# 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. 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