Transcription of Lecture 7 Circuit analysis via Laplace transform
{{id}} {{{paragraph}}}
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› ...
Domain:
Source:
Link to this page:
Please notify us if you found a problem with this document:
{{id}} {{{paragraph}}}