Output resistance of CE amplifier small signal model
Well, we are trying to analyze the following circuit:







simulate this circuit &ndash; Schematic created using CircuitLab

Using Mathematica, I wrote the following code:

In[1]:=FullSimplify[
 Solve[{Ix == I1 + I2, I1 == Ix + I0, I2 == Iy + I6, 
   0 == Iy + I0 + I5, I6 == I3 + I4, I5 == I3 + I4, I1 == (Vx)/R1, 
   I2 == (Vx - V1)/R2, I3 == (V1)/R3, I4 == (V1)/R4}, {Ix, I0, I1, I2,
    I3, I4, I5, I6, V1}]]

Out[1]={{Ix -&gt; (Iy R1 R3 R4 + (R1 + R2) R3 Vx + (R1 + R2 + R3) R4 Vx)/(
   R1 R2 R3 + R1 (R2 + R3) R4), 
  I0 -&gt; -((Iy R3 R4 + (R3 + R4) Vx)/(R3 R4 + R2 (R3 + R4))), 
  I1 -&gt; Vx/R1, I2 -&gt; (Iy R3 R4 + (R3 + R4) Vx)/(R3 R4 + R2 (R3 + R4)),
   I3 -&gt; (R4 (-Iy R2 + Vx))/(R3 R4 + R2 (R3 + R4)), 
  I4 -&gt; (R3 (-Iy R2 + Vx))/(R3 R4 + R2 (R3 + R4)), 
  I5 -&gt; -(((R3 + R4) (Iy R2 - Vx))/(R3 R4 + R2 (R3 + R4))), 
  I6 -&gt; -(((R3 + R4) (Iy R2 - Vx))/(R3 R4 + R2 (R3 + R4))), 
  V1 -&gt; (R3 R4 (-Iy R2 + Vx))/(R3 R4 + R2 (R3 + R4))}}