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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.enter image description here

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2 Answers 2

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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).

enter image description here

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.

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

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  • \$\begingroup\$ I would appreciate if I can some feedback \$\endgroup\$ Commented Jan 21, 2015 at 21:56
  • \$\begingroup\$ Your work is correct but for me it is too long. Looking at it you can see right away Rout = (R2+Rpi)|| (1/gm). \$\endgroup\$
    – emnha
    Commented Mar 13, 2018 at 8:00

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