The JFET equivalent of BJT emitter-follower configuration.
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 \(Z_i\)
\(\boxed{Z_i = R_G}\)
Output impedance \(Z_o\) (set \(V_i = 0\,V\))
\(V_{gs} = -V_o\)
Applying Kirchhoff’s current law at node \(S\).
\(\displaystyle V_{gs} = -V_o\)
\(\displaystyle g_m V_{gs} + I_o = I_{r_d} + I_{R_S}\)
\(\displaystyle -g_m V_o + I_o = \frac{V_o}{r_d} + \frac{V_o}{R_S}\)
\(\displaystyle I_o = g_m V_o + \frac{V_o}{r_d} + \frac{V_o}{R_S}\)
\(\displaystyle I_o = V_o \left(g_m + \frac{1}{r_d} + \frac{1}{R_S}\right)\)
\(\boxed{Z_o = \frac{V_o}{I_o} = \frac{1}{\displaystyle g_m + \frac{1}{r_d} + \frac{1}{R_S}} = r_d \parallel R_S \parallel \left(\frac{1}{g_m}\right)}\)
Voltage gain \(A_v\)
Applying Kirchhoff’s voltage law
\(\displaystyle -V_i + V_{gs} + V_o = 0\)
\(\displaystyle V_{gs} = V_i - V_o\)
\(\displaystyle V_o = g_m V_{gs}\left(r_d \parallel R_S\right)\)
\(\displaystyle V_o = g_m\left(V_i - V_o\right)\left(r_d \parallel R_S\right)\)
\(\displaystyle \frac{V_o}{r_d \parallel R_S} = g_m\left(V_i - V_o\right)\)
\(\displaystyle \frac{V_o}{r_d \parallel R_S} + g_m V_o = g_m V_i\)
\(\displaystyle V_o \left(\frac{1}{r_d \parallel R_S} + g_m\right) = g_m V_i\)
\(\displaystyle A_v = \frac{V_o}{V_i} = \frac{g_m}{\displaystyle \frac{1}{r_d \parallel R_S} + g_m}\)
\(\boxed{A_v = \frac{V_o}{V_i} = \frac{g_m}{\displaystyle \frac{1}{r_d} + \frac{1}{R_S} + g_m} = g_m\left[r_d \parallel R_S \parallel \left(\frac{1}{g_m}\right)\right]}\)
Since \(A_v\) is a positive quantity, \(V_o\) and \(V_i\) are in phase for the JFET source-follower configuration.