用微分方程求这个电路的传递函数

Question

如题所述

Answer 1

由拉普拉斯变换，
对R:Z(s)=R I1(s)=U(s)/R
对L:I2(s)=U(s)/sL+i(0-)/s Z(s)=sL
对C:Z(s)=1/sC I3(s)=sCU(s)-Cu(0-)
令初始条件为零，
I1(s)+I2(s)+I3(s)=I(s)
U(s)/R+U(s)/sL+sCU(s)=I(s)
H(s)=U(s)/I(s)=sLR/(sL+R+s²RLC)