Transcription of s-Domain Circuit Analysis
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s-Domain Circuit Analysis
MAE140 Linear Circuits132s- domain Circuit AnalysisOperate directly in the s- domain with capacitors,inductors and resistorsKey feature linearity is preservedCcts described by ODEs and their ICsOrder equals number of C plus number of LElement-by-element and source transformationNodal or mesh Analysis for s- domain cct variablesSolution via Inverse Laplace TransformWhy?Easier than ODEsEasier to perform engineering designFrequency response ideas - filteringMAE140 Linear Circuits133 Element TransformationsVoltage sourceTime domainv(t) =vS(t)i(t) = depends on cctTransform domainV(s) =VS(s)=L(vS(t))I(s) = L(i(t)) depends on cctCurrent sourceI(s) =L(iS(t))V(s) = L(v(t)) depends on cct+_i(t)vSiSv(t)MAE140 Linear Circuits134 Element Transformations contdControlled sourcesShort cct, open cct, OpAmp relationsSources and active devices behave identicallyConstraints expressed between transformed variablesThis all hinges on uniqueness of Laplace Transforms andlinearity)()()()()()()()()()()()()()( )()(2121212121212121sgVsItgvtisrIsVtritv sIsItitisVsVtvtv=!
MAE140 Linear Circuits 132 s-Domain Circuit Analysis Operate directly in the s-domain with capacitors, inductors and resistors Key feature – linearity – is preserved Ccts described by ODEs and their ICs
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