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 Circuits133Element 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 Circuits134Element 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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