Transcription of Lecture 7 Circuit analysis via Laplace transform
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Lecture 7 Circuit analysis via Laplace transform
S. BoydEE102 Lecture7 CircuitanalysisviaLaplacetransform analysisof generalLRCcircuits impedanceand admittancedescriptions naturaland forcedresponse circuitanalysiswithimpedances naturalfrequenciesand stability7{1 CircuitanalysisexamplePSfragreplacements iuyLRinitialcurrent:i(0)KCL, KVL,and branchrelationsyield: u+Li0+y= 0,y=Ritake Laplacetransforms to get U+L(sI i(0)) +Y= 0; Y=RIsolveforYto getY=U+Li(0)1 +sL=R=11 +sL=RU+L1 +sL=Ri(0)Circuitanalysisvia Laplacetransform7{2in the timedomain:y(t) =1 TZt0e =Tu(t )d +Ri(0)e t=TwhereT=L=Rtwo termsiny(orY): rst termcorrespondsto solutionwithzeroinitialcondition rst termis convolutionof sourcewitha function secondtermcorrespondsto solutionwithzerosourcewe'll see theseare generalproperties.}}
therelationV(s)=Z(s)I(s)iscalledanimpedance description ofthe device † Z iscalledthe(s-domain)impedanceofthedevice † inthetimedomain,v andi arerelatedbyconvolution: v=z⁄i similarly,I(s)=Y(s)V(s)iscalledanadmittance description (Y =1=Z) Circuit analysis via …
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