieved. Table 5.5 Error results (average and standard deviation) between the EM-ANN model and EM simulation for the 1-port microstrip via. ISul Train/test dataset Average error Standard dev. Verification dataset Average error Standard dev. 5.3 z s^ n 0 .0 0 1 0 2 0 .4 5 6 0 .5 2 2 0 .0 0 1 6 2 0 .5 3 7 0 .0 0 2 2 5 0 .5 3 6 0 .0 0 1 0 5 Broadband GaAs 2-port Microstrip Via In addition to the one-port via described above, a two-port via has also been modeled. The same training points were used as for the 1-port via. The structure o f the via is shown in Fig. 5.3 and the input variables and corresponding ranges are given in Table 5.4. Output variables are the magnitudes and phases of Sn and S 2 1 , j i ! Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 44 again referenced to 50 Q. As with the one-port via, best results were obtained by using 15 central composite points and the 14 interior points for training. Ten neurons were required for the hidden layer. Residual error results are given in Table 5.6. Again, an excellent accuracy has been achieved. REFERENCE PLANE 70 1 W, T iH Fig. 5.3 Two-port GaAs microstrip grounding via. Substrate thickness = 4 mil, e=12.9, tanS=0.002, a meaI=4.1x107, and tmeIal = 0.1 mil. Table 5.6 Error results (average and standard deviation) between the EM-ANN model and EM simulation for the 2-port microstrip via. Train/test dataset Average error Standard dev. Verification dataset Average error Standard dev. ISnl Z S „(■) IS2 1 I 0.00361 0.00334 0.413 0.402 0.00680 0.00492 0.442 0.474 0.00420 0.00385 0.434 0.356 0.00881 0.00920 0.771 0.774 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 45 It may be noted that the EM-ANN via models are able to achieve accuracy comparable to EM simulation over the entire 5-55 GHz range. Since a full-wave analysis is used, all the dielectric, conductor, and radiation losses, as well as all parasitic effects, are included. The developed models may now be used in linear analysis and in nonlinear analysis where harmonic frequency components are generated. 5.4 StripIine-to-Stripline Multilayer Interconnect Figure 5.4 shows the structure of a 50 stripline-to-stripline multilayer interconnect for which an EM-ANN model has been developed. Reference planes are set at Wiine/2 from the center of the via. The variable design parameters are the diameter of the via, Dvia, and the diameter o f the ground access opening, Dgnc]. All other parameters are fixed. Model input variables and their ranges are given in Table 5.7. Output variables are the magnitudes and phases o f Si i and S2iEM simulations were performed from 1 GHz to 26 GHz in 5 GHz steps. Interconnect structures for 9 central composite points and 8 additional training/testing points were simulated. In addition, 12 structures were simulated for model verification purposes. Using the 9 central composite points plus the 8 additional points for training the model yielded the best results. Nine neurons were used in the hidden layer. Residual error results are given in Table 5.8. As with the GaAs ground vias, excellent results have been obtained. ! Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. R eference Planes ine 50 oh m strip via gnd ground Fig. 5.4 Stripline-to-stripline interconnect structure with W|ine= 13.675 mil, Zo = 50 ohms, 8r= 2.94, tanS = 0.0012, tmetai = 1.4 mil, Ometai = 5.7xl07. and H = 20 mil. Table 5.7 Variable parameters for stripline-to-stripline multilayer interconnect model. Input Parameter Freauencv Dyia/Wune _____Dmd/Dyia M inimum Value 1 GHz 0.365 1.25 Maximum Value 26 GHz 0.8 6 Table 5.8 Error results (average and standard deviation) between the EM-ANN model and EM simulation for the stripline-to-stripline multilayer interconnect. ISnl Train/test dataset Average error Standard dev. Verification dataset Average error Standard dev. z s i,n IS2 1 I z s 21n 0.00172 0.00164 1.043 0.855 0.00069 0.00087 0.238 0.230 0.00151 0.00128 1.540 1.306 0.00057 0.00054 0.220 0.160 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 47 5.5 Microstrip-to-Microstrip Multilayer Interconnect Figure 5.5 shows the structure o f a 50 O microstrip-to-microstrip multilayer interconnect for which an EM-ANN model has been developed. Reference planes are set at Wbot/2 and WIop/2 from the center of the via for the bottom and top microstrip lines, respectively. The variable design parameters are the diameter of the via. DV13. and the length o f the overhang for the top microstrip line. LoH. All other parameters are fixed. Model input variables and their ranges are given in Table 5.9. Output parameters for this ANN model are the magnitudes and phases of Sn, S i|, and Sii. Reference Planes / \ L oh 50 o h m strip i c r2 r r1 —► t c 5 0 o h m stri p 'via H H Fig. 5.5 Microstrip-to-Microstrip interconnect with Zo = 50 ohms, W ^, = 23 mil, W Iop = 125 mil, eri = 10.2, era = 2.2, tan5 = 0.0012, t^u ] = 1.4 mil, Ometai = 5.7xl07, and H = 25 mil. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 48 EM simulations were performed from 2 GHz to 12 GHz in 2 GHz steps. Interconnect structures for 9 central composite points and 8 additional training/testing points were simulated. In addition, 16 structures were simulated for model verification purposes. Using the 9 central composite points plus the 8 additional interior points for training the model yielded the best results. Eight neurons were used in the hidden layer. Residual error results are given in Table 5.10. As with the previously developed models, excellent results have been obtained. Table 5.9 Variable parameters for microstrip-to-microstrip interconnect model. Input Parameter Freauencv Dvia/^Vbot Loh Minimum Value 2 GHz 0.2 1 mil Maximum Value 12 GHz 0.9 15 mil Table 5.10 Error results (average and standard deviation) between the EM-ANN model and EM simulation for the microstrip-to-microstrip multilayer interconnect. Train/test dataset Average error Standard dev. Verification dataset Average error Standard dev. ISnl ZSuH IS2 1 I ZS2i H IS22I z s 22(°) 0.0009 0.0008 0.745 0.493 0.0003 0.0002 0.083 0.082 0.0011 0.0009 0.798 0.645 0.0010 0.0009 0.752 0.659 0.0003 0.0003 0.083 0.082 0.0013 0.0010 0.813 0.768 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 49 5.6 Model Development Using Prior Knowledge In this section, EM-ANN models are developed using prior knowledge (existing models) about the component to be modeled. The first example is a 2-port broadband GaAs microstrip ground via like the one discussed in Section 5.3. However, when developing the model this time, prior knowledge about the microstrip line characteristic impedances, and knowledge about the inductance o f the via are used. The second example concerned with using a developed EM-ANN model to extend one of its own input parameter ranges. For this purpose, the stripline-to- stripline multilayer interconnect model is used. The prior model is the stripline-tostripline model developed previously, but only the data from 1 GHz to 16 GHz is assumed available. A new model is developed extending the frequency range to 26 GHz. 5.6.1 Two-Port Broadband GaAs Microstrip Ground Via The geometry o f the two-port broadband GaAs microstrip via is shown in Fig. 5.3. As with the previously developed model, the height of the substrate, the dielectric constant, and all loss parameters are considered constant for this example. Frequency, the width of the incoming microstrip lines, W), the side o f the square shaped via pad, W p, and the diameter o f the via hole to ground, Dvia, are the variable input parameters for the EM-ANN model. Input variable ranges are given in Table 5.4. Model outputs are the magnitudes and phases o f Sn and Sit- However, the reference impedances for the S-parameters are now the characteristic impedances of the microstrip lines, eliminating reflection at the ports. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 50 An existing model in an equation form for the inductance o f a microstrip grounding via is given in [53], The existing model was found to give reasonable results at lower frequencies (<15 GHz), but as frequency increased, errors between the model and EM simulation also increased. Inaccuracies o f the model, especially at higher frequencies may be due to pad inductance, pad capacitance, discontinuity effects, and radiation from the via-hole [51, 69]. EM simulations were performed from 5 GHz to 55 GHz in 10 GHZ steps on the same 45 via structures of Section 5.3. Originally, fifteen vias were simulated for training, 14 for simultaneous testing or additional training, and 16 for verification. However, with the use of prior knowledge, it was found that less training data is sufficient for model development. Therefore, more of the simulated data has been used for simultaneous testing. Initial model development used only 7 via structures for training, 22 via structures for testing, and 16 via structures for model verification. EM-ANN models were developed using regular training methods (no use of existing knowledge), the difference method, and the PKI method. The different training methods have been discussed previously in Chapters 2 and 3. Model average error and standard deviation are shown in Table 5.11, Table 5.12, and Table 5.13 for regular training, difference training, and PKI training, respectively. Looking at verification dataset errors, both the difference method and the PKI method provide more accurate models than using regular training methods. In addition, the PKI method provides better accuracy for ISnl and comparable accuracy on other parameters. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 51 Table 5.11 Error results for the 2-port microstrip via using regular training. (7 train structures, 4 inputs, 4 outputs, 5 hidden neurons, 49 weights) Train/test Average error Standard dev. Verification Average error Standard dev. ISUI Z S U (°) IS2 1 I z s 21 (°) 0.0076 0.0114 2.000 2.275 0.0314 0.0389 2.575 3.000 0.0066 0.0085 1.677 1.831 0.0226 0.0244 2.104 2.197 Table 5.12 Error results for the 2-port microstrip via, difference method. (7 train structures, 4 inputs, 4 outputs, 8 hidden neurons, 76 weights) Train/test Average error Standard dev. Verification Average error Standard dev. IS.,1 Z S n (°) IS2 1 I Z S 2I (°) 0.0042 0.0058 1.313 1.803 0.0094 0.0089 2.084 3.174 0.0041 0.0043 0.941 0.908 0.0083 0.0061 1.477 1.387 Table 5.13 Error results for the 2-port microstrip via, PKI method. (7 train structures, 8 inputs, 4 outputs, 5 hidden neurons, 69 weights) Train/test Average error Standard dev. Verification Average error Standard dev. IS 1 |l Z S ,, (°) IS2 1 I Z S 21 (°) 0.0035 0.0087 1.209 1.780 0.0092 0.0122 1.587 1.890 0.0023 0.0023 0.949 1.011 0.0066 0.0077 1.526 1.426 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 52 To further demonstrate the advantages o f incorporating existing knowledge into training, EM-ANN m odels were developed using 15 training vias, 14 test structures, and again 16 verification structures. Model average error and standard deviation are shown in Table 5.14, Table 5.15, and Table 5.16 for regular training, difference training, and PK I training, respectively. W ith more training data, error results for regular training improve. However, verification dataset error results using the difference method and PK I method improve also and still provide better accuracy than regular training. W hat is more important is that when com paring verification dataset errors, the accuracy o f the models trained with only 7 via structures using the difference method and PKI method show comparable or better accuracy than the model developed using 15 training via structures and regular training. Also, note that regular training errors have im proved over those of Section 5.3. The difference in this case is that the characteristic impedances of the connecting microstrip lines are used as terminating impedance. Therefore, when existing knowledge is used for model development, fewer EM sim ulations are needed for a required model accuracy. Table 5.14 Error results for the 2-port microstrip via, re g u la r tra in in g . (15 train structures, 4 inputs, 4 outputs, 13 hidden neurons, 121 weights) O N Train/test Average error Standard dev. Verification Average error Standard dev. 00 ISiil IS2 1 I z s 2I n 0.0020 0.0023 0.528 0.448 0.0065 0.0059 0.620 0.544 0.0041 0.0049 0.714 0.504 0.0105 0.0089 1.061 0.929 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 53 Table 5.15 Error results for the2-port microstrip via, difference method. (15 train structures, 4 inputs, 4 outputs, 12 hidden neurons, 112 weights) Train/test Average error Standard dev. Verification Average error Standard dev. IS,,I Z S „ ( 0) IS21I Z S 2i (°) 0.0013 0.0014 0.628 0.502 0.0036 0.0035 0.731 0.526 0.0026 0.0032 0.709 0.524 0.0047 0.0038 0.983 0.839 Train/test Average error Standard dev. Verification Average error Standard dev. 5.6.2 StripIine-to-StripIine Extension K w Table 5.16 Error results for the 2-port microstrip via, PKI method. (15 train structures, 8 inputs, 4 outputs, 11 hidden neurons, 147 weights) z s n (°) IS2 1 I 0.0017 0.0014 0.538 0.563 0.0032 0.0026 0.662 0.742 0.0021 0.0024 0.782 0.604 0.0038 0.0026 1.087 0.947 Multilayer Interconnect: t-J O IS.il Frequency Range For this example, existing knowledge in the form o f an already trained EMANN model is used to extend the range o f one o f its own input variables, frequency. The structure of the 50 Q stripline-to-stripline multilayer interconnect has been discussed in Section 5.4. Suppose an EM-ANN model has been developed for the frequency range of I GHz to 16 GHz, but it is desired to extend the models frequency range up to 26 GHz. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 54 In this case, prior knowledge is in the form of the S-parameter response o f the existing EM-ANN model up to 16 GHz. To extend the frequency range, the regular training method, the difference method, and the PKI method have been employed. EM simulations have been performed on 29 interconnect structures for the 16 GHz to 26 GHz range in 5 GHz steps. Five structures were used for training, 12 structures for simultaneous testing, and 12 structures for final model verification. As with the 2-port microstrip via model, data that was originally simulated for training has been placed in the testing dataset. Model average error and standard deviation are given in Table 5.17, Table 5.18, and Table 5.19 for the regular training method, the difference method, and the PKI method, respectively. Significant improvements in verification dataset errors are observed for both the difference method and the PKI method over regular training, especially for ISnl and Z S n - Also, the PKI method provides lower error results on ISiiI, Z S n , IS2il. Results on Z S 21 are comparable. As with the 2-port microstrip via model, addition of further data points to the training dataset leads to increased accuracy for all training methods. EM-ANN models were developed using 9 training vias, 8 test structures, and again 12 verification structures. Model average error and standard deviation are shown in Table 5.20, Table 5.21, and Table 5.22 for regular training, difference training, and PKI training, respectively. Again, use o f existing knowledge allows more accurate model development with fewer EM simulations than regular training. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 55 Table 5.17 Error results for the stripline-to-stripline interconnect frequency extension model, regular training. (5 train structures, 3 inputs, 4 outputs, 10 hidden neurons, 84 weights) Train/test Average error Standard dev. Verification Average error Standard dev. IS,,I Z S „° IS2 1 I Z S 2i° 0.00411 0.00666 3.802 3.847 0.00142 0.00160 0.443 0.416 0.01640 0.02021 7.540 7.862 0.00441 0.00455 0.845 0.841 Table 5.18 Error results for the stripline-to-stripline interconnect frequency extension model, difference method. (5 train structures, 3 inputs, 4 outputs, 13 hidden neurons, 108 weights) Train/test Average error Standard dev. Verification Average error Standard dev. is ,, i Z S ,,° IS2 1 I Z S 21° 0.00470 0.00366 1.984 1.618 0.00171 0.00156 0.481 0.315 0.00906 0.01121 3.360 3.205 0.00336 0.00436 0.638 0.521 Table 5.19 Error results for the stripline-to-stripline interconnect frequency extension model, PKI method. (5 train structures, 7 inputs, 4 outputs, 8 hidden neurons, 102 weights) Train/test Average error Standard dev. Verification Average error Standard dev. IS,,I Z S ,,° IS2 1 I ZS210 0.00322 0.00073 2.609 2.498 0.00089 0.00057 0.267 0.227 0.00849 0.00845 2.903 3.149 0.00275 0.00273 0.609 0.773 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 56 Table 5.20 Error results for the stripline-to-stripline interconnect frequency extension model, regular training. (9 train structures, 3 inputs, 4 outputs, 11 hidden neurons, 92 weights) Train/test Average error Standard dev. Verification Average error Standard dev. is,,i ZSn° IS2 1 I Z S 2i° 0.00178 0.00207 2.069 2.320 0.00093 0.00080 0.211 0.196 0.00611 0.00732 4.583 4.154 0.00197 0.00262 0.422 0.435 Table 5.21 Error results for the stripline-to-stripline interconnect frequency extension model, difference method. (9 train structures, 3 inputs, 4 outputs, 13 hidden neurons, 108 weights) Train/test Average error Standard dev. Verification Average error Standard dev. IS,,I ^S n° IS2 1 I Z S 2i° 0.00216 0.00202 0.896 0.579 0.00082 0.00060 0.294 0.217 0.00584 0.00661 2.318 1.821 0.00193 0.00269 0.373 0.348 Table 5.22 Error results for the stripline-to-stripline interconnect frequency extension model, PKI method. (9 train structures, 7 inputs, 4 outputs, 10 hidden neurons, 124 weights) Train/test Average error Standard dev. Verification Average error Standard dev. IS 1 ,1 Z S ,,0 IS2 1 I Z S 2i° 0.00139 0.00194 1.279 1.559 0.00055 0.00066 0.144 0.108 0.00470 0.00545 2.367 1.524 0.00173 0.00241 0.419 0.320 I Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 57 5.7 Integration o f EM -ANN Models with a Network Simulator After training, the EM-ANN models were integrated into a microwave network simulator (HP-MDS [49]). Fig. 5.6 compares the new EM-ANN one-port via model (NET1) with HP-Momentum results and the current MSVIA element available in HP-MDS. Note that the MSVIA reference plane is at the center o f the hole, while our reference plane is at the edge o f the pad. Therefore, a more accurate model, also shown in Fig. 5.6, may be constructed by adding additional HP-MDS elements such as MSSTEP, MSTL, and MSOC to account for the pad length and the step in width. However, the constructed HP-MDS model cannot accurately characterize the via hole over the entire range o f the input variables, whereas the EMANN via model can. Excellent results are achieved by the EM-ANN models when compared to HP-M omentum [48] simulations. Simulation times for NET1, MSVIA, and HP-Momentum on an HP 700 workstation are shown in Table 5.23. Note that the new EM-ANN model does not require a significant increase in simulation time over the current HP-MDS model. Table 5.23 Comparison of simulation times for the GaAs via described in Fig. 5.6. The times for MSVIA and NET1 are averaged over 100 frequency points. HPMomentum results are for 1 frequency point. M odel HP-MDS, MSVIA HP-M omentum N etl (EM-ANN Model) Simulation Time 0.37 sec 12.48 min 0.54 sec Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 58 1 t — ■ 0.98 ------------- II 0.96 (/) 0.94 -- msvia + comp NET1 msvia HP-MOM 0.92 0.9 15 25 35 FREQUENCY (GHZ) 45 55 45 55 (a) 190 180 170 5 160 LU ° 150 msvia + comp NET1 msvia HP-MOM 140 130 120 5 15 25 35 FREQUENCY (GHz) (b) Fig. 5.6 Comparison of EM-ANN model (NET1), HP-Momentum (HP-MOM), HPMDS via element (msvia), and MSVIA with added components (m svia + comp). GaAs via with cr = 12.9, HSUb= 4 mil, tmetai=0.1 mil, CTmelai=4.1xl07, tan5 = 0.002, W„Wp= 0.3875, Dvia/Wp =0.4, and W,/Hsub = 0.3375. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 59 5.8 Optimization of Component Structure Once an EM-ANN model has been developed, it can be used to find the optimal physical structure o f a component for a given application. This can be accomplished by using standard techniques such as random and gradient optimization [49]. To demonstrate the usefulness o f optimization, an example is considered. Example: Stripline-to-Stripiine Multilayer Interconnect For this EM-ANN model, two variable physical parameters are: the diameter of the via and the diameter o f the ground access opening. This structure has been considered in [62] and it was found that good performance was obtained as long as the diam eter of the via was large and the ratio o f the diameter o f the ground access to that o f the via was near 4.2:1. In fact, this ratio is the same as that o f the inner and outer conductors of a 50 £2 coaxial line with £r = 2.94. However, only a limited number of structures were simulated. One would expect that the ratio for the stripline-to-stripline interconnect might be less than for a coaxial line, increasing the capacitance of the structure in order to compensate for only having a partial outer conductor. Initial values for the physical parameters were set at 0.3 for Dyi/Wi and 6.0 for Dgnd/Dyia. These are clearly not optimal values. Optimization was completed by maximizing the transmission coefficient yielding DVja/Wi = 0.77 and Dgnd/Dvia = 3.4. These results agree well with our expectations as mentioned previously. 1 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. CHAPTER 6 MULTICONDUCTOR MULTILAYER COUPLED TRANSMISSION LINE DESIGN USING ANN MODELS * The use of multilayer circuit configurations is increasing due to the compactness and the increased design flexibility that may be achieved. Although multilayer circuit configurations have been widely used for digital and low frequency systems, their use at RF and microwave frequencies is limited. Directional couplers and baluns, implemented in multilayer configurations, have appeared in recent years [70-74]. In addition, the design o f filters in multilayer configurations has been demonstrated, but they are limited to broadside coupled symmetrical strip configurations [75-77]. In the past, RF and microwave circuits have generally been fabricated in single-layer configurations [78, 79]. Often, very tightly coupled lines are needed, but are difficult to fabricate in single-layer configurations. Multilayer configurations overcome this difficulty because o f the flexibility in overlapping coupled lines on different layers. This makes it convenient to design tightly coupled sections. Also, ' This work has been carried out in collaboration with Choonsik Cho w hose project is aimed at synthesis o f multilayered circuits. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 61 multilayer circuits can be implemented in both homogeneous and inhomogeneous layered dielectric media. Recently, a methodology for the design o f multilayer asymmetric coupled line circuits has been proposed [80]. In this approach, network modeling and synthesis procedures are used to derive normal mode parameters (NMPs) for various multilayer coupled line sections, which constitute the circuit to be designed. Evaluation of physical geometry to realize the NMPs for each coupled section is not straight forward. An optimization procedure is used to arrive at physical dimensions for the coupled line sections by comparing desired NMPs with those obtained by analysis of the physical geometry. A problem associated with this optimization approach is the presence of local minima, which can cause the optimization routine to stall instead of finding the desired global minimum. Also, optimization can be very time consuming and depends heavily on the selection of initial physical dimensions. This chapter focuses on the use o f ANNs, in place o f time consuming optimization routines, for evaluation o f the physical geometry for multiconductor multilayer coupled line sections. Both synthesis (NMPs to the physical geometry) and analysis (physical geometry to NMPs) ANN models have been developed. Problems associated with synthesis using ANNs are discussed. As an example o f the proposed methodology, the design of multilayer coupled line filters, using ANNs, is demonstrated. i Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 62 6.1 Synthesis of Asymmetrical M ultilayer Coupled Line Sections The synthesis procedure takes NMPs (desired response) and provides the physical geometry required to achieve this response. An example o f a multilayer coupled line configuration is shown in Fig. 6.1. It consists of an asymmetrical coupled line section in an inhomogeneous dielectric medium. Both layer-to-layer coupling and same layer coupling are shown. A synthesis approach for the geometry of multilayer coupled line sections for use in multilayer filter design, proposed in [80], is shown in Fig. 6.2. Beginning with circuit specifications, J-parameters (admittance inverter parameters) are derived for each coupled line section. selected values of Z0l, For (impedances at two ends of a coupled line section), and another design parameter, ‘a’, related to coupling, NMPs are derived. NMPs are the different voltage ratios (Rc and R J , mode impedances (Zci, Z*i, Z ^, and Z ^ ), and phase velocities for the two normal modes, known as c- and n- modes, used to characterize asymmetrical coupled line sections [81-83]. Four o f the NMPs (Rc, R*. Zd and Z ,i) are utilized to obtain the physical dimensions (for selected substrate, h, and £r values) of each coupled line section by using an optimization routine. This optimization process compares the NMPs obtained from specifications with those calculated from the physical geometry by evaluating capacitance and inductance matrices [81-83] as an intermediate step. The capacitance and inductance matrices, for a specific coupled line geometry, are determined using Segmentation and Boundary Element Method (SBEM) analysis [84]. This process (contained inside the dotted block A in Fig. 6.2) continues in an iterative manner until desired results are Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 63 Same Layer Layer-to-Layer I I | W* W 1I I w1( ,w2 I air £r2 T I I I I £ r1 / / / / / a / / / / / / / / / / / / ///A//y/ / / / / / / —►is r*— —i►is Fig. 6.1 Exam ple o f a multiconductor multilayer coupled line geometries in an inhomogeneous medium. Both layer-to-layer and same layer coupling sections are shown. Circuit Specifications .(•parameters Choose Zot and Zq2 for each coupled line section ( or 'a' reselected) Nonnal mode parameters lor each coupled section SBEM Optimize for physical dimensions NMPs acceptabli No Yes and Results Fig. 6.2 Procedure for the design o f asymmetric multilayer coupled line sections using optim ization [80]. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 64 obtained. If the desired agreement with NMPs is not obtained, Zoi, Z ^ , and ‘a' are altered to obtain a new set of NMPs, which yield the same circuit performance. The optimization procedure is repeated with this new set of parameters. Thus we have two levels of iterations involved in this design procedure. Optimization is used to determine the physical geometry o f the coupled line sections because no closed-form expressions for deriving physical dimensions from NMPs are available. Also, the solution to the problem is not unique. In other words, different coupled line sections can produce the same values o f the 4 selected NMPs. It should also be noted that the choice o f NMPs for a desired circuit response is not unique because of selection of parameters Zq|, Z 0 2 , and ‘a’. Therefore, as shown in Fig. 6.2, the terminating impedances, Zoi and Z 0 2 , and ‘a’, for each coupled line section can be chosen to provide realizable physical dimensions. For a more detailed discussion see [80, 84], One problem associated with optimization procedures is the likelihood of finding a local minimum instead o f the desired global minimum. In this case, selection of initial physical values for the coupled line sections is very important. Also, optimization can be very time-consuming as will be shown. 6.2 ANN M odeling Methodology for M ultilayer Asymmetric Coupled Lines In order to bypass the problems associated with optimization, ANN models may be used. ANN models can be used to effectively determine physical values for coupled line sections from given NMPs (synthesis). ANN models may also be Ji 1 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 65 developed which give the correct S-parameter response based upon the physical geometry (analysis) for use in commercial microwave circuit simulators. The SBEM method is used to provide the training data for both the synthesis and analysis models. Training data is obtained by specifying physical parameters and their ranges for the multilayer coupled line sections under consideration. Simulations are carried out to obtain the L and C matrices corresponding to the physical geometry. These L and C matrices can then be easily converted into NMPs by analytical techniques [84], Therefore, a set of NMPs, corresponding to a specific physical geometry, is obtained. This data can be used to develop both synthesis and analysis models for the design of asymmetric multilayer coupled line circuits. 6.2.1 Analysis Model The development o f the analysis model is straightforward. Models are developed for each type o f coupled line section using the methodology discussed in Chapters 2 and 3. Physical parameters, such as the width o f each line and the spacing between their edges, are used as ANN models inputs as shown in Fig. 6.3. The outputs are the elements o f the L and C matrices corresponding to the coupled line configuration. Once the L and C matrices have been obtained, they can be used to determine the NMPs and consequently the S-parameters o f a given coupled line section. Analysis models m ay be linked to commercial microwave circuit simulators for circuit analysis and optimization. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 66 ► Ln W, ► l 12 Wo Analysis ANN model for a single coupled line section for a selected set of £r1, h1t and h2 ► L 22. ► Cn ► C-|2 C 22 Fig. 6.3 Analysis ANN model for asymmetric m ultilayer coupled line sections. -► W1 Synthesis ANN model for a single coupled line section for a selected set of s r1, s^, and h2 ►s Fig. 6.4 Synthesis ANN model for asymmetric multilayer coupled line sections. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 67 6.2.2 Synthesis Model The synthesis model is developed by using normal mode parameters as inputs to the ANN model as shown in Fig. 6.4. The desired physical parameters for the coupled line section are the outputs. This is known as an inverse modeling problem because the input and output variables are interchanged from characterization. For such problems there exists a well-defined forward (analysis) problem which is characterized by a single-valued mapping. However, for inverse problems, the mapping can often be multi-valued, with values o f the inputs for which there are several valid values for the outputs. In this case, if a least-squares error approach is used, the neural net tends to approximate the average o f the target data [38]. This can lead to poor network performance since the average o f several solutions is not necessarily itself a solution. Another problem associated with inverse modeling is the coverage o f the input variable space by the selected training data. For the forward problem, it is possible to select points for ANN training which characterize the entire space spanned by the input variables. However, when the roles o f the input and output variables are interchanged for inverse modeling, full characterization o f the new input space most likely is not achieved. Therefore, there can be valid input vectors (within the input space) for the ANN model which produce incorrect results due to the absence of training data for particular regions o f input space. The problem for asymmetrical coupled line design, as mentioned previously, is that the mapping from physical parameters to NMPs is single-valued, while the Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 68 inverse mapping from normal mode parameters to physical parameters can be multi valued. For problems involving many input and output variables, where visualization o f the data is not straightforward, it can be very difficult to determine whether there are regions of input space for which the target data is multi-valued. It can also be difficult to determine if and where there are regions o f input variable space which have not been characterized by the available training data. Therefore, a method for determining the accuracy o f the model outputs is needed. The method for verifying the accuracy of the synthesis model outputs is shown in Fig. 6.5. First, the desired normal mode parameters are used as inputs for the synthesis ANN model, giving physical parameters as outputs. The outputs o f the synthesis model are then used as inputs to the analysis model, which is a single valued mapping, to determine the L and C matrices for the geometry obtained from the synthesis model. From the L and C matrices, NMPs are calculated and transformed to 4-port S-parameters [84]. These 4-port S-parameters are then compared to the 4-port S-parameters obtained from the NMPs 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 o f NMPs (input variables), the NMPs are altered by changing Zoi, Zq2 , and/or ‘a’. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 69 Circuit specifications C hange Zoi and Z02 to modify J-parameters J-param eters Normal m ode param eters for e ach coupled section C hange ‘a‘ to modify NMPs No Com pare sp ecs Y es acceptable Stop Analysis ANN Synthesis ANN for verification m odel R esu lts Fig. 6.5 Modified synthesis procedure for asymmetric multilayer coupled line sections using ANN models in place o f optimization. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 70 6.3 Multilayer Filter Design using ANN Models As an example o f the proposed methodology, the design o f multilayer coupled line filters, using ANN models, is presented in this section. The geometry of the type o f filter under consideration is shown in Fig. 6.6. Specifically, it is a two-layer asymmetric coupled line filter in an inhomogeneous medium consisting o f 3 coupled line sections. There are two types of open-ended coupling sections, each o f length UA at the desired center frequency of the filter. Sections 1 and 3 couple layer I to layer 2, while section 2 couples from layer 1 to layer 1. The height and dielectric constant of each layer are taken as h i= 3 1 mils, hi=lO mils, and erI= srz = 2.2 (refer to Fig. 6.1). Fig. 6.6 Top view of a 2-layer coupled line filter consisting o f 3 coupled line sections. Sections 1 and 3 couple from layer 1 to layer 2 and section 2 couples from layer 1 to layer 1. Input and output ports are on the top o f layer 2. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 71 6.3.1 A N N Model Development for Coupled Line Sections Both synthesis and analysis models have been developed for layer-to-layer coupling and same layer coupling on layer 1 for the design of 2-Iayer coupled line Filters. Variable parameters for the model inputs and their corresponding ranges are given in Table 6.1 for layer-to-layer coupling, and in Table 6.2 for same layer coupling on layer 1. Parameter ranges were chosen based on previous work on multilayer coupled line filters [85]. SBEM analysis has been used to provide the training data for ANN model developm ent. Also, since SBEM analysis for this geometry is not time consuming (1000 simulations take 40 minutes on an HP700 workstation), DOE techniques were not used to choose simulation points. Instead, a uniform grid of points was chosen to provide the training data. Table 6.1 Variable input parameters and corresponding ranges for the layer 1 to layer 2 coupling section model. w, w 2 s Min. 1 mm 1 mm -1 mm Max. 5 mm 5 mm 1 mm Table 6.2 Variable input parameters and corresponding ranges for the layer 1 to layer 1 coupling section model. W, W, S Min. 1 mm 1 mm 0.25 mm Max. 5 mm 5 mm 2 mm i Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 72 Analysis ANN model error results and model specifics are given in Table 6.3 for layer-to-layer coupling and in Table 6.4 for same layer coupling on layer 1. Each model has 3 inputs (W |, W 2, and S) and 6 outputs (C n, Q 2, C22, L n, L |2, and L22) which constitute the L and C matrices for a given input geometry. Relative errors are given in addition to absolute errors for better interpretation o f results. Low errors are achieved confirming the accuracy o f the developed models. Table 6.3 Error results for the layer 1 to layer 2 coupling line section analysis model. (725 train/test examples, 25 verify; 3 inputs, 6 outputs, 15 hidden neurons, 156 weights)___________________________________________________________________ Train/test A vg. Error Std. Dev. % A vg. Error 7c Std Dev. Verification A vg. Error Std. Dev. 7c Avg. Error 7c Std. Dev. c„ C|2 c„ (pF/m.) (pF/m) (pF/m) Lu (nH/tn) (nH/m) (nH/m) 0.933 0.768 0.346 0.299 0.886 0.734 1.630 1.406 0.899 0.862 2.340 1.811 0.790 0.567 2.084 1.390 0.970 0.687 0.759 0.554 2.249 2.290 0.922 0.660 0.792 0.500 0.346 0.313 1.059 0.577 1.167 0.851 0.856 0.619 2.816 1.885 0.695 0.476 2.185 1.496 1.207 0.501 0.596 0.395 2.403 2.624 1.110 0.714 L-22 Table 6.4 Error results for the layerl to layer 1 coupling line section analysis model. (645 train/test structures, 25 verify; 3 inputs, 6 outputs, 15 hidden neurons, 156 w e i g h t s ) ______ ______ ______ ____________________________________________ c„ Train/test Avg. Error Std. Dev. (pF/m) Cn (pF/m) C 22 (pF/m) Lit (nH/m) L|2 (nH/m) L 22 (nH/m) 0.516 0.451 0.139 0.089 0.457 0.372 1.788 1.518 0.445 0.588 1.639 1.563 7c A vg. Error 7c Std. Dev. Verification A vg. Error Std. Dev. 0.447 0.322 2.075 2.061 0.419 0.313 0.813 0.592 2.277 2.643 0.743 0.612 0.373 0.290 0.181 0.119 0.346 0.231 1.409 1.168 0.426 0.438 1.489 1.331 7c A vg. Error 7c Std. Dev. 0.313 0.206 2.360 1.407 0.366 0.289 0.653 0.429 2.385 2.252 0.679 0.588 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 73 Synthesis ANN model error results and model specifics are given in Table 6.5 for layer-to-layer coupling and in Table 6.6 for same layer coupling on layer 1. These models each have 4 inputs (Rc, l/R*, Zc, and Z*) and 3 outputs (W[, W2, and S). Note that instead of using R* as an input, 1/R* has been used. This is due to discontinuities which tend to ±oo as R* changes sign. Using 1/R* reduces the effects o f the discontinuities and allows an accurate model to be developed. Since good model accuracy has been achieved, there does not seem to be a significant problem with multi-valued outputs for the same inputs. Table 6.5 Error results for the layerl to layer 2 coupling line section synthesis model. (725 train/test examples, 25 verify; 4 inputs, 3 outputs, 13 hidden neurons, 107 weights) Train/test Average error Standard dev. Verification Average error Standard dev. W, (mm) W2 (mm) S (mm) 0.036 0.028 0.061 0.049 0.024 0.021 0.034 0.027 0.079 0.046 0.015 0.015 Table 6.6 Error results for the layerl to layer 1 coupling line section synthesis model. (645 train/test examples, 25 verify; 4 inputs, 3 outputs, 14 hidden neurons, 115 weights) Train/test Average error Standard dev. Verification Average error Standard dev. W, (mm) W2 (mm) S (mm) 0.023 0.018 0.056 0.047 0.034 0.028 0.023 0.019 0.044 0.029 0.036 0.024 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 74 6.3.2 Design Example: 2-Layer Coupled Line Filter The developed ANN models have been used to design a 2-layer coupled line filter having the specifications given in Table 6.7. Physical dimensions, obtained from the ANN models, for each coupled line section are given in Table 6.8. To determine the accuracy o f the ANN model outputs, comparisons were made between the modeled 4-port S-parameters o f each coupled line section with those obtained from specifications at the desired center frequency. Again, these 4-port S-parameters are for general coupled lines and have been used to determine whether the output of the synthesis model is valid for the given input NMPs. Error bounds for an acceptable solution have been set at 0.01 for magnitude and 5° for angle. Angle error was not considered when the magnitude o f a given S-parameter was below 0.01. The 4-port S-parameters can then be transformed into the appropriate 2-port S-parameters, which characterize the open-ended, UA coupling sections used for filter design. Table 6.7 Filter specifications used for the design o f a 2-layer asymmetric coupled line filter. C enter frequency Ripple Bandwidth Ripple Level N um ber o f coupled sections Sri = Sr2 hi h2 2 GHz 7.5 % 0.5 dB 3 2.2 31 mil 10 mil Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 75 Table 6.8 Physical dimensions obtained from ANN models for the 2-layer filter example. Filter specifications are given in Table 6.7. Section # 1 2 3 W | (mm) 1.50803 1.71022 2.95975 W 2 (mm) 2.93213 3.06325 2.79627 S (mm) 0.05418 0.79071 -0.08822 3.2259 W„ W0 (mm) Zoi (SI) 60 60 40 Zo2 (J2) 50 40 50 The modeled filter response is shown in Fig 6.7 along with the response obtained from SBEM analysis o f the coupled line sections as given in Table 6.8. Also, center frequency, ripple bandwidth, ripple level, and 3 dB bandwidth are given in Table 6.9. Analysis ANN models for each coupled line section have been linked to a commercial microwave circuit sim ulator (HP-MDS [49]) to obtain the filter response. Excellent agreement is obtained confirming the accuracy of the ANN coupled line models. If the 0.7 dB ripple level is unacceptable, the filter response may be optimized to obtain the desired 0.5 dB ripple using the ANN analysis models. The optimized filter dimensions are given in Table 6.10. Filter response is given in Table 6.11 and shown in Fig. 6.8. Note that only small changes in physical parameters were necessary to achieve the desired response. These changes are on the order of the errors for the ANN models given in Table 6.5 and in Table 6.6. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 76 Table 6.9 Comparison of two-layer filter responses. 3 dB Bandwidth (%) - Ripple Level Specification Center Frequency (GHz) 2 (dB) 0.5 Ripple Bandwidth (%) 7.5 ANN l.98 11.11 0.702 7.87 SBEM 1.98 10.86 0.748 7.83 1.25 1.5 Frequency (GHz) 1.75 2 2.25 2.5 2.75 -10 -20 ■o Su_ANN -30 -40 -50 Fig. 6.7 Two-layer filter response. Both ANN modeled (light solid lines) and SBEM (dark dashed lines) results are shown. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 77 Table 6.10 Optimized physical dimensions obtained from ANN models for the 2layer filter example. Filter specifications are given in Table 6.7. Section # 1 2 3 W ( (mm) 1.52068 1.70905 3.00076 W 2 (mm) 2.94101 3.06157 2.69997 S (mm) -0.00732 0.75217 -0.10564 3.2259 Wi? W0 (mm) Zoi (H) 60 60 40 Zo2(Q) 50 40 50 Table 6.11 Comparison o f optimized two-layer filter responses. 3 dB Bandwidth (%) - Ripple Level Specification Center Frequency (GHz) 2 (dB) 0.5 Ripple Bandwidth (%) 7.5 ANN (opt.) 1.98 11.61 0.456 8.08 SBEM (opt.) 1.98 11.36 0.501 8.02 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 78 Frequency (GHz) 1.25 1.5 2.25 1.75 2.5 2.75 -10 -20 -30 Sn_SBEM -40 Si i_ANN -50 Fig. 6.8 Two-layer filter response. Both ANN m odeled (light solid lines) and SBEM (dark dashed lines) results are shown. 6.3.3 Comparison o f 2-Layer Filter Optimization Method Design Using ANN Method and A filter w ith the same specifications given in Table 6.7 has also been designed using the optimization method discussed in Section 6.1. Table 6.12 gives the physical dimensions, while Table 6.13 gives the center frequency and bandwidth parameters of the designed filter. The filter performance param eters obtained by using ANN modeling are also repeated here for comparison. I Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 79 Table 6.12 Physical dimensions obtained from optimization method for the 2-layer filter example. Filter specifications are given in Table 6.7. Section # 1 2 3 W | (mm) 1.4928 1.7078 2.9706 W 2 (mm) 2.9259 3.1520 2.7987 S (mm) 0.0535 0.7880 -0.0904 Wj, W 0 (mm) 3.2259 Zo, (£2) 60 60 40 Z o2(Q) 50 40 50 Table 6.13 Center frequency and bandwidth parameters for the 2-layer filter designed using the optimization method. Also, the response of the filter using ANN modeling is repeated here for comparison purposes. 3dB Bandwidth (%) - Ripple Level Specification Center Frequency (GHz) 2 (dB) 0.5 Ripple Bandwidth (%) 7.5 OPT. 1.98 10.86 0.539 7.68 ANN 1.98 11.11 0.702 7.87 The filter designs using the optimization method and ANN modeling are comparable. The ripple level for the ANN design is slightly larger than desired. However, optimizing the physical geometry slightly, using the analysis ANN models, resulted in the correct response. Note that no analysis models are available when using the optimization method. I Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 80 The advantage of using ANN models for the filter design is a large savings in required CPU time. Table 6.14 gives the CPU time on an HP700 workstation and the number of design iterations (changes in physical geometry) required to arrive at the final filter dimensions. Also given is the amount o f time required for optimization of the filter response using ANN analysis models linked to HP-MDS [49]. It is evident that using ANN models for the filter design results in a much more efficient process than using optimization methods. Both designs were carried out on an HP700 workstation. For the design comparison, only ‘a’ was allowed to change. Zoi and Zo2 were held constant for each section. Table 6.14 Two-layer filter design times and required iterations for ANN modeling and the optimization method o f [80], # iterations CPU time 1 4 0.0379 sec. 2 8 0.0758 sec. 3 3 0.0284 sec. 2 0.76 sec. 1 4212 64 min. 11 sec. 2 1634 125 min. 4 sec. 3 1285 19 min. 1 sec. Section ANN: ANN optimization using HP-MDS: Optimization: 6.4 Discussion It has been demonstrated that ANN modeling offers an accurate and efficient alternative to optimization methods for the design of multilayer coupled line circuit Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 81 components. Circuit elements can be designed in a small fraction o f the time using ANN models. Another advantage o f the ANN modeling approach for m ultilayer circuit design is the availability o f analysis models, which can be linked to com m ercial microwave simulators. These analysis models can be used in conjunction with other component models and optimization routines, available within com m ercial microwave circuit simulators, for the design and optimization o f larger circuits. Analysis models are not available when using the optimization method for m ultilayer coupled line circuit design. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. CHAPTER 7 DESIGN AND OPTIMIZATION OF CPW CIRCUITS USING EMANN MODELS FOR CPW COMPONENTS Use o f coplanar waveguides (CPW) in micro wave/mm-wave integrated circuits offers several advantages due to the physical configuration o f the CPW line. These include: the ease o f mounting shunt and series lumped components, low radiation losses, low dispersion, and the avoidance o f the need for thin fragile substrates. These advantages make CPW an attractive choice for development o f M MICs. Currently, design software available for C PW circuits is inadequate because o f the non-availability of accurate and efficient models for CPW discontinuities such as bends, T-junctions, steps-in-width, short and open stubs, etc. Accurate characterization and modeling o f these components are vital for accurate circuit simulation and increased first-pass design success. Much effort has been expended in developing accurate and efficient methods for electromagnetic (EM) simulation o f CPW discontinuities [86-118]. However, the time-consuming nature of EM simulation limits the use o f these tools for interactive CAD and circuit optimization. Equivalent circuit models generally available for CPW discontinuities require certain assumptions to be made which may or may not be Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 83 valid over the desired range of operation. CPW discontinuities have also been characterized by measurements [119, 120], generating a library of data, which is generally valid only for the structures measured. This method of characterization is also very time-consuming. As an alternative to the above, EM -ANN models for CPW components suitable for use in interactive MMIC design and optimization have been developed. No assumptions about component behavior are made when developing the EM-ANN models. Full-wave EM simulation has been employed to characterize the CPW components. EM -ANN models have been developed for CPW transmission lines (frequency dependent Z q and £re), 90° bends, short circuit stubs, open circuit stubs, step-in-width discontinuities, and symmetric T-junctions. Air-bridges are included where needed to suppress the unwanted slot-line mode [121]. All models have been developed using HP-Momentum [48] for EM simulation and its adaptive frequency sampling (AFS) feature, with the exception o f the CPW transmission line model. This was due to the unavailability of Zo information for CPW lines in the particular version of Momentum available at the time this work was completed. Common parameters for all models are the substrate parameters (£r = 12.9, HSUb = 625 pm, tanS = 0.0005) and air-bridge parameters (Ha = 3 pm and W a = 40 pm). Once developed, these EM-ANN models are linked to a commercial microwave circuit simulator where they provide accuracy approaching that o f the EM simulation tool used for characterization o f the CPW components over the entire ranges of the model input variables. In addition, the developed models allow for very fast, accurate Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 84 electromagnetic/circuit optimization within the framework of the circuit simulator environment. Circuit design using the developed EM-ANN CPW models is demonstrated by two exam ples: a CPW folded double stub filter and a 50 Q, 3 dB power divider circuit. Optimization of circuit responses have been performed and compared to the full-wave simulation results o f the entire circuits, showing excellent agreement. 7.1 EM -ANN Modeling o f Chamfered CPW 90° Bends In this section, EM-ANN models are developed for two different chamfered CPW bend structures as shown in Fig. 7.1. Air-bridges are placed near CPW bends in order to reduce the unwanted slot-line mode which tends to radiate [121]. The slotline m ode is generated in CPW bends due to the path length difference for the two slots. The inclusion of air-bridges, however, adds unwanted capacitance, which can degrade the performance of the bend. In addition to compensating for the reactances associated with the bend, chamfering provides a simple way to partially compensate for the effects of the air-bridges. This section investigates the effects o f chamfering on the S-parameters for the CPW 90° bends shown in Fig. 7.1. Optimal chamfering values are determined for the different bend structures. CPW bends of the type shown in Fig. 7. la have been studied in [88], but only for b=0 and b=W+G. The work reported in [88] is extended by determining the optimal chamfer for each bend structure. The compensated CPW bend shown in Fig. 7.1b is a novel structure which has been shown, by EM simulation, to improve upon the return loss and the insertion loss o f the conventional chamfered bend o f Fig. 7.1a. I Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 85 (a) -«S- W (b) Fig. 7 .1 CPW 90° bend structures with W a = 40 pm, Ha = 3pm, HSUb = 625 pm, er = 12.9, and tan8 = 0.0005. (a) Conventional chamfered bend and (b) novel compensated bend (Ha is height o f air-bridge above the substrate, Wa is the width of the air-bridge, and HSUb is the substrate thickness.) Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 86 EM-ANN models are developed for the CPW bends and are used to determine optimal chamfer values. All air-bridge parameters are held constant in order to concentrate on the effects caused by the chamfering of the bends. 7.1.1 Optimally Chamfered Conventional CPW Bend An EM-ANN model has been developed for the CPW bend structure shown in Fig. 7.1a. Variable inputs for the EM-ANN model are W, G, b/bmax, and frequency. Model outputs are S-parameters. Substrate material used is GaAs (£r = 12.9), and the thickness is 625 pm for all results included here. Air-bridges are 40 pm wide (Wa), 3 pm (Ha) above the GaAs surface, and are positioned at the bend discontinuity as shown. Note, all air-bridge parameters are held constant in order to concentrate on the effects caused by the chamfering of the bends. EM simulations were performed on 17 bend structures, included within the range o f parameters given in Table 7.1. Characteristic impedances used for port terminations have been determined from linecalc [68]. Five different values of chamfer were simulated for each bend, with b/bmax ranging from 0 to I. The strip comer was chamfered by a proportional amount given by bW/(W+G). EM simulation data was separated into training/test (165 examples) and verification (300 examples) datasets for model development. Ten neurons were used in the hidden layer. Error results (EM-ANN model compared to EM simulation) are shown in Table 7.2. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 87 Table 7.1 Variable parameter ranges for C PW components. Max. 50 GHz 120 pm 60 pm Min. 1 GHz 20 pm 20 pm Frequency W G Table 7.2 Error results (average and standard deviation) between the EM-ANN model and full-wave simulation for the optimally chamfered C PW bend. Train/test dataset Average error Standard dev. Verification dataset Average error Standard dev. ISml ZS „(•) IS2 1 I Z S2i(°) 0.000701 0.000632 0.102 0.104 0.000293 0.000270 0.034 0.029 0.000966 0.001058 0.124 0.141 0.000354 0.000339 0.048 0.039 It was determined that indeed there exists an optimal chamfer for each structure, especially when analyzing the return loss, 201ogiolSnL The developed EMANN model can reproduce the trends in S-parameters determined by the changes in the physical structure of the CPW bend. Using this model, the optimal chamfer for each bend is determined. Fig. 7.2 shows the optimal chamfer, b/bmax, versus W/G for minimum return loss, as determined by the EM-ANN model. The optimal chamfer as a function of W /G is given by b/bmax = 0.2102 ln(W/G) + 0.7677 = 1 for 0 < W/G <2 for W/G > 2.5 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. (7.1) 88 0.8 X n CQ E ^ 0.6 0 .4 b/bmax 'm a x = 0 .2 1 0 2 ln (W /G ) + 0 .7 6 7 7 0.2 0 0 .5 1 1 .5 2 2 .5 W/G Fig. 7.2 Optimal chamfer for return loss versus W /G for the conventional CPW 90° bend. (Fig. 7.1a.) 7.1.2 Novel Compensated CPW Bend An EM-ANN model has been developed for the novel compensated CPW bend structure, proposed here, shown in Fig. 7.1b. This novel bend is capable of improving upon the performance o f the already discussed optimally chamfered CPW bend. Variable input parameters for the model are W, G, and frequency. Model outputs are S-parameters. For this novel bend, the optimum chamfer for the strip is found to be the maximum allowable by air-bridge placement. EM simulations have been performed on 17 bend structures, included within the range o f parameters given in Table 7.1, to provide training/test (45 examples) and verification (35 examples) i Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 89 datasets for model development. Ten neurons were used in the hidden layer. Error results for the developed EM-ANN model are shown in Table 7.3. Table 7.3 Error results (average and standard deviation) between the EM -ANN model and full-wave simulation for the compensated bend. Train/test dataset Average error Standard dev. Verification dataset Average error Standard dev. 7.1.3 ISnl Z S „(°) IS21 I Z S 2i(°) 0.000784 0.000518 0.680 0.513 0.000584 0.000390 0.363 0.261 0.001390 0.000861 1.022 0.759 0.000705 0.000365 0.447 0.380 CPW Bend Comparisons The novel compensated CPW bend structure is found to improve the return loss over the optimally chamfered conventional bend, as shown in Table 7.4. This is believed to be due to a decrease in capacitance as the slot width at the com er is increased, thereby compensating for the increase in capacitance due to the air-bridges. Improvements are also seen in the insertion loss. Note that all air-bridge parameters remain the same as in the case for the optimally chamfered CPW bend. Comparisons between unchamfered CPW comer, optimally chamfered conventional bend, and the novel compensated bends are shown in Fig. 7.3 for CPW bend structures with W = 70 pm and G= 20 pm, corresponding to Zo=35 Q . Note that all air-bridges and reference planes are at the same positions. Based on the results shown in Fig. 7.3 and in Table 7.4, the new compensated bend provides significant improvements in return and insertion loss over the other CPW bend structures. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 90 Improvements are also seen when comparing the optimally chamfered bend results to the comer (unchamfered) bend. -10 -20 - - -30 - -4 0 - - 5 C om er -50 - - Opt. Chamf. -60 Comp. Bend -70 17 6.5 34 50 Frequency (GHz) 0 2 “ -0 .0 5 -- «T -0.1 + (0 o ^ -0 .1 5 + o '■E 0) (0 £ - 0.2 Corner - - Opt. Chamf. -0 .2 5 + Comp. Bend -0 .3 6.5 17 34 50 Frequency (GHz) Fig. 7.3 Comparison of unchamfered (Comer), conventional (Opt. Chamf.), and novel (Comp. Bend) CPW bends. W = 70 pm, G=20 pm, 8,= 12.9, and HSUb=625 pm. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 91 Table 7.4 Comparison of return loss for the conventional optimally chamfered bend and the novel compensated bend for several structures. (Frequency = 50 GHz) w G (pm) (pm) 70 120 70 35 105 105 70 7.1.4 60 40 20 55 55 25 40 Optimally Chamfered bend Return loss (dB) Novel bend Return loss (dB) -13.89 -12.96 -21.51 -17.27 -12.50 -15.76 -16.36 -20.92 -16.36 -26.94 -20.18 -17.02 -19.33 -21.41 Improvement (dB) 7.03 3.40 5.43 2.91 4.52 3.57 5.05 CPW 90° Bend with Air-Bridge Height as an Input Parameter As an example of using prior knowledge (existing models) for ANN model development, an input parameter is being added to an existing EM-ANN model using regular training methods, the difference method, and the PKI method. The structure of the CPW 90° bend under consideration is shown in Fig. 7.1a. Variable input parameters for the original EM-ANN model are frequency, W, and G. Model outputs are S-parameters. Substrate material used is GaAs (£r = 12.9) and the thickness (Hsub) is 625 pm for all results included in this section. Air-bridges are 40 pm wide (Wa) and are positioned at the bend discontinuity as shown. Originally, the height o f the air-bridge (Ha) was held constant at 3 pm. For the new model, Ha is to be added as an input parameter. The new model variable input parameters and corresponding ranges are given in Table 7.5. EM simulations have been performed over the 1 GHz to 50 GHz frequency range for various air-bridge Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 92 heights on 5 training structures (120 examples), 6 simultaneous test structures (140 examples), and 6 model verification structures (140 examples). Table 7.5 Variable input parameter ranges for the CPW 90° bend. Frequency W G Ha Min. 1 GHz 20 pm 20 pm 3 pm Max. 50 G H z 120 pm 60 pm 9 pm Model average error and standard deviation are given in Table 7.6, Table 7.7, and Table 7.8 for the regular training method, the difference method, and the PKI method, respectively. Both the difference method and the PKI method show increased accuracy over regular training for the same num ber o f training points. Also, the PKI method gives slightly better accuracy than the difference method. This example demonstrates the advantage o f using prior knowledge for adding new input parameters to existing ANN models. For the model developed using regular training methods, more data would be required to obtain lower errors. However, when using prior knowledge, information about old input parameters is present, allowing additional EM simulations to be concentrated on capturing the trends of the new input parameter. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 93 Table 7.6 Error results for the variable air-bridge height CPW bend model, regular training. (5 train structures, 4 inputs, 4 outputs, 14 hidden neurons, 130 weights) Train/test Average error Standard dev. Verification Average error Standard dev. ISul ZS„0 IS2il Z S 2I° 0.0047 0.0042 2.871 3.718 0.0027 0.0024 0.917 0.657 0.0049 0.0043 2.592 2.432 0.0027 0.0025 1.080 0.882 Table 7.7 Error results for the variable air-bridge height CPW bend model, difference method. (5 train structures, 4 inputs, 4 outputs, 15 hidden neurons, 139 weights) Train/test Average error Standard dev. Verification Average error Standard dev. is , , i ZSn° IS21I z s 2,° 0.0017 0.0014 1.213 1.744 0.0006 0.0005 0.197 0.126 0.0018 0.0015 1.886 2.463 0.0009 0.0011 0.271 0.253 Table 7.8 Error results for the variable air-bridge height CPW bend model, PK I method. (5 train structures, 8 inputs, 4 outputs, 13 hidden neurons, 179 weights) Train/test Average error Standard dev. Verification Average error Standard dev. IS.,1 ZSn° IS2,I Z S 21° 0.0011 0.0010 1.161 1.285 0.0006 0.0004 0.227 0.114 0.0015 0.0012 1.559 1.787 0.0006 0.0001 0.227 0.215 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 94 7.2 EM-ANN Modeling of CPW Transmission Lines An EM-ANN model characteristics of CPW has been transmission developed lines. for frequency dependent Variable input parameters and corresponding ranges are given in Table 7.1. Model outputs are frequency dependent Zq and 8re. The EM-ANN model has been trained using PCAAMT* [122], a program which provides full-wave solutions for printed transmission lines and general multilayer geometries. The training/test dataset consisted o f 265 examples, while the verification dataset contained 51 examples. Twenty neurons were used in the hidden layer. Error results between the developed EM-ANN model and the full-wave solution for the trainmg/test and verification datasets are shown in Table 7.9. Table 7.9 Error results (average and standard deviation) between the EM-ANN model and EM simulation for the CPW transmission line. Train/test dataset Average error Standard dev. Verification dataset Average error Standard dev. Zo (a) Zo (%) £re 0.105 0.098 0.234 0.224 0.00283 0.00248 0.111 0.112 0.243 0.238 0.00341 0.00240 ' Momentum (ver. A .02.20) could not be used for this purpose because value o f Zo is not available for CPW. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 95 7.3 EM-ANN Models for CPW Opens and Shorts Open and short circuit stubs are important components for many circuit designs such as filters and impedance matching networks. The geometries o f the short and open components considered are shown in Fig. 7.4 and in Fig. 7.5, respectively. Variable input parameters and corresponding ranges for model development are given in Table 7.1. Model outputs are S-parameters. Typical output responses for an open and a short circuit with reference planes at the discontinuities are shown in Fig. 7.6. For each model, EM simulations have been performed on 17 structures over the 1 G H z to 50 GHz frequency range. For the short circuit model development, 71 examples were used in the training/test dataset and 46 examples for the verification dataset, requiring 5 neurons in the hidden layer. Open circuit model development was accomplished using 95 examples in the training/test dataset, 53 examples for the verification dataset, and 6 neurons in the hidden layer. Error results for the training and verification datasets are given in Table 7.10 for the short circuit and in Table 7.11 for the open circuit. G A W V G Fig. 7.4 CPW short circuit geometry. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 96 G_ A W JL G Fig. 7.5 C PW open circuit geometry. 10 - 20 30 40 50 0.1 - 0.2 - 0.3 - 0.4 £■o -0-5 CD - 0.6 - 0.7 - 0.8 - 0.9 frequency (GHz) 180 150 120 90 60 -op en .S li -shoft_Stt 30 0 10 20 -r -*r -30 -60 fre q u e n c y (GHz) Fig. 7.6 S-parameter response for CPW open and short circuits. W = 70 pm, G = 60 pm, and reference planes at the discontinuities. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 97 Table 7.10 Error results (average and standard deviation) between the EM-ANN model and full-wave simulation for the CPW short circuit. T rain/test dataset Average error Standard dev. Verification dataset Average error Standard dev. ISnl Z S in (°) 0.000248 0.000350 0.396 0.271 0.000381 0.000412 0.964 0.867 Table 7.11 Error results (average and standard deviation) between the EM-ANN model and full-wave simulation for the CPW open circuit. Train/test dataset Average error Standard dev. Verification dataset Average error Standard dev. 7.4 ISnl Z S n (°) 0.000481 0.000633 0.332 0.373 0.000520 0.000892 0.634 0.676 EM -ANN M odeling o f C PW Step-in-W idth CPW step-in-width discontinuities are used extensively in circuit design for introducing impedance changes. The geometry of the step-in-width, for which an EM-ANN model has been developed, is shown in Fig. 7.7. Variable input parameters are frequency, Wi, W2, and G. Also, only structures where Wi < W 2 were used for model development due to the nature o f the step. Parameter ranges are given in Table 7.1. Model outputs are S-parameters. A typical output response is shown in Fig. 7.8. EM simulations have been performed on 30 structures over the 1 GHz to 50 GHz frequency range, providing 95 training/test examples and 55 verification examples. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 98 Eight neurons were used in the hidden layer. Residual errors are shown in Table 7.12 and (as for other models developed) are negligible for design applications. X i G A G A Wo W 1 i G f G A Fig. 7.7 CPW step-in-width geometry. Table 7.12 Error results (average and standard deviation) between the EM -ANN model and full-wave simulation for the step-in-width. Train/test dataset Average error Standard dev. Verification dataset Average error Standard dev. ISnl ^S n(°) IS2 1 I ZS2i(°) 0.000864 0.000721 0.435 0.454 0.000792 0.000840 0.321 0.286 0.001214 0.001023 0.553 0.579 0.000986 0.001032 0.457 0.390 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 99 50 -8 - - d B (S 1 1 ) TJ -12 d B (S 2 1 ); -1 6 --20 frequency (GHz) 180 150-- a n g (S 1 1 ) a n g (S 2 1 ) 05 30 -- -30 40 50 frequency (GHz) Fig. 7.8 S-parameter response for a 71 Q to 50 Q CPW step-in-width transition. W ( = 20 pm, W2 = 70 pm , G = 60 pm, and reference planes at the discontinuity. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 100 7.5 EM-ANN Modeling of CPW Symmetric T-junctions The symmetric T-junction under consideration is shown in Fig. 7.9. Variable model input parameters are frequency. Win, Gjn, Wout, and Gout. Param eter ranges are given in Table 7.1. Model outputs are S-parameters. A typical output response is shown in Fig. 7.10. EM simulations have been performed on 25 structures over the 1 GHz to 50 GHz frequency range, providing 155 training/test examples and 131 verification examples. Fifteen neurons were used in the hidden layer. Model error results are shown in Table 7.13 for both the training/test and verification datasets. out out out out © Fig.7.9 CPW symmetric T-junction geometry. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. I II 20 -2 40 50 -• 1k dB(S11) dB(S33) i db(S13) I dB(S23) | -10 • • -12 frequency (GHz) 180 120 TO -- ang(S11) ang(S33) ang(S13) ang(S23); 60 •• O) -60 frequency (GHz) Fig. 7.10 S-parameter response for a typical CPW symmetric T-junction. Win = W out = 70 pm, Gin = Gout = 60 pm, and reference planes at the air-bridge locations. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 102 Table 7.13 Error results between the EM-ANN model and EM simulation for the CPW symmetric T-junction (average and standard deviation). Input branchline port is Port I, and the output ports on the main line are Ports 2 and 3. IS„I 4S„ ° ISI3I Z S 13° ISijI Z S 23 0 IS33 I Z S 33° Train Avg. Stdev. 0.00150 0.00128 0.754 0.696 0.00071 0 .0 0058 0 .1 7 6 0 .1 7 2 0.00084 0.00097 0.246 0.237 0 .0 0 1 0 6 0.00109 0.633 0.546 Verify Avg. Stdev. 0.00345 0.00337 0.782 0.674 0 .0 0 0 8 8 0 .0 0 0 8 5 0.141 0 .1 2 5 0.00126 0.00105 0.177 0.129 0.00083 0.00068 0.838 0.717 7.6 CPW Circuit Design Examples 7.6.1 CPW Folded Double-Stub Filter The first CPW circuit design example is a CPW folded double-stub filter as shown in Fig. 7.11. For this design W = 70 pm and G = 60 pm, yielding Zq = 50 Q. CPW EM-ANN models used are CPW transmission line, 90° compensated bends, short circuit stubs, and symmetric T-junctions. The filter has been designed for a center frequency of 26 GHz. Ideally, the length of each short circuit stub and the section of line between the stubs should have a length of X74 at 26 GHz. However, due to the presence of discontinuities, these lengths need to be adjusted. Design and optimization have been accomplished using HP-MDS [49] network simulator and EM-ANN models for various components. Parameters to be optimized are l SWb and lmjd. Initial values for these lengths were determined and the structure simulated, showing a less than ideal response. The circuit was then optimized, using gradient descent, to provide the desired circuit response. The effect of optimization was reductions in line lengths. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Results are 103 shown in Fig. 7.12 for the original design, optimized design, and full-wave EM simulation of the entire optimized circuit. Excellent agreement is obtained betw een the optimized EM -ANN circuit design and the full-wave EM simulation over the 1 GHz to 50 GHz frequency range. This demonstrates applications of EM -ANN models in CPW circuit design. i G_ A W jr. G_ fI Fig. 7.11 CPW folded double-stub filter geometry. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 104 0 ^ -10 -- -20 - - 10 20 30 40 50 to S’ ■° - 3 0 - Opt. EM-ANN i -40 - - - Org. EM-ANN -50 frequency (GHZ) 200 150 ■* 100 o> o> <a -- 50 -- 53 -50 --100 EM-ANN Opt. -150 - - EM-ANN Org. -200 frequency (GHz) (a) Fig. 7.12(a) S|i for C PW folded double-stub filter for the optimized EM-ANN circuit (EM-ANN Opt.), the original EM-ANN circuit (EM-ANN Org.), and EM simulation (EM sim.). Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. I 105 0 <2. ■O -10 - - -20 -- 10 20 30 40 50 EM-ANN Opt. -30 g EM sim. ■ - - EM-ANN Org. -40 frequency (GHz) 200 150 - - EM-ANN Org. 100 50 -20 -50- ■ -100 5D \ - - -150 - -200 frequency (GHz) (b) Fig. 7.12(b) S 21 for CPW folded double-stub filter for the optimized EM-ANN circuit (EM-ANN Opt.), the original EM-ANN circuit (EM-ANN Org.), and EM simulation (EM sim.). Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 106 7.6.2 CPW 50 £2,3 dB Power Divider The second CPW circuit design example is a 50 Q , 3 dB power divider, shown in Fig. 7.13. For this design, EM -ANN models for CPW transmission lines, 90° compensated bends, T-junctions, and step-in-width transitions are used. The power divider has been designed for a 3 dB pow er split between the output ports at 26 GHz. Ideally, 7JA, 70.7 Q line sections are used to transform the 50 Q output impedance at Ports 2 and 3 into 100 £2 loads at the T-junction. Due to the presence of discontinuities, the lengths of the transformers need to be adjusted. Input and output lines are 50 Q (W = 70 pm, G = 60 pm) and transformer lines are approximately 71 £2 (W = 20 pm , G = 60 pm). Again, HP-MDS [49] has been used for design and optimization. The optimizable parameter for this design is the length of the transformer line section, ltrans. An initial value for 1 ,^ was determined. After the initial design failed to meet the prescribed design criteria, optimization was performed, resulting in a shorter iine length than initially determined. Resuits are shown in Fig. 7.14 for the original design, optimized design, and full-wave EM simulation o f the entire optimized circuit. As with the double-stub filter design, excellent agreement has been obtained between the optimized EM-ANN circuit design and EM simulation results over the entire 1 GHz to 50 GHz range. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 107 trans trans G l< W H G © Fig. 7.13 CPW power divider geometry. I Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 108 0 10 20 30 40 50 EM-ANN Opt. | EM sim. - - EM-ANN Org. ^ - 10-1 CO m ■° -1 5 - - - 20-- -25 frequency (GHz) 180 150 -- 120 -- 90 -U) 60 -EM-ANN Opt. g 30 -- EM sim ■ - - B/t-ANN O rg .: 20 30 40 frequency (GHz) (a) Fig. 7.14(a) Sn for CPW power divider for the optimized EM-ANN circuit (EMANN Opt.), the original EM-ANN circuit (EM-ANN Org.), and EM simulation (EM sim.). Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 109 0 10 20 30 40 50 0 ■1 2 -3 -4 -5 -6 -7 -8 -9 -10 frequency (GHz) 200 150 100 a> EM-ANN Opt. : g EM Sim. • - -EM-ANNOrg. 50 -50 20 5) -100 -150 -200 frequency (GHz) (b) Fig. 7.14(b) S 21 for CPW power divider for the optimized EM-ANN circuit (EMANN Opt.), the original EM-ANN circuit (EM-ANN Org.), and EM sim ulation (EM sim.). Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 110 Use of EM-ANN models for CPW components has allow ed accurate and efficient design and optimization o f the CPW filter. Thus, we note that the EM-ANN modeis provide EM optimization capabilities. Optimization time for the EM -ANN circuit was only 3 minutes and required 7 circuit analyses. T he am ount o f time required to provide EM simulation results for 17 frequency points for the entire filter circuit was approximately 14 hours on the same HP 700 workstation. Optimization time for the power divider circuit was only 2 minutes and required 6 circuit analyses. EM simulation time for the entire power divider, at 15 frequency points, totaled almost 11 hours on this HP 700 workstation. This confirms that substantial savings in time are achievable by using EM-ANN component models, especially when optimization is desired, requiring numerous circuit solves and when these components are to be used over and over in different circuit designs. It should be mentioned that even larger and more com plex circuits can be designed using the developed EM-ANN models. EM simulation o f large, complex circuits is limited by the computer resources available, and in many cases is not practical. With EM-ANN component modeling, these difficulties are overcome. 7.7 Discussion Results presented in this chapter demonstrate clearly the application o f the EM-ANN modeling approach for developing efficient and accurate models for various CPW components and discontinuities. Models developed for CPW lines, open-ends, shorts, steps-in-width, bends, and T-junctions can be conveniently used for efficient and accurate design o f various kinds o f CPW circuits. The two examples I i Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Ill of circuit design and optimization reported in this chapter and verification o f final design by comparing with electromagnetic simulation results validate the modeling and design approach developed. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. CHAPTER 8 EM-ANN MODELS FOR DESIGN OF CPW PATCH ANTENNAS This chapter explores the use of radiating elements using open-ended coplanar waveguide (CPW) resonators to provide an alternative for printed slot antennas and microstrip patch antennas. Motivation for exploring these antenna structures arises from the ease of connecting CPW resonators to CPW lines, which have received much attention due to several advantages of CPW lines over microstrips as discussed in Chapter 7. Further investigation of these radiating structures requires development of simple network models (like the transmission line model for microstrip patch antennas) which may be used for designing these antennas. However, unlike in the case for microstrip antennas, no work has been reported in the literature on wide strip CPW lines or open-end discontinuities and their radiating properties. Therefore, the focus o f this chapter is on the development of accurate and efficient EM-ANN models for wide strip CPW lines, CPW open-end discontinuities (including radiation conductance modeling), and feed discontinuities used for connecting CPW resonators to CPW lines. These models are then used within commercial microwave simulators for CPW patch antenna design. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 113 8.1 Radiation Characteristics o f CPW Line and Open End The radiation characteristics o f the CPW line open-end shown in Fig. 8.1 have been studied, using HP Momentum [48], to determine the effects o f varying the strip width, W, and the gap spacing, G. The substrate used is Duroid 5880 (8r = 2.2 and HSUb = 31.25 mil). The open-end geometry lies in the x-y plane as shown. The polar angle, 0, is measured from the z-axis towards the x-y plane and the azim uthal angle, (j), from the x-axis towards the y-axis in the x-y plane. 8.1.1 Radiation from a Wide CPW Line Figure 8.2 shows the simulated radiation pattern of a CPW line (W =1.5 cm, G=0.01 cm, and L=3 cm) terminated at two ends by matched loads (without an open end). The length, L, is A72 (CPW wavelength) at 5 GHz. The plane o f the pattern is perpendicular to the gaps (<|) = 90°). The fields in the gaps are 180° out o f phase and Ee contributions from the two gaps cancel in the broadside direction. However, since W+2G is large, perfect cancellation does not occur for values of 0 away from 0°. This radiation from a line section is different from that in a microstrip patch antenna where the dominant radiation is only from the two open ends. 8.1.2 Radiation from CPW Open-Ends A large width, W, is needed to increase the radiation from the CPW open ends as with microstrip patch antennas. Therefore, rough guidelines for this work are that G needs to remain small and W should be as large as possible as long as the radiation from the line is at an acceptable level. To illustrate this, several CPW open ends have been simulated. Figure 8.3 shows the effects o f increasing G on the H-plane (<{>= 90°) i Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 'end y X Fig. 8.1 O pen-end CPW geometry. ca Broadside r u B1 Cl JC ou i L tJ Fig. 8.2 Simulated radiation patterns (E q and E^) o f a CPW line (W =1.5 cm, G=0. cm, L=3 cm and f = 5 GHz) w ithout an open end. The plane o f the pattern perpendicular to the gaps (<j>= 90°). Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 115 ( u r \j i (a) a uj (b) Fig. 8.3 Far-Field radiation patterns (Ee and E^) at 5 GHz for two open-ended CPWs with W = 1.5 cm, L=3 cm, Gend = 0.85 cm, and different gap widths ((j) = 90°). (a) G = 0.5 cm and (b) G = 0.01 cm. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 116 radiation pattern o f the open-ended line. The strip width, W, is kept at X j A for these simulations and the spacing, Gemi, is held constant. As G is increased, the radiation from the CPW line increases (Eg) until it is as strong as the radiation from the openend (H^), Fig. 8.3a. Lines with smaller gaps show less radiation, Fig. 8.3b. Figure 8.4 shows the effects o f increasing W. The gap, G, is held constant for these simulations, along with the spacing, Gen(j. We note from this figure that as W is increased, the radiation from the line increases also. Therefore, for this modeling effort, small gaps will be used along with smaller conductor widths to reduce the radiation from the line. Another reason for using small gaps is the presence of higher order modes on the CPW line at the open-end discontinuity. Figure 8.5 illustrates the effects o f gap width by showing the magnetic current distribution within the gaps. For the desired CPW mode, the magnetic currents within the slots o f the line should be in opposite direction and contain only x-directed, not transverse (y-directed), components. Notice that for the open-end with wider gaps, higher order modes extending well into the CPW line are present and contribute to the far field radiation since the transverse magnetic current components are in phase in the two gaps and thus add in the far field. For the open-stub with smaller gaps, higher order modes are not as visible. Since the transmission line model assumes only one mode (TEM) on the line, it is not a good candidate for modeling CPW antennas using CPW lines with wide gaps. However, y-directed magnetic current components, in the gaps near the open-end. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 117 have the same polarization as the magnetic current at the open-end and are therefore not undesirable from a radiation point o f view. s) C9 (a) o (b) Fig. 8.4 Far-Field radiation patterns ((J) = 90°) at 5 GHz for two open-ended CPWs with G = 0.05 cm, Gend = 0.85 cm, L=3 cm, and different conductor widths (W). (a) W = 1.5 cm and (b) W = 2.0 cm. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 118 (a) 111 tiax£03r (b) Fig. 8.5 Magnetic current distributions for two CPW open-ends with W = 1.5 cm, Gcnd = 0-85 cm, L=3 cm , and different gap widths at 5 GHz. (a) G = 0.5 cm and (b) G = 0.1 cm. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 119 8.2 Transmission Line Equivalent o f a Rectangular CPW Patch 8.2.1 Transm ission Line Model for CPW Antennas Transmission line models for microstrip patch antennas have been studied extensively [123]. In the same manner, a transmission line model for CPW antenna design can be developed. Figure 8.6 shows the antenna structure without the feed line and an equivalent transmission line model. The transmission line model consists of a length of CPW transmission line open-circuited at the two ends. Thus, the patch can be represented by a uniform length of transmission line o f characteristic impedance Z q and phase velocity u p (or propagation constant, (3=co/up). For this model, the assumption is that the line is operating in the TEM CPW mode and is lossless, which is a fair assumption when the conditions o f Section 8.1 (small values o f G) are met. The fringing fields associated with the open ends are represented by lumped admittances, consisting of a radiation conductance, Gr, and an edge capacitance, C. ’end C > Fig. 8.6 Ideal CPW patch antenna geometry and corresponding transmission line equivalent circuit model. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 120 8.2.2 EM-ANN Model for CPW Transmission Line An EM-ANN model for wide conductor CPW transmission lines on Duroid 5880 (£r = 2.2 and Hsub = 31.25 mil) has been developed for use in C band antenna (4 GHz to 7 GHz) design. Model input variables and corresponding ranges are given in Table 8.1. Outputs o f this ANN model are Zq and (3 for the CPW line. Since the training data was relatively inexpensive to obtain for this component, EM simulations were performed, using HP Momentum [48], for a uniform distribution over the input variables’ ranges. HP-Momentum is able to provide values for Re(Zo) and P for CPW lines. The train/test dataset consisted of 140 input/output examples and the verification dataset contained 62 examples. The optimal ANN structure contained 6 hidden layer neurons (38 weights). Error results for the training and verification datasets are given in Table 8.2, and show excellent accuracy. Typical trends for Zo and p are shown in Fig. 8.7 and are consistent with those reported elsewhere for CPW lines with smaller strip widths [1]. Table 8.1 Input variables and ranges for CPW transmission line model. Input Parameter Maximum Value Minimum Value Frequency 4 GHz 7 GHz W 0.5 cm 2 .0 cm G 0.05 cm 0 .2 cm Table 8.2 Error results (average and standard deviation) for the CPW line model. Z olQ ) Train/test A verage error Standard dev. Verification Average error Standard dev. 3 (rad/m) 0.109 0.075 0.147 0 .150 0.145 0.0 9 4 0.138 0.126 1 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 121 124 68 ■•123 122 ■ * - ■ 121 S 58 ■■ 118 0.5 1.25 0.75 1.5 W (cm ) (a) 120.5 ■•120 + 119.5 £ ■•119 g ■■118.5 ca. N 60-- 117.5 0.07 0.09 G (cm ) (b) 180 160 60 - ■ • ■140 58 ■■ ■• 120 57 ■> ■ ■ 56 100 80 Frequency (GHz) ( C) Fig. 8.7 Typical trends for Zo and p (phase constant) with (a) f = 5 GHz, G = 0.05 cm, and W variable, (b) f = 5 GHz, W = 1.5 cm, and G variable, and (c ) W = 1.5 cm, G = 0.05 cm, and frequency variable. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 122 8.2.3 EM-ANN Model for CPW Open-End Effects An EM-ANN model for CPW open-end effects, including radiation conductance, has been developed. Substrate parameters are the same as those for the CPW transmission line model. Variable input parameters and their corresponding ranges are given in Table 8.1. For this model, the open-end spacing, Gend. is set equal to 0.5(W+2G). EM -ANN model outputs are the magnitude and phase o f S n . The reflection coefficient, S n , for the open-end is obtained by simulating a Xl2 line and finding input impedance at the far end. This choice of output parameters allows easier insertion of the m odel into commercial microwave simulators. A DOE central composite design, as discussed in Chapter 3, was used to obtain the EM simulation data for training. The parameters for the central composite design were frequency, W , and G. Frequency is needed in the experim ents’ design due to the fact that }J2 lines are needed for open-end characterization. Initially, 15 examples were used for training, 14 for testing, and 10 for verification. However, errors were not as low as desired. Therefore, the 14 test examples were added to the training dataset for a total o f 29 examples. The final model contained 10 hidden layer neurons (62 weights). Error values for the final model are given in Table 8.3. We note that excellent accuracy has been achieved. Radiation Conductance and Capacitance The radiation conductance and capacitance o f the open end may be obtained from the EM-ANN model by noting that S n is the reflection coefficient o f the open- Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. i 123 Table 8.3 model. Error values (average and standard deviation) for the CPW open-end Train/test Average error Standard dev. Verification Average error Standard dev. ISnl Z S „(°) 0.0032 0.0029 0.493 0.418 0.0043 0.0037 0.728 0.623 end. When the line length used to characterize the open end is )J2 long and the line is lossless, the load (that is, the open-end) impedance may be found as Zl 1+ Su = Z j-— — 1—on (8.1) Taking the inverse o f ZL to obtain YL yields the radiation conductance as Gr = R c (Y l ) (8.2) C = h !^ (8.3) and the end capacitance as CO As noted, this technique for finding the load impedance is valid only for lossless transmission lines. Therefore, when radiation from the line increases, as Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 124 described in Section 8.1, the values o f Gr and C are not only for the open-end, but also include the effect of radiation from the line. However, the EM-ANN model with Sn as the output still gives useful results, but Gr and C for the open-end alone cannot be extracted using this sim ple method. Using the guidelines for values of W and G given in Section 8.1, trends for Gr and C have been determ ined and are shown in Fig. 8.8 and in Fig. 8.9. For the results shown, the value o f the spacing, Gend, at the open end has been held constant. Notice in Fig 8.8a that Gr increases slightly and C decreases as the gap width, G, is increased. These results are expected due to the slight increase in radiating area at the top and bottom of the open-end and the added distance between conductor and ground plane. Both Gr and C increase as the center strip width, W, is increased, due to the increase in radiating area, as shown in Fig. 8.8b. Fig. 8.9 shows the behavior of Gr and C versus frequency for two different values of W. In Fig. 8.9a, the capacitance remains fairly constant over m ost of the frequency range and then decreases sharply. Since it is expected that C should only have a slight frequency variation, the extraction technique, as described earlier, may not be valid for the points that show a sharp decrease. The reason for this is that as frequency increases, the patch becomes electrically wider (W = "kJA at 5 GHz), increasing radiation from the line used to characterize the stub. Therefore, for this case, the results up to only about 5.5 GHz are reasonable for the open-end characterization (i.e., not affected significantly by radiation from the CPW line itself)- Fig. 8.9b shows results o f Gr and C versus frequency for a lower value o f W (1cm). Notice that C remains fairly constant over the entire frequency range as one would expect. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 125 0.3 - - 0.25 4 -= - ■ 3 -- 0.2 -- 0.15 2 IT B -- - 0.1 - - 0.05 0.01 0.03 0.05 0.07 0.09 0.11 G (cm) (a) 0.3 - - 0.25 2.5 - - 0.2 O) -- 0.15 1.5 d - - 0.1 -- 0.05 0.5 1 1.1 1.2 1.3 1.4 1.5 1.6 W (cm) (b) Fig. 8.8 Trends o f the radiation conductance, Gr, and capacitance, C, for a CPW open-end with Gend=0.85 cm at 5 GHz. (a) G variable and W=1.5 cm . (b) W variable and G=0.05 cm. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 126 0.35 -■ 0.3 - - 0.25 -- 0.2 LL a. -- 0.15 " 0.1 - - 0.05 4.5 5 5.5 6 6.5 Frequency (GHz) (a) 0.3 2 .5 0.25 0.2 u. 1.5 -- 0.15 -- 0.5 0.1 ■* 0.05 Frequency (GHz) (b) Fig. 8.9 Trends o f the radiation conductance, G r, and capacitance, C, for a CPW open-end with Gend=0.8 cm versus frequency, (a) W=1.5 cm and G=0.05 cm. (b) W=1 cm and G=0.05 cm. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 127 8.2.4 CPW Patch Antenna Design W ithout Including Feed Effects Now that models for the CPW line and the CPW open-end have been developed, the ideal CPW patch antenna design (ignoring feed discontinuities) may be carried out. Again, the geometry under consideration is shown in Fig. 8.6. For the ideal case, if the ends o f the patch are perfect open circuits, the length of the patch, L, for resonance would need to be Xl2, providing maximum and equal voltages at the patch ends and a real input impedance. M aximum values o f the voltage at the patch ends corresponds to the maximum radiated power. W hen the ends of the patch are not perfect open circuits, the length of the patch is reduced below X/2 due to the edge susceptance. The resonant patch length, in this case, is determined by the condition o f having a real input impedance along the patch, which also provides equal and maximum voltages at the patch ends [123J. Using the EM-ANN models for CPW line and open-end (developed earlier in this chapter) within a commercial microwave simulator, the patch length, L, is determined by optimization and the patch antenna can be simulated . Voltage probes may also be used to check the voltages at the patch ends. Results o f several ideal CPW patch antenna designs are given in Table 8.4. The results include antenna designs with wide impedance bandwidths (ISnl < -10 dB) in the range of 7.7% to 14.2% for W =1.5 cm. As discussed previously, some o f the results (when W is wide) may include radiation from the CPW line also, but an attempt has been made to keep this to a minimum. As will be demonstrated in the next section on practical realization o f these CPW antennas, wide bandwidths can be achieved. Note that the Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 128 bandwidth of a conventional microstrip patch antenna with W = 1.5 cm is approximately 1%. Table 8.4 Ideal CPW patch antenna designs. Antenna W = 1.0 cm G = 0.05 cm f = 5 GHz W = 1.0 cm G = 0.1 cm f = 5 GHz W = 1.5 cm G - 0.05 cm f = 5 GHz W = 1.5 cm G = 0.1 cm f = 5 GHz W = 1.0 cm G = 0.05 cm f = 4.5 GHz W = 1.5 cm G = 0.05 cm f = 4.5 GHz 8.3 G r (mS) C (pF) L (cm) BW (%) 0.878 0.201 2.052 36 0.978 0.193 1.989 4.9 3.015 0.296 1.767 12.0 3.575 0.294 1.648 14.2 0.682 0.205 2.337 3.0 2.049 0.294 2.103 7.78 CPW Patch Antenna Design Including Feed Discontinuities Practical realization o f a CPW patch antenna design requires inclusion o f a way to feed the antenna. Feed discontinuities can alter antenna performance and need to be included and compensated for during design. The feed arrangement used for this work is shown in Fig. 8.10. The patch is fed by a high impedance line on the radiating edge. A radiating edge feed has been chosen to keep the design symmetric in order to avoid excitation o f slot line mode on the patch. Also, ease o f fabrication is a consideration. If a feed on the non-radiating edge is desired, it needs to be a dual feed in order to keep symmetry. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 129 7 ////////////A Fig. 8.10 C PW patch fed on the radiating edge and its corresponding transmission line model. 8.3.1 EM -ANN M odel for Feed Discontinuities Variable input parameters for the model are given in Table 8.1. The incoming feed line has to be kept narrow in width in order to minimize interference with radiation from the radiating edge, but has to be wide enough to be realizable using available fabrication facilities. Therefore, the incoming line has been chosen to have W = 0.1 cm , G = 0.05 cm, and Z<, » 96 Q. The output parameters for this model are the magnitudes and phases of S n , S 2 1 , and S 2 2 - EM simulations have been performed on 27 structures over the 4 GHz to 7 GHz frequency range providing 111 training/test examples and 42 verification examples. The optimal ANN structure contained 15 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. ! 1 130 hidden layer neurons (156 weights). Error results are given in Table 8.5. As with the other models, excellent accuracy is obtained. Table 8.5 Error results (average and standard deviation) for the CPW feed discontinuity model. Train/test Average error Standard dev. Verification Average error Standard dev. 8.3.2 IS„I Z S „(°) IS2il Z S 21 (°) IS22I Z S 2 2 (°) 0.0034 0.0032 0.596 0.621 0.0032 0.0029 0.654 0.529 0.0035 0.0028 0.824 0.921 0.0046 0.0041 0.794 0.761 0.0040 0.0039 0.699 0.550 0.0046 0.0034 1.215 1.225 C PW Patch A n ten n a Design Using EM -ANN M odels CPW patch antennas may now be designed using the EM-ANN models developed for the CPW open-end, CPW line, and feed discontinuities. As an example, a CPW patch antenna has been designed at 5 GHz with W = 1.5 cm and G = 0.1 cm. The ideal patch length for this antenna has been determined in Section 8.2.3 and is given in Table 8.4 (fourth row). The layout o f the antenna is shown in Fig. 8.11. CPW section ‘a’ was designed by optimization using ANN models to yield a real value of impedance at its input. Impedance at the input of this section was found to be 821 Q. Three matching sections have been included to transform the input impedance from 821 Q to 50 Q for measurement purposes. The option o f stub matching was not selected because that would need incorporation o f air-bridges. Table 8.6 and Fig. 8.12 compare return loss for the EM -ANN model (EM-ANN), EM simulation using H P’s M omentum [48] (EMsim), and measurement (meas). Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 131 Excellent accuracy is achieved by the EM -ANN model design when compared with EM simulation and measurement. Note that the bandwidth (ISnl < -10 dB) is much less than for the ideal patch (2.7% versus 14.2%) with no feed discontinuities. Therefore, some alternative feed arrangement may be able to yield wider bandwidth from this class of antennas. the EM-ANN models. What needs to be stressed, however, is the accuracy of Other feeding arrangements, such as a feed on the non- radiating edge, can be designed and m odeled in the same manner. Radiation patterns from EM simulation and measurement are shown in Fig. 8.13. radiation (z>0, above the metallized layer) is shown. Only top-side Bottom-side (below the substrate) radiation is o f comparable magnitude. Fig. 8.11 Layout o f CPW patch antenna design. Electrical parameters referenced to the resonant frequency of 4.99 GHz. Table 8.6 Comparison o f resonant frequency and bandwidth for EM-ANN modeling, EM simulation, and measurement. Center Frequency % Bandwidth EM-ANN 4.99 GHz 2.6% EM simulation 5.01 GHz 2.6% Measured 5.09 GHz 2.7 % Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 132 4 4.5 5 5.5 6 0 _ -10 00 s (0 -20 tf > ° -30 c EM-ANN | 3 -40 EMsim | a> cc m ea& ^j -50 -60 F r e q u e n c y (GHz) Fig. 8.12 Comparison o f return loss for the CPW patch antenna shown in Fig. 8.11. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 133 -100 50 -50 03 2, 100 10 O 5 o Q. ■o 0N> 30 -40 75 E E _ th eta_ sim E.phi.slm E _ th e » a _ m e a s E _ p h l_ m e a s 56 -66 Angle_Theta (degrees) (a) -100 m 2, w 0) 50 -50 100 10 3 o Q. TJ 0) N 75 E -40' 50 E _ th e t a _ s l m E .p h L sIm E _ th e t a _ m e a s E _ph l_m ecn -66 Angle_Theta (degrees) (b) Fig. 8.13 Far field radiation patterns for the antenna shown in Fig. 8.11. (a) E-plane (<(>= 0°) and (b) H-plane (<j>=90°). Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 134 8.3.3 CPW Patch Antenna Design Optimization Using EM-ANN Models To show the usefulness o f the EM-ANN modeling approach, we are able to investigate the effects of changing certain design parameters on the response o f the C PW patch antenna. An exam ple o f this is changing the patch length from its ideal length. The effects o f changing the patch length will be demonstrated using the antenna o f the previous section. It has been noted that for several values of the patch length a loop forms in the S n plot on the Smith Chart due to the nature of the CPW patch antenna (curve A l) and the effects of the feed structure (curve B l) as shown in Fig. 8.14. The ideal patch w ith no feed structure is labeled as A l. As the feed section (FS in Figs. 8.11 and 8.16), which is effectively a high impedance CPW line, is added, a loop forms another resonance created by the feed section length. The response after the feed section (FS) is added is labeled B 1. Next, adding the incoming feed line, which has an impedance o f 96 Q, the response is rotated around the smith chart to the real axis for matching purposes. C 1. Note that the loop has effectively been pulled out. By experimentation it has been found that increasing the patch length increases the size of the loop as shown in Fig. 8.15. If the antenna can be designed at a frequency where the loop appears, a wider bandwidth can be achieved. For this purpose, the length of the incoming feed line can be adjusted, rotating the loop to the real line. One thing to note, however, is that increasing the patch length may effect the radiation pattern as will be shown. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 135 B1 Al Fig. 8.14 Effects o f radiating edge feed section and line on CPW patch antenna (W=1.5 cm G=0.l cm and Gentj=0.85 cm) S u response. (A l) Ideal patch with no feed (Lpatch=l.6465 cm). (B l) Addition of feed section. (C l) Addition o f incoming feed line. Al Fig. 8.15 Effects of increasing the patch length (LpatCh= 1.937 cm). (A l:L a= O cm and B l: La=3.4cm.) Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 136 A CPW patch antenna has been designed, fabricated, and measured with a longer than ideal patch length in order to increase the bandwidth. The layout o f the antenna, designed using EM-ANN models, is shown in Fig. 8.16. No impedance transforming sections were required since a match directly to 50 Q was possible. CPW length ‘a’ acts as a matching section between patch input point T where Zjn= 169.7 Q + j4 1 .14 at 5.56 GHz. Impedance o f section ‘a ’ is 96 Q. A wide bandwidth has been achieved for this antenna as seen in Table 8.7 and in Fig. 8.17. The return loss for the EM simulated antenna is only down about -2 0 dB at resonance due to a slight mismatch. For a perfect match (according to EM simulation), the length of section ‘a’ (La) needs to be reduced by 0.025?i (0.123 cm). However, La was left at the ANN model result (3.4 cm) for fabrication and measurement. EM-ANN modeling, EM simulation and measurements agree well. The EM simulated and measured E-plane and H-plane radiation patterns are shown in Fig. 8.18. Only the top-side radiation pattern is shown. Radiation from the bottom side is comparable. Note that the radiation from the line (Eq) is only down at about -1 0 dB at points. This radiation can be reduced by decreasing the strip width (W) and the gap width (G), as discussed previously. The radiation pattern for this case shows more of a main lobe shift than the ideal case. For the ideal case, the main lobe shift was approximately 9°, while it is around 15° for the antenna o f Fig. 8.16. The modeling using EM -ANN models compares well with EM simulation and measurement, validating the approach. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 137 0.85 cm 0.85 cm Fig. 8.16 Layout for CPW patch antenna with longer than ideal patch length. All dimensions are in cm. Electrical parameters referenced to the resonant frequency of 5.56 GHz. Table 8.7 Comparison of resonant frequency and bandwidth for EM-ANN modeling, EM simulation, and measurement. CPW patch antenna with longer than ideal patch length. Center Frequency % Bandwidth 4.5 Measured 5.49 GHz 14.5 % EM simulation 5.54 GHz 11.69 % EM-ANN 5.56 GHz 14.03 % 5.5 6.5 7.5 S ' -10 -20 • • _i meas EMsim DC -40 •• EM-ANN -50 Frequency (GHz) Fig. 8.17 Comparison of return loss for the longer than ideal patch length CPW patch antenna. 1 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. I I 138 -90 -60 30 -30 -10 CL -- -15 - - -20 - -25 - - E _1heta_m eos 'E _ th e ta_ slm Angle_theta (degrees) (a) -100 -50 0 50 100 0 -o 3 oQ. TS 0) N E o z E _ p h l_ slm -40 - “ E _ th eta_ slm *"“ E _ p h l _ m 0a s ►““ E_th eta_ m eaj Angle_theta (degrees) (b) Fig. 8.18 Far field radiation patterns, measured and EM simulation, (a) E-plane (<(> = 0°). Only E_theta is shown due to antenna damage during measurement, (b) H-plane (<J)=90°). Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 139 8.4 Discussion This chapter has presented a novel antenna configuration, the CPW patch antenna, designed by using EM-ANN modeling approach. The radiation properties of the CPW open-end with a wide center strip have been studied. Recommendations for antenna design resulting from this study may be summarized as follows: • • • Use small gap widths (G) to reduce CPW line radiation Strip width (W) should be as large as possible to increase radiation from the ope:, end, but not large enough where cross-polarization radiation from the CPW line becomes a problem Length o f the CPW patch may be adjusted to increase radiation bandwidth EM -ANN models have been developed for design and optimization o f CPW patch antennas. Designed antennas show excellent agreement with EM simulation and measurement. This chapter has mainly been concerned with the modeling aspect o f the CPW patch antenna. Several interesting observations, including the wide bandwidth observed theoretically as well as experimentally, call for continued detailed investigations. Radiation properties of wide strip CPW lines also warrant further study. Also, different feeding arrangements, such as on the non-radiating edge, need to be studied in order to explore if such a feed can lead to the wide bandwidth shown by the ideal case with no feed. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. CHAPTER 9 SUMMARY AND FUTURE WORK 9.1 EM-ANN M odeling Methodology A novel approach for accurate and efficient modeling of microwave and mm- wave passive components by using electromagnetically-trained Artificial Neural Network (EM-ANN) software modules has been presented in this thesis. The proposed technique uses the Design o f Experiments (DOE) methodology to identify various component parameter values for which electromagnetic simulations need to be carried out in order to capture characteristic input/output relationships. Use of the DOE approach allows for a minimum number o f EM simulations that need to be performed. Simulation results are then used to train the ANN model, using physical parameters as inputs, to provide the correct component response (i.e. S-parameters) over the desired frequency range. Simultaneous training and testing, as well as a ‘simple-to-complex’ approach is used for obtaining optimal ANN architectures. Since ANNs have been shown to have the ability to learn from data, to generalize patterns in data, and to model highly nonlinear relationships, the trained model is valid for the entire ranges of the input variables. It may be noted that no circuit Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 141 models (in terms of lumped elements etc.) are involved in the derivation o f ANN models. Once EM-ANN models have been created, they are easily inserted into a commercial microwave circuit simulator. It has been shown that EM-ANN models provide accuracy approaching the EM simulation tool used for providing training data, but at much less computational expense. Optimization techniques can also be used with the trained EM-ANN models to find optimal component structures for given circuit design applications. Optimization is performed within the circuit simulator environment, which is very fast compared to EM simulation. This is advantageous for interactive CAD o f microwave circuits. Prior knowledge in the form o f existing models (analytical, empirical, EMANN, etc.) has been used for ANN model development. The advantage o f using prior knowledge is the reduction o f training data (EM Simulations) that needs to be supplied to the ANN in order to capture the desired input/output mapping accurately. This implies that the input/output mapping is simplified by the use o f prior knowledge. A reduction in the amount o f training data needed for model characterization is very advantageous since EM simulation accounts for a major portion of the EM-ANN model development time. Two simple methods, the difference method and the PKI method, for incorporation of prior knowledge into ANN training have been discussed and demonstrated in this thesis. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 142 9.2 EM-ANN Modeling Examples 9.2.1 M icrostrip Vias and M ultilayer Interconnects An ANN model has been developed to provide microstrip line characteristic impedance (Zo) and effective dielectric constant, £re. The main purpose o f this example was to show a situation where training the ANN on relative error is more desirable than training on absolute error. When training on relative error, the average model error and standard deviation summed to less than 1%. This was not the case when training on absolute error. EM-ANN models have been created for I- and 2-port microstrip grounding vias. While models for microstrip vias exist, they were found to be lacking in accuracy at high frequencies. The EM-ANN microstrip via models have been developed for the 5 GHz to 55 GHz frequency range. Therefore, the EM-ANN models may be used for high frequency design or in nonlinear circuit design where harmonics are present. As an example of modeling o f multilayer interconnects. EM-ANN models have been created for a stripline-to-stripline interconnect and a microstrip-tomicrostrip interconnect. Models for these two interconnects did not exist previously. However, with the EM-ANN modeling methodology presented in this thesis, accurate and efficient models have been created which can be used for design and optimization of multilayer circuits. Prior knowledge has been used to create two models. Both the difference method and the PKI method (discussed in Chapter 3) were used for model development and comparisons have been made. The first model was for a 2-port Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 14 3 microstrip via. The prior knowledge, in this case, was an equation for the inductance o f the via. In the second exam ple, a previously developed stripline-to-stripline multilayer interconnect model was used as prior knowledge to extend one o f its own input parameters’ range. In both situations, use o f prior knowledge resulted in lower error than regular training (no prior knowledge) on the same training data. Therefore, use of prior knowledge has been shown to be an effective means for reducing the amount o f data needed for ANN model development. This is very important when data is costly/time-consuming to obtain as is the case with EM simulation. The developed models have been linked to a com m ercial microwave circuit simulator where they can be used for circuit design and optim ization. Component optimization has also been demonstrated. 9.2.2 M ulticonductor M ultilayer Coupled Transmission Line Models A methodology for the synthesis (leading to physical dimensions) of multilayer asymmetric coupled microstrip lines using ANN models has been presented. Both synthesis and analysis models have been developed. Models are appropriate for synthesis o f m ultilayer circuits like filters, baluns, and directional couplers. Accuracy comparable to other optimization methods for multilayer filter design has been achieved, but in a small fraction o f the time. The proposed methodology has been dem onstrated by the design o f a 2-layer coupled line filter. Synthesis of these multilayer m icrowave circuit components has not been reported elsewhere. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 144 9.2 3 EM-ANN Models for CPW Components Accurate and efficient EM -ANN models, valid from 1 GHz to 50 GHz. have been developed for the purpose o f forming a library o f coplanar waveguide (CPW ) circuit components. M odeled components include: CPW transmission lines (frequency dependent Z q and ere), 90° bends, short circuit stubs, open circuit stubs, step-in-width discontinuities, and symmetric T-junctions. These models can be conveniently used for efficient and accurate design of various kinds of CPW circuits. Design and optimization o f a CPW folded double stub filter and a 50 G , 3 dB power divider circuit, using only the developed CPW EM-ANN models, has been demonstrated. Results were compared to EM simulation o f the same structures, showing excellent agreement over the entire 1 GHz to 50 GHz frequency range. This is the first report of using only ANN models for the design o f larger circuits. Considerable attention has been paid to the modeling of various CPW 90° bend structures. EM-ANN models have been developed for optimally chamfered CPW 90° bends and a novel compensated CPW 90° bend. It has been shown that chamfering the com er of 90° CPW bends provides a simple way to improve their performance. The optimal cham fer for a conventional CPW bend, where both the slot and strip comers are chamfered, has been determined and reported for the first time. Also, a novel compensated CPW bend structure, where only the strip is chamfered, has been developed as part o f this research. This novel compensated CPW bend has been shown to reduce the return loss from that in the conventional optimally chamfered CPW bend by 3 to 7 dB. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 145 As an example o f the use o f prior knowledge, an EM-ANN model has been developed for a bend where the air-bridge height is added as an input parameter. An EM-ANN CPW bend model, without air-bridge height as an input parameter, has been used as prior knowledge. Again, less EM simulation data was required for model development for desired model accuracy. 9.2.4 EM-ANN M odels for Design o f CPW Patch Antennas A novel antenna configuration, the CPW patch antenna, designed by using EM-ANN modeling approach, has been presented in this thesis. The radiation properties of the CPW open-end with a wide center strip have been studied. EMANN models have been developed for the design and optimization o f CPW patch antennas. Using the developed EM-ANN models, CPW patch antenna geometry has been optimized to provide a wide bandwidth response. In fact, much wider bandwidths than those reported results for single-layer microstrip patch antennas have been demonstrated. This portion o f research clearly demonstrates the usefulness o f ANN modeling for the design o f novel components where little or no information is known. 9.3 Future Work 9.3.1 Nonlinear Active Device Modeling A potential application o f ANNs, which has not been explored to date, is modeling of nonlinear active microwave devices (HBTs, MESFETs, HEMTs), including thermal effects. The devices could be characterized by making time- domain current and voltage measurements. Training o f the ANN would be Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 146 accomplished using this data. The resulting model could then be used in commercially available microwave circuit simulators for the design of nonlinear circuits, such as pow er amplifiers, oscillators, and mixers. 9.3.2 ANN M odel Development for Passive Components using Measured Data ANN models could be created using measured data instead of EM simulation. The result would be fabrication process specific models, which in many instances may be desirable. However, measured data inherently contains noise. ANNs are ideal for this situation since they have the ability to model complex input/output relationships, even in the presence o f noise [9.1]. 9.3.3 CPW Patch Antenna Several interesting observations about CPW patch antennas, including the wide bandwidth observed theoretically as well as experimentally, call for continued detailed investigations. Radiation properties of wide strip CPW lines also warrant further study. Also, different feeding arrangements, such as on the non-radiating edge, need to be studied in order to explore if such a feed can lead to the wide bandwidth shown by the ideal case with no feed. 9.3.4 ANN of Complete Circuit Modules In this thesis, models have been developed for certain passive components and then the components are combined to form larger circuits. This is an acceptable method when interactions (couplings) between components are not significant. However, as circuits become more compact, interactions between components will inevitably increase. In this situation, ANN models could be developed for complete circuit topologies, such as amplifiers, filters, etc. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 147 9.3.5 Synthesis of Components Synthesis o f components has problems associated with it as discussed in Chapter 6. If the inverse mapping is multi-valued and a least-squares error approach is used, the neural net tends to approximate the average o f the target data. Also, It can be difficult to determine if and where there are regions o f input variable space which have not been characterized by the available training data. Future work in this area should be directed at solving these problems. i i Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. BIBLIOGRAPHY [1] K.C. Gupta, Ramesh Garg, and I.J. Bahl, Microstrip Lines and Slotlines 2nd ed., Artech House, Boston, MA, 1996. [2] Inder Bahl and Prakash Bhartia, Microwave Solid State Circuit Design, John W iley and Sons Inc., New York, NY, 1988. [3] K.C. Gupta, Ramesh Garg, and Rakesh Chadha, Computer-Aided Design o f M icrowave Circuits, Artech House Inc., Dedham, MA, 1981. [4] David M. Pozar, Microwave Engineering, Addison-Wesley Publishing Company Inc., 1993. [5] V.K. Sadhir, I.J. Bahl, and D.A. 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M emyei et al., “New Cross-T Junction for CPW Stub-Filters on M MIC’s,” IEEE M icrowave and Guided Wave Letters, Vol. 5, No. 5, pp. 139-141, May 1995. [97] M. Naghed et al., “A New Method for the Calculation o f the Equivalent Inductances o f Coplanar Waveguide Discontinuities,” M TT-S Int. Microwave Symp. Dig., 1991, pp. 747-750. [98] A. Omar et al., “A Versatile Moment Method Solution o f the Conventional and M odified Coplanar Waveguide T-Junctions,” IEEE Trans, on Microwave Theory and Techniques, Vol. 41, No. 4, pp. 687-692, Apr. 1993. [99] R. Simons et al., “Modeling o f Some Coplanar Waveguide Discontinuities,” IEEE Trans, on Microwave Theory and Techniques, Vol. 36, No. 12, pp. 1796-1803, Dec. 1988. [100] M. Naghed et al., “Equivalent Capacitances of Coplanar Waveguide Discontinuities and Interdigitated Capacitors Using a Three-Dimensional Finite Difference Method,” IEEE Trans, on Microwave Theory and Techniques, Vol. 38, No. 12, pp. 1808-1815, Dec. 1990. [ 101] M. Drissi et al., “ Analysis o f Coplanar Waveguide Radiating End Effects Using the Integral Equation Technique,” IEEE Trans, on M icrowave Theory and Techniques, Vol. 39, No. 1, pp. 112-116, Jan. 1991. [102] B. Isele and P. Russer, “The M odeling o f Coplanar Circuits in a Parallel Computing Environment,” MTT-S Int. Microwave Symp. Dig., 1996. pp. 1035-1038. [103] N. I. Dib et al., “A Comprehensive Theoretical and Experimental Study of Coplanar W aveguide Shunt Stubs,” M TT-S Int. Microwave Symp. Dig., 1992, pp. 947-950. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. I 157 [104] M. Yu et al., “Analysis o f Planar Circuit Discontinuities Using the QuasiStatic Space-Spectral Domain Approach,” MTT-S Int. M icrowave Symp. Dig., 1992, pp. 845-848. [ 105] R. D oem er et al., “M odeling o f Passive Elements for Coplanar SiGe MMICs,” M TT-S Int. Microwave Symp. Dig., 1995, pp. 1187-1190. [106] H. Jin and R. Vahldieck, “Full-Wave analysis of Coplanar Waveguide Discontinuities Using the Frequency Domain TLM M ethod,” IEEE Trans, on M icrowave Theory and Techniques, Vol. 41, No. 9, pp. 1538-1542, Sep. 1993. [107] M. Yu et al., ‘Theoretical and Experimental Characterization o f Coplanar W aveguide Discontinuities,” IEEE Trans, on M icrowave Theory and Techniques, Vol. 41, No. 9, pp. 1638-1640, Sep. 1993. [108] F. Alessandri et al., “A 3-D Matching Technique for the Efficient Analysis of Coplanar MMIC Discontinuities with Finite M etallization Thickness,” IEEE Trans, on Microwave Theory and Techniques, Vol. 41, No. 9, pp. 1625-1629, S e p .1993. [109] A. Tran and T. Itoh, “Full-Wave Modeling o f Coplanar Waveguide Discontinuities with Finite Conductor Thickness,” IEEE Trans, on Microwave Theory and Techniques, Vol. 41, No. 9, pp. 1611-1615, Sep. 1993. [110] C. Chiu and R. Wu, “A Moment Method Analysis for Coplanar Waveguide Discontinuity Inductances,” IEEE Trans, on Microwave Theory and Techniques, Vol. 41, No. 9, pp. 1511-1514, Sep. 1993. [111] N. I. Dib et al., “Characterization o f Asymmetric Coplanar Waveguide Discontinuities,” IEEE Trans, on Microwave Theory and Techniques, Vol. 41, No. 9, pp. 1549-1557, Sep. 1993. [112] N. I. Dib et al., “ A Theoretical and Experimental Study of Coplanar W aveguide Shunt Stubs,” IEEE Trans, on Microwave Theory and Techniques, Vol. 41, No. 1, pp. 38-44, Jan. 1993. [113] H. Klingbeil et al., “FDFD Full-Wave Analysis and M odeling o f Dielectric and Metallic Losses o f CPW Short Circuits,” IEEE Trans, on Microwave Theory and Techniques, Vol. 44, No. 3, pp. 485-487, Mar. 1996. [114] K. Beilenhoff et al., “Open and Short Circuits in Coplanar M M IC’s,” IEEE Trans, on Microwave Theory and Techniques, Vol. 41, No. 9, pp. 1534-1537, Sep. 1993. I Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 158 [115] M. Mao et al., “Characterization o f Coplanar Waveguide Open End Capacitance - Theory and Experiment,” IEEE Trans, on Microwave Theory and Techniques, Vol. 42, No. 6, pp. 1016-1024, Jun. 1994. [116] W. Harokopus, Jr. and P.B. Katehi, “Radiation Loss from Open Coplanar Waveguide Discontinuities,” MTT-S Int. Microwave Symp. Dig., 1991, pp. 743-746. [117] C. Wguyen et al.. “Analysis of Coplanar W aveguide Multiple-Step Discontinuities,” IE E E AP-S Symposium, 1993, pp. 185-188. [118] Y. Lin, “Characterization o f Coplanar W aveguide Open-End and Short-End Discontinuities by the Integral Equation Method,” Asia-Pacific Microwave Conf. Digest, 1993, pp. 29-32. [119] P. Pogatzki et al., “A Comprehensive Evaluation o f Quasi-Static 3D-FD Calculations for more than 14 CPW Structures - Lines, Discontinuities, and Lumped Elements,” M TT-S Int. M icrowave Symp. Dig., 1994, pp. 1289-1292. [120] P. Pogatzki and O. Kramer, “A Coplanar Element Library for the Accurate CAD of (M)MICs,” Microwave Engineering Europe, Dec./Jan. 1994. [121] M. Riaziat et al., “Coplanar W aveguides used in 2-18 GHz Distributed Amplifier,” MTT-S Int. Microwave Symp. Dig., 1986, pp. 337-338. [122] PCAAMT, ver. 2.0, EM-CAD Laboratory, Polytechnic University o f New York, Brooklyn, NY, 1990. I Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. APPENDIX A A.1 User-Defined Linear Model Subroutine This C code subroutine links a generic ANN model, consisting o f up to inputs and 10 outputs, to HP-MDS. The majority o f the code is a template. Cc added by the user to define a model is shown in bold. * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * File: Description: net2p.c Model codefor the user-compiled linear model: "net2 p" Created: 16 Nov 1995 RCS: SHeader S 13:29:12 * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * The function ,,u_net2p_evalO" is the function that calculates S-parameters. The function ”u_net2p_query0" 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. The function "u_net2p_dispose()” frees any memory allocated by u_net2 p_eval(). * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * #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. 1 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. * and malloc.h */ #include "usermodel.h" #include <stdlib.h> #include ”nn_sub2p" y * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * Here is a list o f preprocessor macros which are used to access the * parameters of this device: * */ #define PARAM_il #define PARAM_i2 #define PARAM_i3 #define PARAM_i4 #define PARAM_i5 #define PARAM_i6 #define PARAM_i7 #deftne PARAM_i8 #define PARAMJ9 #define PARAM_i 10 #define PARAM_data_ftle 0 1 2 3 4 5 6 7 8 9 10 static int u_net2 p_evai(): static int u_net2 p_query(): static void u_net2 p_dispose(): /* * * « * * * * * * * * * * * * * * * * * * * * * * * * * M a t* * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * The USER_PARAM data structure describes the parameters used by this * device. * *1 static USER_PARAM u_net2p_params[ ] = { { "il", /* name */ NULL, NULL. IP_READABLEIIP_DIFFERENTIABLEIIP_SETTABLEIIP_MODIFIABLEI[P_REQUlRED. REAL.TYPE. . 00001. /* default value if real or integer */ /* default imag value if complex */ /* default string if string (next line) */ NULL }, ( "i2 ". /* name */ NULL. NULL. IP_READABLEIIP_DIFFERENTIABLEIIP_SETTABLEIIP_MODIFIABLEIIP_REQUIRED. REAL.TYPE, 0 0 . , .00001 . /* default value if real or integer */ /* default imag value if complex */ I* default string if string (next line) */ NULL }. { ”i3". /* name */ NULL. NULL. IP_READABLE!lP_DIFFERENTIABLEIIP_SETTABLEIIP_MODIFIABLEIIP_REQUIRED. REAL_TYPE, 0 0 . , Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. .0 0 0 0 1 . . /* default value if real or integer */ 0, /* default imag value if complex */ /* default string if string (next line) */ NULL I, { "i4". /* name */ NULL. NULL, 0 ip _ r e a d a b l e iip _ d if f e r e n t ia b l e iip _ s e t t a b l e iip _ m o d if ia b l e iip _ r e q u ir e d . REAL.TYPE. .0 0 0 0 1 , 0. /* default value if real or integer */ 0. /* default imag value if complex */ /* default string if string (next line) */ NULL ), { "i5", /* name */ NULL, NULL, IP.READABLEIIP.DIFFERENTIABLEIIP.SETTABLEIIP.MODIFIABLEIIP.REQUIRED. REAL.TYPE. .0 0 0 0 1 . 0, /* default value if real or integer */ 0, /* default imag value if complex */ /* default string if string (next line) */ NULL ). { ”i6 ", /* name */ NULL. NULL. IP_READABLEIIP_DIFFERENTIABLEIIP_SETTABLEIlP_MODIFIABLElIP_REQUIRED. REAL.TYPE, .0 0 0 0 1 . 0, /* default value if real or integer */ 0. /* default imag value if complex */ /* default string if string (next line) */ NULL }. { ”i7". /* name */ NULL, NULL. IP_READABLE!IP_DIFFERENTIABLEIIP_SETTABLEI1P_V10DIFIABLEIIP_ REQUIRED, REAL.TYPE, .0 0 0 0 1 , 0, /* default value if real or integer */ 0. /* default imag value if complex *1 /* default string if string (next line) */ NULL ), ( "i8 ", /* name */ NULL, NULL. IP.READABLEIIP.DIFFERENTIABLEIIP.SETTABLEIIP.MODIHABLEIIP.REQUIRED. REAL.TYPE, .0 0 0 0 1 , 0. /* default value if real or integer */ 0, /* default imag value if complex */ /* default string if string (next line) */ NULL ), { "i9", /* name */ NULL. NULL, IP.READABLEIIP.DIFFERENTIABLEIIP.SETTABLEIIP.MODIFIABLEIIP.REQUIRED. REAL.TYPE, .0 0 0 0 1 , 0, /* default value if real or integer */ Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. i /* default imag value if complex */ /* default string if string (next line) */ NULL }, { "ilO". /* name */ NULL. NULL. IP_READABLEIIP_DlFFERENTIABLEIIP_SETTABLEIIP_MODIRABLEIIP_REQUIRED, REAL.TYPE, 0 . .00001. /* default value if real or integer */ /* default imag value if complex */ /* default string if string (next line) */ NULL }. { "data.file", /* name */ NULL. NULL. IP.READABLEIIP.SETTABLEIIP.MODIFIABLEIIP.REQUIRED, STRING.TYPE. 0 0 . . 0, /* default value if real or integer */ /* default imag value if complex */ /* default string if string (next line) */ NULL } 0 0 . . ): ^ * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * The USER.MODEL data structure describes the device, and any parameters * used by it. tic */ USER.MODEL u_net2p = { 1. ''net2 p'\ NULL, 2, u_net2 p_params. sizeof(u_net2p_params) / sizeoftUSER.PARAM), MODEL.EV ALU ATES.S, u_net2 p_eval, u_net2 p_query, u_net2 p_dispose 1: ^* * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * u_net2p_eval() calculates S-parameters. This is the * main model evaluation routine. * */ static int u_net2p_eval(Name, Rags, Omega, Matrix. NumberOfPorts, Parameters, Substrate, SavedData) char *Name; int Rags; RealNumber Omega; ComplexNumber *Matrix; int NumberOfPorts; USER.DATA ‘ Parameters: struct SubstrateModelData ‘ Substrate; void “ SavedData; Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. { RealNumber I[10],0[10],pi,theta; CompIexNumber param; char ctmp[50]; pi=3.14159265358973; I[0i=0mega/(2.0*pi*1.0e9); * Get input parameters fro m sim ulator * I[lI=UGET_REAL_VALUE(Parameters[PARAMJl]); I[21=UGET_REAL_VALUE(Parameters[PARAM_i21); I[31=UGET_REAL_VALUE(Parameters[PARAM_i3]); I[4]=UGET_REAL_VALUE(Parameters[PARAMJ41); I[5]=UGET_REAL_VALUE(Parameters[PARAM_i5]); I[6]=UGET_REAL_VALUE(Parameters[PARAM_i6]); I[7]=UGET_REAL_VALUE(Parameters[PARAM_i7]); I[8]=UGET_REAL_VALUE(Parameters[PARAM_i8]); I[9)=UGET_REAL_VALUE(Parameters[PARAM_i9]); I[10]=UGET_REAL_VALUE(Parameters[PARAMJ10]); strcpy(ctmp,UGET_STRING_VALUE(Parameters[PARAM_data_filel)); * Call feed-forw ard A N N routine * neural_net2p(I,0,ctmp); * Process A N N outputs and send S-parameters back to circuit sim ulator theta=(0[ 1]*pi)/180.0; param.ReaI=O[0]*cos(theta); param.Imag=O[0]*sin(theta); CMPLX_ASSIGN(MATRIXl_ELEMENT(Matrix, NumberOfPorts, 1,1), param); CMPLX_ASSIGN(MATRIXl_ELEMENT(Matrix, NumberOfPorts, 2,2), param); theta=(0[3]*pi)/180.0; param.Real=0[21*cos(theta); param.Imag=0[2]*sin(theta); CMPLX_ASSIGN(MATRIXl_ELEMENT(MatrLx, NumberOfPorts, 2,1), param); CMPLX_ASSIGN(MATRIXl_ELEMENT(Matrix, NumberOfPorts, 1,2), param); param.Reai=50.0; param.lmag=0.0; CMPLX_ASSIGN(MATRIXl_Z(Matrix, NumberOfPorts, 1), param); CMPLX_ASSIGN(MATRIXl_Z(Matrix, NumberOfPorts, 2), param); return (YES); } /****************************************************************************** * * u_net2 p_query() is used only if "read-only” parameters exist. If this * model does not have any "read-only" parameters, this routine does not have Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. * 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_net2p_query(Parameter!D, NumberOfPorts, Parameters, Substrate, SavedData. Value) int ParameterlD; int NumberOfPorts; USER_DATA ‘ Parameters; struct SubstrateModelData ‘ Substrate; void “ SavedData; USER_DATA ‘ Value; ( /* Initialization */ USET_DATA_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 (ParameterlD) { default: /* * If this is parameter is not handled by this routine, just * exit. */ break; I return (YES); I /* * * * * * * * « * * * c * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * u_net2 p_dispose() is used to free memory that was allocated and stored * on the "saved_data" parameter of the u_net2 p_eval() function. * If you do not use the ''saved_data” parameter o f u_net2p_eva!(), you * do not need to modify this routine. * */ static void u_net2p_dispose(SavedData) void “ SavedData; { if (‘ SavedData) ( /* * Free any additional data here. */ free( ‘ SavedData): } } /* * Local Variables: * c-indent-levcl: 4 * c-continued-statement-offset: 4 * c-brace-offset: -4 * c-argdecl-indent: 0 * c-labcl-offset: -4 * End; */ Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. A.2 Feed-Forward ANN Subroutine neural_net2p(I,0,ctmp) double I[L0],O[10]; char ctmp[50]; { int i,j,k,r,c,l; double minmax[21 )[2], w l[5 0 ][l l],w 2[10][51],IN [l 1]; double sum, net[50],f[511,net2[I0],ON[10|; float x; FILE *fpt; * Read input file containing E M -A N N model information * fpt=fopen(ctmp,,’r"); fscanf(fpt,”9fcd%d%d".&i,&k,&j); for(r=0;r<i+k;++r) { for(c=0;c<2;++c){ fscanf(fpt,”%e",&x); minmax[r][c]=x;}} for(r=0;r<j;++r){ for(c=0;c<=i;++c) { fscan f( fpt,"■ % e " ,& x); wl[r][c]=x;>} for(r=0;r<k;++r){ for(c=0;c<=j;++c) { fscanf(fpt.’’%e",&x); w 2[r][c]=x;n fclose(fpt); * Normalize Inputs between 0 and 1 * IN[0]=1.0; for(r=k;r<i+k;++r) { IN[r-k+I l=(I[r-k]-minmax[r][0])/(minmax[r][l]-minmax[r][0]);} * Multiply normalized inputs by first set o f weights and pass through logistic activation function * f[0]=1.0; for(r=0;r<j;++r){ sum=0.0; for( c=0 ;c<=i;+ +c) { sum=sum+w 1[r][c]*IN[c];} net[r]=sum; f[r+1]= 1,0/C 1.0+exp(-net[r]));} Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 166 * M ultiply by second set o f weights, and pass through logistic activation function * for(r=0;r<k;++r){ sum=0.0; for(c=0;c<=j ;++c){ sum=sum+w2[r][c]*f[c];} net2[rl=sum: ON[rj=l.0/(1.0+exp(-net2[r])); * Denormalize outputs * 0[rl=((ON[r]-0.2)*(minmax[r][l]-minmax[r][0])/0.6)+minmax[r][0];} } i Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 167 A.3 Sample EM-ANN Model Input File The following EM-ANN model file is that o f a CPW short circuit stub. 3 2 5 * # o f inputs * * # o f outputs * * # o f neurons in the hidden layer * * Max. and Min. values for outputs * 9.870000e-01 1.057610e+02 I.000000e+00 1,786330e+02 * Max. and Min. values for inputs * to to 1.000000e+00 .000000e+01 .000000e+01 5.000000e+01 1.200000e+02 6.000000e+01 * First layer of weights between the input and hidden layers 3.762740e+00 -3.657379e-0I 1.029619e+00 5.309179e+00 2.I92086e+00 -4.328468e+00 -2.988256e-01 -2.771775e-01 -5.236892e+00 4.126552e-02 -1.223319e-02 -5.204754e+00 1.435307e+00 8.790260e-0l -1.41749 le+00 -1.898849e+00 -1.391095e+00 -4.185616e+00 1.659987e+00 9.686552e-01 * Second layer of weights between the hidden and output layers * -3.219908c+00 2.860686e+00 -2.718878e+00 1.958229e+00 -3.04206le+ 00 3.117409e+00 3.816633e-rOO -3.497359e+00 2.358216e+00 3.028646e-02 8.417108e-01 3.96I452e-01 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. I APPENDIX B USER-DEFINED LINEAR MODEL LIBRARY FOR CPW COMPONENTS Appendix B contains instructions for installing a distributable user-defined linear model library for use with HP-MDS [49]. The library consists o f various CPW passive component EM -ANN models useful for microwave design. Refer to Chapter 7 for a description o f available CPW models. The CPW library is available for distribution with instructions provided for installation. References contained in the instructions refer to the reference manuals provided with HP-MDS. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 169 Installing the CPW Library of Components 1) Creating and preparing a directory (Ref. DTR-V9 Creating Device and Model Libraries, p. 5-8 The purpose o f this step is to create and prepare a directory to copy necessary files into for user-compiled linear model development. Example: mkdir models cd models run /usr/..appropriate path..7hp85150/lib/mnsmodels/modelprepare note: The path for the modelprepare program is dependent on your specific software installation path. 2) Copy library file, icon file and ANN model files to models directory a) copy cu_cpw.a (library file) and cpw jm ods (icon file) to models directory b) create a directory under your models directory for the CPW ANN models ex. mkdir /...Vmodels/cpw_models c) copy CPW A N N models to cpw_models directory 1) cpw_line, use as Zo_mod for all models except for cpw_bend 2) cpw_bend_line, use as Zo_mod for all models except for cpw_bend 3) cpw_open, CPW open circuit model 4) cpw_short, CPW short circuit model 5) cpw jbend , CPW compensated bend model 6) cpw_step, CPW step model (port 1 always has the smaller W) 7) cpw_tee, CPW symmetric T-junction (port 1 is the input port, ports 2 and 3 are the symmetric ports) 8) cpw_cap_ab, air-bridge capacitance model used with T-junction Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 170 3) Edit libraries file (Ref. DTR-V9 Creating devivce and model libraries, pp. 5-38 to 5-44) Initially the libraries file will contain: m m tttttiiitiiiitm tttittiiiiiu itiiiiitiittitttititiiiiim iiiiiiiiiiiiiiiiiiH itiiitiitiiu iitiiiitt # Description user-compiled linear models, C function name declare_user_models Edit the file to look as follows: MmtittittttittittitMtmtnttttttitiitttiiiiitittiiittititimifHiiittiitiuiiimttnmittttitit # Description #user-compiled linear models, declare_user_models CU CPW models, 4) C function name cu_cpw_install Edit M akefile Edit OTHER_LIBRARIES to look as follows: OTHER_LEBRARIES= cu_cpw.a 5) Type make and press return At this point you will have an executable program called inns, which is the simulator with the desired library. This simulator file must be switched with the one currently in use. copy /..Vmodels/mns to /usr/ /hp85150/lib/mns800 note: save the old mns800 file as mns800.old for example. note: make sure to change permissions so that everyone can use the newly created simulator file. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 171 6) Read design icons file into MDS To use the newly installed models, the design icons file must be read into MDS. Once these design icons are created, they can be used in the same manner as other MDS components. run mds click Browse/open click unix system change to directory where cpw_mods has been stored (models) click on cpw_mods click OK A design file cpw_mods should appear on your mds screen. This design file contains the icons for all cpw models. To use these models single click on each one to highlight them. Then execute perform/add to menu. To place these models into a schematic, execute insert/component. A list o f the new cpw components should appear. Click on the desired model and use as you woud any other mds model. 7) Notes on model usage Within MDS model: • All inputs for W, G, 1, etc. are in pm. (Ex. W= 20, W equal 20 pm) • Input correct path to ANN model file names ( Ex. ‘usr/local/watson/mds/models/cpw_models/cpw_line’) • Step model: Port 1 is always the side with the smaller metal width (Wl) • T-Junction: This is a symmetric T-junction. Port 1 is the port at the bottom o f the T. Ports 2 and 3 are the symmetric ports. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. IMAGE EVALUATION TEST TARGET ( Q A - 3 ) 150mm IIW IG E . I n c 1653 East Main Street Rochester, NY 14609 USA Phone: 716/482-0300 Fax: 716/288-5989 0 1993. Applied Image, Inc.. AH Rights Reserved Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.

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