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Transistor Amplifier Circuit

Model a transistor amplifier circuit that dispatches the voltage in a nonlinear fashion.

The input voltage varies sinusoidally. The circuit contains a transistor that modifies the voltage in a nonlinear way:
Wolfram Language code: ve[t_] := (4 / 10) Sin[200 Pi t]; v23[t_] = β (Exp[(v2[t] - v3[t]) / .026] - 1);
Use Ohm's law and Kirchhoff's current law to determine the governing equations for each node:
Wolfram Language code: node1 = c1 (v2'[t] - v1'[t]) == v1[t] / r0 - ve[t] / r0; node2 = c1(v1'[t] - v2'[t]) == (1 - α)v23[t] + v2 [t] / r1 + v2[t] / r2 - vb / r2; node3 = c2 v3'[t] == v23[t] - v3[t] / r3; node4 = c3(v4'[t] - v5'[t]) == vb / r4 - v4[t] / r4 - α v23[t]; node5 = c3(v4'[t] - v5'[t]) == v5[t] / r5; ics = {v1[0] == 0, v2[0] == vb / 2, v3[0] == vb / 2, v4[0] == vb, v5[0] == 0};
Specify the parameters associated with the circuit:
Wolfram Language code: params = {vb -> 6, r0 -> 1000, r1 -> 9000, r2 -> 9000, r3 -> 9000, r4 -> 9000, r5 -> 9000, α -> 99 / 100, β -> 10 ^ -6, c1 -> 10 ^ -6, c2 -> 2 10 ^ -6, c3 -> 3 10 ^ -6};
Solve and visualize the system:
Wolfram Language code: transistorSol = NDSolve[{node1, node2, node3, node4, node5, ics} /. params, {v1, v2, v3, v4, v5}, {t, 0, 0.2}, Method -> {"EquationSimplification" -> "Residual"}, MaxSteps -> 100000] ;
Wolfram Language code: Plot[Evaluate[{v3[t], v4[t]} /. transistorSol], {t, 0, 0.2}, PlotRange -> All, ImageSize -> 400, PlotLegends -> {Style["Node 3", 14], Style["Node 4", 14]}, Frame -> True, FrameLabel -> {Style["Time", 18], Style["Voltage (V)", 18]}]