OUTPUT Impedance

I wish to find the output impedance of the circuit in the attachment. I have drawn the AC Equivalent of the circuit but I don't know how to come out with the Formula for the Output Impedance.

I would appreciate if someone can help me.

2 Answers

The output impedance is, by definition, the impedance seen at the output terminals of the AC model. Thus you only have to apply the definition of impedance: apply an independent voltage source at the output (with arbitrary voltage $V_s$) and determine, using usual circuit analysis techniques, the current $I_s$ that the voltage source delivers into the terminals (which will depend on $V_s$ in a linear fashion, since the AC model is linear).

Afterwards compute the ratio $\frac{V_s}{I_s}$ and that is your $Z_{out}$:

$Z_{out} = \dfrac{V_s}{I_s}$

If you did your computations correctly the $V_s$ dependency of the numerator and denominator should cancel out, giving an expression involving only the AC circuits parameters.

I have done the analysis and I have an equation as you suggested. Please kind check if this is correct.

• I would appreciate if I can some feedback – Sidney S. Ebot Jan 21 '15 at 21:56
• Your work is correct but for me it is too long. Looking at it you can see right away Rout = (R2+Rpi)|| (1/gm). – anhnha Mar 13 '18 at 8:00