MMMM This page intentionally left blank Fastanalyticaltechniquesfor electricaland electroniccircuits Today,theonlymethodofcircuitanalysisknowntomostengineersandstudentsisnodalor loopanalysis.Althoughthisworkswellforobtainingnumericalsolutions,itisalmostuselessfor obtaininganalyticalsolutionsinallbutthesimplestcases. Inthisuniquebook,Vorpe´riandescribesremarkablealternativetechniquestosolve,almost byinspection, complicatedlinear circuitsin symbolic formand obtain meaningful analytical answersforanytransferfunctionorimpedance. Although not intended to replace traditional computer-based methods, these techniques provideengineerswithapowerfulsetoftoolsfortacklingcircuitdesignproblems.Theyalso have great value in enhancing students’ understanding of circuit operation. The numerous problems and worked examples in this book make it an ideal textbook for senior/graduate coursesorareferencebook. Thisbookwillshowyouhowto: • uselessalgebraanddomostofitdirectlyonthecircuitdiagram, • obtainmeaningfulanalyticalsolutionstocomplexcircuitswithreactiveelementsanddepend- ent sources by reducing them to a set of simple and purely resistive circuits which can be analyzedbyinspection, • analyzefeedbackamplifierseasilyusingthesimplestandmostnaturalformulation, • analyzePWMconverterseasilyusingthemodelofthePWMswitch. OriginallydevelopedandtaughtatinstitutionsandcompaniesaroundtheworldbyProfessor DavidMiddlebrookatCaltech,theextendedandnewtechniquesdescribedinthisbookarean indispensablesetoftoolsforlinearelectroniccircuitanalysisanddesign. Vatche´Vorpe´rianreceivedhisPhDinElectricalEngineeringin1984fromtheCaliforniaInstitute ofTechnologyandjoinedthefacultyofElectricalEngineeringatVirginiaTechinthesameyear. In1991hejoinedtheJetPropulsionLaboratorywhereheiscurrentlyaseniormemberofthe technicalstaff. Hehas publishedover35conferenceandjournalpapersin thefieldof power electronicsandhastaughtmanyprofessionaladvancementcoursestoindustry. MMMM Fast analytical techniques for electrical and electronic circuits Vatche´ Vorpe´rian JetPropulsionLaboratory CaliforniaInstituteofTechnology           The Pitt Building, Trumpington Street, Cambridge, United Kingdom    The Edinburgh Building, Cambridge CB2 2RU, UK 40 West 20th Street, New York, NY 10011-4211, USA 477 Williamstown Road, Port Melbourne, VIC 3207, Australia Ruiz de Alarcón 13, 28014 Madrid, Spain Dock House, The Waterfront, Cape Town 8001, South Africa http://www.cambridge.org ©Cambridge University Press 2004 First published in printed format 2002 ISBN 0-511-01637-9 eBook (netLibrary) ISBN 0-521-62442-8 hardback To my parents Edward and Azadouhi Vorpe´rian MMMM Contents Preface xi 1 Introduction 1 1.1 Fastanalyticalmethods 1 1.2 Inputimpedanceofabridgecircuit 2 1.3 Inputimpedanceofabridgecircuitwithadependentsource 4 1.4 Inputimpedanceofareactivebridgecircuitwithadependentsource 8 1.5 Review 11 Problems 11 References 14 2 Transfer functions 15 2.1 Definitionofatransferfunction 15 2.2 Thesixtypesoftransferfunctionsofanelectricalcircuit 17 2.3 Determinationofthepolesofanetwork 19 2.4 Determinationofthezerosofatransferfunction 24 2.5 Thecompleteresponse,stabilityandtransferfunctions 34 2.6 Magnitudeandphaseresponse 41 2.7 First-ordertransferfunctions 43 2.8 Second-ordertransferfunctions 48 2.9 Review 52 Problems 53 3 The extra elementtheorem 61 3.1 Introduction 61 3.2 Nulldoubleinjection 62 vii viii Contents 3.3 TheEETforimpedanceelements 74 3.4 TheEETfordependentsources 88 3.5 Review 98 Problems 99 References 106 4 TheN-extraelementtheorem 107 4.1 Introduction 107 4.2 The2-EETforimpedanceelements 108 4.3 The2-EETfordependentsources 130 4.4 TheNEET 137 4.5 AproofoftheNEET 147 4.6 Review 153 Problems 154 References 162 5 Electronicnegative feedback 163 5.1 Introduction 163 5.2 TheEETfordependentsourcesandformulationofelectronicfeedback 164 5.2.1 Gainanalysis 164 5.2.2 Driving-pointanalysis 170 5.2.3 Loopgain 175 5.3 Doesthiscircuithavefeedbackornot?Thisisnotthequestion 179 5.4 Gainanalysisoffeedbackamplifiers 180 5.5 Driving-pointanalysisoffeedbackamplifiers 195 5.5.1 Inputimpedanceforcurrentmixing 196 5.5.2 Outputimpedanceforvoltagesensing 200 5.5.3 Inputadmittanceforvoltagemixing 204 5.5.4 Outputadmittanceforcurrentsensing 209 5.6 Loopgain:amoredetailedlook 213 5.7 Stability 218 5.8 Phaseandgainmargins 226 5.9 Review 233 Problems 234 References 251