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DESIGN AND MODELLING OF MICROWAVE CIRCUITS

USING OPTIMIZATION METHODS

By

SHAHROKH DAIJA VAD, B. Eng.

A Thesis

Submitted to the School of Graduate Studies

in Partial Fulfilment of the Requirements

for the Degree

Doctor of Phil.osophy

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McMaster Cniv~rsity

·June 1986

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To my mother Camellia, and in loving

memory army uncle Manouchehr.

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DESIGN AND MODELLING OF MICROW AVE CIRCUITS

USING OPTIMIZATION METHODS

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DOCTOR OF PHILOSOPHY (1986)(Electrical Engineering)

McMASTER lJNIVERSIT¥Hamilton, Ontario

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TITLE:

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Desi"n and Modelling of Micr'owav~ Circuits l.:singOptimizatIon Methods ',". Y'

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J,W, Bllndler, Professor', D~partment Qf Eiec'tric~l andComputer Engineerir!g " ,.. '.. . . . ' ..B.Se. (Eng.), ~h.D., D.Sey(Eng.) (University of London)DJ.C., (Ifuperial College) •P.Eng. Wrovince'ofOntario)C..ERg., P.l.E.E. (UniteqKingdom)Fellow, I:E.ELE. •Fellow, Royal Society ofCan~a ,.

ShahrokhDaijavad, B: Eng. (E,E:)'(McMaster University) 0, ,

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ABSTRACT

This thesis addresses itself to the computer-aided design and modelling of

microwave circuits using efficient minimax and et. optimiz~tion techniques.

Recent algorithms for nonlinear mini~ax and e1 'optimization arc

reviewed. The features of the el norm; itstheor~tieal properties and the necessary

con~itions for optimality are discussed.,

f ;.A comparative example with e2 optimizatiop iUustrates the rqbu~tnessof el

for the .particular applications of this 'thesis; Efficient gradient a~ation

~echniques,.applicable to both minimax and ~I optimization, are presented.. ;

A simplifi.ed -and straightforward treatment of sensitivities for two"port~.~ '.

networRs, cascaded and branched cascaded st"'ctures is introduced. The objective is. "

to 'calculate the ,sensitivities efficiently, without appealing to the alljo.int network

concept, A novel proof of a recent, result in sensitivity analysis of loss!ess and

reciprocal tWe>,ports'is presented.

Design of manifold' type wav~gUide'mllltiprel\ershas been considered as a '

major· application for bolh mini~ax optimization and. the. fheoretic,\1 work in'. .

branched cascaded network sensitivity analysis. Components of the multiplexer

.' - . ~ .structure a,nd nonideal effects such as 'dissipation and dispersion are discussed and a

step-by-step implementation of an algorithm to calculate 'particular responses and. . ... '.. ~ .

'sensitivities .i~ presented. Examples of-the design of 3-, 12- and ,16-channel, 12 GHz

. \ -,'.' ~u.~tiple,,!,ersillustrate the practicality of the approach presenfed.

A new approach to modelling of microwave devices which exploits the

theoretical i*Operties of the el norm is presente,d. The concept of m\llti·circuit '.

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is discussed.

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•measurements is introduced and its· merits in obtaining unique and self-consistent

parlimete.rs are discussed; The technique ,is applied t/modelling of mUlt~"couPledcavity fi)ters and GaAs FET's. The application of efflient modelling techniques in

developing algorithms for postprdQuction tuning and il establishing\he relationship·. I.

between physical parameters of a device and its equiy\1lent circuit model paramete~s,. I .

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!ACKNOWL'EDGEMENTS

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The. author wishes to ,exp,ress his appreciation to D'1'J.W. Bandler for his

encourage~eht, exPert guidance and supervision throughout th~ course tlf this work.. '.He also thanks Dr.C.R. Carter and Dr. A.A.'Smith, members of his'su~ervisory. ,comm,itte", for their cOlltinuing interest.

The,~uthoracknowledges the opportunity given to him by OJ. J.W. Bandler

to be involyed in indust,rial projects developed1>y Optimization Systems Associates," .~.

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Specifically, the author has ,benefitted from.the industrial input and expertiseI • I '.

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p,rovided by ComDev Ltd. of Cambridge, Onta:rio in the design of multiplexers and

modelling' of'multi.coupled cavi~ fi;ters. Useful technical disc~ssions with R. Tong,.1

L. Zaifman",nd H.:AuYeung of the same company, and their assistance in preparing

measurement data for filters ere acknowledged.,C

. It is the author's pleasure to acknowledge inspiring discussions with hisI '

colleague~ S.H. then; Q.J:·Zhang, M.l;: Rena~lt and Dr. W. Kelll'rmann. Many"

. sugge~tions by S.H. Chen have helpecl the author to develop, improve and tes~ ..<0';;--..

ideas.

The ,ssis~nce'of S. Pan of McMaster l:niversity in running some of the

'problem;'in modelling Is acknowlWged.

• The fi~ancial assistance provided by the :-Iatural Sciences and Engineering

Research Council of Canada: through Grants A7239 and G1l35 as well as. a,postgrnduate scholarship': the Department of Electrical and Computer, Engineering

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through a Teaching Assistantship and the Ministry of Colleges and Universi ties

through an Ont/lrio Graduate Scholarship is gratefully acknowledged.

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.Thanks go to the Engineering Word Processing Centre for their expert

typing Ois manuscript.

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TABLE 0l1CONTENTS

ABSTRACT

ACKNOWLEDGEMENTSv

LI.STOFFIGURES

LIST OF TABLES

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CHAPTER 1

CHAPTER 2

INTRODUCTION

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MINIMAX AND l\OPTIMIZATION TE~HNIQJJ-E'S- NEW ADVANCES .. . /

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2.1 . Introduction

2.2 Minimax Optimization Techniques . ' .2.2.1 . Design Specifications and Error Functions2.2.2 Formulation of.the Minimax Optimization

Problem2.2.3 N~nlinear Programming Using Minimax

Optimization. 2.2.4 Review ofMinimax Algorithms

2.3 ei,Optimization Techniques,2.3,1, .Formulation of the Problem2.3.2 Review of e\ Algo~hmg2.3.3 Necessary Conditions for Optimality of el

Problems .2.3.4 Illustration oftl Approximation

. 2.4.. Efficient Gradient'Approximations .•2.4.1 Introduetory Remarks

. 2.4.2 Method ofPerturbation2.4.3 Brvyden Update

. 2.4.4 'Special Iterations ofPowell

2.5 Concluding Remarks

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'.. TABLE OF CONTENTS (continued)

PAGE

4.1 Introduction'

3.3 Lossless Two-Ports

~.1 Introduction

CHAPTER 3 SENSITIVITY ANALYSIS OF TWO-PORTS ANDCASCADED STRUCTURES - SIMPLEALGEBRAiC APPROACHES 29

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DESIGN OF MULTIPLEXING NETWORKS

4.2· Basic Components ofa Multiplexer Structure. 4.2.1 The Overall Configuration

4.2.2 Multi-Coupled Cavity Filters4.2.3 Waveguide Manifold4.2.4 Junctions4.2.5' Inp!1t-Output Transformers, Impedance Inverters

and Summarizing Tables

4.3' Multiplexer Optimization4.3:1 Formulation of the Problem4.3.2 The Overall Structure ofa Computer

Implementation4.3.3 Detailed Description of~ Implementation for

Response and Sensitivity Evaluation

3.4 Cascaded Structures3.4.1 Review ofConcepts3.4.2 Thevenin and Norton Equivalent Networks3.4.3 Branched Cascaded Networks3.4.4 . Various Frequency Responses and Sensitivity

Formulas3.4,5 An Interesting Result in Sensitivity Evaluation

ofBranched Cascaded Networks3.5 Concluding Remarks

3.2 . GeneralTwo-Ports3.2:1 Unterminated Two-ports3.2.2 Second-Order Sensitivities3.2.3 . Computational Considerations

. 3.2.4 Terminated Two-Ports3.2.5 S-Pa\"ameter Sensitivities

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TABLE OF CONTENTS (continued)

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FIGURE

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An example of multiple objectives in filter design.

Approximations usinge! and e2 optimizations. •

Block representation and two-port equivalent of a. circuitcharacterized by its'2dmittance matrix. .,

Thevenin and Norton equivalents at reference planes i andj.

The branched cascaded network under consideration.

A 3-portjunction.

Detail ofthe kth secti~nof a branched cascaded circuit.

Thevenin and Norton equivalents at reference planes i andjwhere reference plane j is in a branch. -.

The basic structure of an N-branched cascaded network.

The simplified structure of the branched cascaded network whenbranch output port t is of interest. .

Equivalent circuit of a contiguous band multiplexer.

Illustration of specifications for a 3-channel multiplexer...

Typical structures for longitudinirual-mode C~Vity filters.

Unterminated coupled-cavity filter illustrating the couplingcoefficients. . . .

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4.5. Five channel multiplexer, illustrating the flexibility in choice of .responses to be optimized and frequency bands of interest. . 86

. 4.6 Functional blocks of the computer package for multiplexersimulation, sensitivity analysis lind optimization, 87

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Modification of the filter equivalent matrix y to include inputand output ideal transformers. . .

Inpu~ admittance fOJ" a filter.terminated by conductance GL· .

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LIST OF FIGURES (continued)

FIGUR~ PAGE

4.9 Effect of an impedance inverter on Yin of Fig. 4.8. 93

4.10 Filter-ju'1ction combination. 94

4.11 Cascade combination ofa filter-junction and waveguide spacingforming a complete section. . 9&

'4.12 Multiplexer structure after reduction to a simple ~ascaded

network. 97

4.13 All the possible products ofadjacent sectiofl.matrices. 98

4.14 Simplified multiplexer·structure for the calculation ofcommonport renection coefficient. 100

4.15 . Simplified multiplexer structure for the calcuhition ofchanneloutput voltage. 101.

4.16 Responses of the 12-channel multiplexer at the start of theoptimization process. 108

4.17 Responses of the 12-channel multiplexer with optimizedparameters. liD

4.18 Responses of the 3-channel multiplexer at the starting point. 112

4.19 Respi,~ofthe 3-chaI\nel multiplexer at the solution. 113

4.20 Responses ofa nonideal16-channel multiplexer obtained fromthe optimalI2-channel'strucGure by growing one channel at a·time. 115

5.·1 Modelling ofan npn transistor. 122

5.2 Simple RC network. 124

5.3 Measured and modell~d responses of the 6th order filter beforeadjusting the screw. 138

5.4 Measured and modelled responses of the 6th order filter afteradjusting the screw. 139

5.5 Measured and modelled responses of the 8th order filter beforeadjusting the iris. 143

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LIST OF FIGURES (continued)

·5.6 Measured and modelled responses of the 8th order filter aneradjusting the iris.

5.7 Equivalent circuit ofcarrier-mounted FET.

5.8 Cross section ofn-FET structure.

5.9a Smith Chart display ofS-parameters in modelling of theNEC700. Measured and modelled &.!1 parameter.

5.9b Smith Chart display of8-parameters in modelling of theNEC700. Measured and modelled S12 parameter.

5,9c Smith Chart display of8-parameters in modelling of theNEC700. Measured and modelled S11 and &.!2 parameters.

5.10 Smith Chart display of8-parameter,s for device B1824-20C,before and after adjustment of parameters.

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5.11 The variation ofcoupling values in a 6th order filter as theposition of the screw which dominantly controls M12 changes.

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5.12 The/variation ofcoupling values in a 6th order filter as theposition ofthe.screw which dominantly controls M34 changes.

5.13 The variation ofcoupling values·in a 6th order filter as theposition of the screw which dominantly controls MS6 changes.

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LISTOFTABLES

TABLE PAGE

2.1 Approximation problem using e1 and e2. n,-,',

3.1 Sensitivities ofopen-circuit impedance matrixwithrespectto some possible network parameters. 35

3.2 Various frequency response expressio~s. 3!l

3.3 Various frequency responses and their sensitivities.' 59•

4.1 Transmission matrices for subnetworks in the multiplexerstructure., 80

4.2 First-order sensitivities of the transmission matricesin Table 4.1. 82

5.1 Results for the 6th order filter example. 137

5.2 Results for the 8th order filter example. 141

§3 Results for the NEC700 FEl' example. 148-5.4 Results for the GaAs FET B1824-20C example. 154"

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1INTRODUCTION

Ove~ thp. past 20 years, computer,aided design (C~D) techniques havo

developed" into an integral part of methods used for solving most ~ngineering

problems. [n the past decade, the astonishi;,g'cost reduction.in computer coinpon~nis

, and the availability of personal computers has generated further enthusiasm to use'

efficient and powerful CAD techniques, The use of highly interactivesoftwa,re

systems and the capabilit;"of hi~h resolution graphical displays has changed the", .

image of CAD techniques from a topic understandable only by.specialists to a

powerful tool serving every practicing engineer, .

Design of microwave filter~ using optimization methods is one of th~

earliest applicati0!ls for CAD'techniques in electrical en~neeri!,g, ·In 'recent y-ears,

software systems for modelling'and design of microwave circuits h~ve been developed

which are capable of handling most commonly used microwave devices. The applica,

tion of such general purpose, software systems to design problems requiring multiple,

objectives of costr\eduction, design' centering,to'lerance optimizatio~ and post­

production tuning, anci lVodelling problems with complex and uncertain, circuit. .~.-.'

equivalent topologies, necessitates the use of state-of-the-art optimization teehniques:

Unfortunately, while highly efficient optimization algorithms have been developed in

. c . ~. '. tthe last decade, the algorithms used in most microwave software systems afe th~ ones

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described by mathematicians 10-15 years ago. There.,e two major factors

~ontributingto'such a sizeable gap.

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... ~he .first fnctor is thnt the 'implementation;of~onlinearminimax and e1 '

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(;, algorithms:whose charncteristic fenti..u'es cno be e"pl,oited in many' engineering" . . 0,' f. .

problems and' have bee", the subject ~f most rocent advancemen'ts in optimization'" . . . '

techl.!:iques, is genernll1 compli~aied, This has led; f9; instance, tot~e 'use ofthe more1" . I (., .. •• _ '.

t, stra.ightf~rwnrd lenst squares .optilIltzntion with the ,limitation on iinenrity of

contiPl"ninti\n most rriicrownve ';"ftware.systems. 'It should be'mentioned that' a. ~ ~ - .

,,' . nonlinear pr~grammingpr~blem with n~nlinenr constraints can be easily formulated,,, - . ,. ,.

.~ ...tis a minimax problem.

, .Th~ second fnctor which has helped the' use 'of. rather old non·gradient

.'. l' _. •optimizntion tochniques (e.g" the rnndom' optimizntion in SUPER·COMPACT 1986

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. nnll TOUeHSTONE 1985) to continue, is -the difficulties relnted to sensitivity, .'c

annlysrll of mnny micrownve circuits as required by the ndvnnced grndient-bnsed, . " ." ( . ~

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optimizntion' methods. Deriving' e:",ilicit sensitivity, expressions is dimcult or, '

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impossible"in some micrownve problems'" On the, other hnnd,' ~sing numerical~ r .

difTe.r~ntintions to esti~nte' the grndient~';':t,every ite~aiion of an optim\z,ation

~. procedur.e becomes prohibitivelJi e~pensive when ntte'mptingto,solve Inrge problems.

" .Thisthesis nddresses itse.Jf to modelling'nnd design of micrownve circuits

usingrecent,minimnx and el optiIJIization techniques, A mnjor pnrt of the thesis)s',: j

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<:oncerned with a simpli.fied tnintment of sensitivity annlysis applicnble to' genernl, ,

t~o.ports, cascnded nn~ brnnChed'~~scnded structur~s tiue~:ly'en,countered.;n~_c

micrownve nren. The sensitivities nre'directly used," conj...nction with powerful '

minlmJx nnd t[ nlgorithIils which will'be described in 'some 'detail. We do notJ ..' •

presume to be nble to cnlculate exnc~ sensitivities for all misrownve structures.

Therefore, efficient grndientnpproximation techniques "(ill be described which enable

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us to use minimax and £1 algodthms in problems in which exact gradient evaluation

is not feasible,, '

The concellis described in design and modelling are applied to microwave

d'~vices such as multi-coupled cavity filters. waveguide mapifold type multiplexers"

and GoAs FET's" These devices are all of current siinifican~interest to resea'-rchers. "

and en'gineers due to their applicati<in in satellite communication systems,

Chapter 2 deals ";ith the use of minimax and el optimization techniques'in.' , - ... . . ....

, computer-aided design, Problem for'mulations for ,both types of optimizations are

!pyen, The'existing minimax'algorithms are reviewed briefly and the H~ld 'and

~adsen algorithm, <!ilild and Madse~ 19~1) ,is described'. For, nonlinear e1

olltiriiiiation, the'Hald and Madsen'algori'thm (Hald and Madsen 1985) [so reviewed

'a~d"the feal:ures of the el norm are, eltplained using necessary conditions for.optimality. ,For problems in which exact gradient evaluation is not feasible. a recent·

",method for ellicient gradientapproximatio·ns. as applied to both minimax andel'.' '.

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opti~izations, is'described, " '"

" In. Chipter q, simple algebraic approac~es are presented which reduce .the

networks described. by their nodal admittance matrices to equivalent unterminated

" , twocports wi~h ~im'~ltan~ous sensitivity analysis, The origin~lity of the appr!ach iies" . , .' .'.. . .. '" .',

in the r.ict that there, isno need to appeal to the adjoint network concept, Secol\d-order

sensitivities ahdcomputational efTort ~re' discussed, The original idea by Bandler., '.

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Rizk and Abdel~Malek(1978) in efficient simulati~n'and sensitivity ana:ly.sis ?f

caecaded' networks is,extended to the branched cascaded~tructu~eawith arbitrary

junctions, The individual componen~~,of the structure, apart from the' three-port.. "

'junctions, are two-Ports w,hich may have been deduced by the reduction ofcomplicated", .,

~etworks using the aforementioned algebraic approaches, A new proof for a rec~nt I

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result in sensitivity analysis of lossless recipr""al t\\(o-ports is presented and a ne:.v

and interesting ~esult in sensitivity evaluation of branehed'cascaded netW<>l'ks is

derived..

Chapter 4 covers the design of multiplexing networks using the minimax

optimization in detail. This is one of the largest nonlinear optimization problems ever -

demonstrated in microwave circuit design. Models for individual components of the

multiplexer with· nonideal effects such as dissipation, dispersion and j~nction

susceptance;' are pres'ented. The branched cascaded sensitivity analysis is effectively

used and 3-, 12- and 16-channel multiplexers are designed in· reasonable

computational times.

In Chapter 5, microwave device modelling techniques are considered. The

existing techniques in typical eommercially available software systems as well as

more advaneed techniques in modelling are reviewed. A new formulation for

modelling using the concept of multi-circuit·measurements is presented. 'We discuss'.,

the merits of this tech!'ique in obtaining unique. and self-consistent models., The

technique is applied to modelling of multi-coupled cavity filters and GaAs FET's. The.

applieation ofeflicient modelling techniquesiin developing. algorithms for post-

prod'uetion tuning is briefly discussed.. . ' .

We conclude i~ Chapter 6 with some suggestions for further research.

The' author contrib~te(f substantially to the following original

developmentS presentoid in this the~is:

(l)' .An integrated treatment of 'sensitivities for two-ports: cascaded and

branched cascaded structures using simple algebraic approaches.

. (2)- ,A new proof of';' result in.sensitivity analysis of reciprocal lossless

two-ports..