Determine \(g_m\) and \(r_d\) from the specification sheets.
\(\boxed{g_m = g_{fs} = y_{fs}}\)
\(\boxed{r_d = \frac{1}{g_{os}} = \frac{1}{y_{os}}}\)
If \(g_{fs}\) or \(y_{fs}\) is not available, determine \(g_m\) using the values of \(V_{GS}\) and \(I_D\) from the DC biasing arrangement.
\(\boxed{g_m = \frac{2I_{DSS}}{\left|V_P\right|}\left(1 - \frac{V_{GS}}{V_P}\right) = \frac{2I_{DSS}}{\left|V_P\right|} \sqrt{\frac{I_D}{I_{DSS}}}}\)
Once the levels of \(g_m\) and \(r_d\) are determined, the AC equivalent model can be substituted between the appropriate terminals. Set all capacitors and DC sources to short-circuit equivalent.
Input impedance \(Z_i\)
\(\boxed{Z_i = R_1 \parallel R_2}\)
Output impedance \(Z_o\) (set \(V_i = 0\,V\))
\(\boxed{Z_o = r_d \parallel R_D}\)
Voltage gain \(A_v\)
\(\displaystyle V_o = -g_m V_{gs} \left(r_d \parallel R_D\right)\) \(\displaystyle V_{gs} = V_i\) \(\displaystyle V_o = -g_m V_i \left(r_d \parallel R_D\right)\)
\(\boxed{A_v = \frac{V_o}{V_i} = -g_m\left(r_d \parallel R_D\right)}\)
Note that the equations for \(Z_o\) and \(A_v\) are the same as obtained for the fixed-bias and self-bias (with bypassed \(R_S\)) configurations. The only difference is the equation for \(Z_i\), which is now sensitive to the parallel combination of \(R_1\) and \(R_2\).