Question 8.53: Find the phasor gain K = VO/VS and input impedance ZIN of th......

The Analysis and Design of Linear Circuits [1399573]

Find the phasor gain $K=\mathrm{V}_{\mathrm{O}} / \mathrm{V}_{\mathrm{S}}$ and input impedance $Z_{\mathrm{IN}}$ of the circuit in Figure P8-53.

fig 8.53

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Use node-voltage analysis to solve the problem.

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Script File

clear all
syms Vs Va Vo
% Create the node-voltage equations
Eqn1 = (Va-Vs)/(-15e3j) + Va/20e3 + (Va-Vo)/(-25e3j);
Eqn2 = (Vo-Va)/(-25e3j) + (Vo-Vs)/10e3;
Soln = solve(Eqn1,Eqn2,Va,Vo);
Vo = Soln.Vo;
K = double(Vo/Vs)
MagK = abs(K)
PhaseK = angle(K)*180/pi
% Find the input current to compute the input impedance
Iin1 = (Vs-Vo)/10e3;
Va = Soln.Va;
Iin2 = (Vs-Va)/(-15e3j);
Iin = Iin1+Iin2;
Zin = double(simplify(Vs/Iin))
K =
847.2873e-003 - 28.1313e-003i
MagK =
847.7542e-003
PhaseK =
-1.9016e+000
Zin =
21.3235e+003 - 9.7059e+003i

\begin{aligned}& K=\mathrm{V}_{\mathrm{O}} / \mathrm{V}_{\mathrm{S}}=0.8473-j 0.0281=0.8478 \angle-1.9016^{\circ}.\\ \\& Z_{\mathrm{IN}}=21.32-j 9.706 ~\mathrm{k} \Omega.\end{aligned}

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