13. The Laplace Transform in Circuit AnalysisECE209-12-1 13. The Laplace Transform in Circuit Analysis 13.1 Circuit Elements in the s Domain The Laplace Transform of V(t) and I(t) are {}() ()Vs vtL=, {}() ()Is itL= a. A Resistor in the s Domain Ohm’s Law () ()vt Rit= -+ v(t)baR The Laplace Transform is () ()Vs RIs=, ()()VsIsR= R+a-bV(s) b. An Inductor in the s Domain ()()di tvt Ldt= L1 2-+av(t)b The Laplace Transform is 0() () (0) ()Vs LsIs i LsIs LI−=−=− 00()1() ()Vs LI IIs VssL sL s+==+ sL1 2V(s)+ba- b+sL1 2aV(s) - i(t) I(s) i(t) I0 I(s) LI0 I(s) I0/sECE209-12-2 b. An Capacitor in the s Domain ()()dv tit Cdt= av(t)Cb+- The Laplace Transform is 0() () (0) ()Is CsVs v CsVs CV−=−=− 00()1() ()Is CV VVs IssC sC s+==+ b+1/sCV(s) -a 1/sC+ -aV(s)bi(t) V0 I(s) I(s) CV0 V0/sECE209-12-3 13.2 Circuit Analysis in the s Domain Ohm’s law in the s domain () ()Vs ZIs= where Z is s-domain impedance of the element. A resistor has an impedance of R ohms An inductor has an impedance of sL ohms An capacitor has an impedance of 1/sC ohms The rules for combining impedance in the domain are the same s for frequency-domain circuits. Kirchhoff’s laws apply to s-domain current and voltage. Algebraic ( ) 0Is=∑ Algebraic ( )
View Full Document
Unlocking...