Fast analytical techniques for electrical and electronic circuits

492 Pages·2004·12.86 MB·English

by  Vatche Vorperian

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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.
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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
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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