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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..Circuitanalysisvia Laplacetransform7{3 Analysisof generalLRCcircuitsconsidera circuitwithnnodes andbbranches,containing independentsources linear elements(resistors, op-amps.)}}}

Thevenin,Nortonequivalents † nodalanalysis Circuit analysis via Laplace transform 7{19. example: PSfragreplacements Iin Vin 3› ...

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