I was studying negative feedback in voltage amplifiers. I found this on Wikipedia for calculating input resistance as shown below.
Following the similar method, I tried to calculate the output resistance with feedback \$Z_{of}\$.
Connected a voltage source \$V_o\$ which supplies a current \$I_o\$. Applying Kirchoff's voltage law to the output loop, we have
\$V_o = I_oZ_o + A_v.V_{in}\$
For negative feedback, \$V_{in} = V_x - V_f\$ and \$V_f = \beta V_o\$. Therefore
\$V_o = I_oZ_o + A_v.(V_x - \beta V_o)\$
\$V_o = I_oZ_o + A_v.V_x - A_v.\beta V_o\$
\$V_o + A_v.\beta V_o = I_oZ_o + A_v.V_x\$
\$V_o(1 + A_v.\beta) = I_oZ_o + A_v.V_x\$
Dividing both the sides by \$I_o\$, we get
\$Z_{of} = \frac{Z_o}{(1 + A_v.\beta)} + \frac{(A_v.V_x)}{(I_o)(1 + A_v.\beta)}\$
The above expression is what I am getting. But the answer is \$Z_{of} = \frac{Z_o}{(1 + A_v.\beta)}\$. I am getting an extra term \$\frac{(A_v.V_x)}{(I_o)(1 + A_v.\beta)}\$.
What is the mistake in my calculation? Please help.