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.
\(\boxed{g_m = 2k\left(V_{GS} - V_{GS(Th)}\right)}\)
\(\boxed{k = \frac{I_{D(on)}}{\left( V_{GS(on)} - V_{GS(Th)} \right) ^ 2}}\)
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 \(Z_o\)
\(\boxed{Z_o = r_d \parallel R_D}\)
Voltage gain \(A_v\)
\(\displaystyle V_{gs} = V_i\)
\(\displaystyle V_o = -g_m V_{gs}\left(r_d \parallel R_D\right)\)
\(\displaystyle V_o = -g_m V_i\left(r_d \parallel R_D\right)\)
\(\boxed{A_v = \frac{V_o}{V_i} = -g_m\left(r_d \parallel R_D\right)}\)
The negative sign for \(A_v\) reveals that \(V_o\) and \(V_i\) are out of phase by \(180^\circ\).