Question 8.54: Find the phasor gain K = VO/VS and input impedance ZIN of th......
Find the phasor gain K=\mathrm{V}_{\mathrm{O}} / \mathrm{V}_{\mathrm{S}} and input impedance Z_{\mathrm{IN}} of the circuit in Figure P8-54.
Use node-voltage analysis to solve the problem.
Script File
clear all
syms Vs Va Vo
Eqn1 = (Va-Vs)/100 + Va/(-100j) + (Va-Vo)/100j;
Eqn2 = (Vo-Va)/100j + Vo/100;
Soln = solve(Eqn1,Eqn2,Va,Vo);
Vo = Soln.Vo;
K = double(simplify(Vo/Vs))
MagK = abs(K)
PhaseK = angle(K)*180/pi
% Compute the input current to find Zin
Va = Soln.Va;
Iin = (Vs-Va)/100;
Zin = double(simplify(Vs/Iin))
K =
200.0000e-003 -400.0000e-003i
MagK =
447.2136e-003
PhaseK =
-63.4349e+000
Zin =
200.0000e+000 -100.0000e+000i
\begin{aligned}& K=\mathbf{V}_{\mathrm{O}} / \mathbf{V}_{\mathrm{S}}=0.2-j 0.4=0.4472 ~\angle-63.43^{\circ} .\\ \\& Z_{\mathrm{IN}}=200-j 100~ \Omega .\end{aligned}