# Electrical – Maximum voltage gain

bjtcircuit analysisgain

Consider the following circuit:

It is required to calculate the small signal voltage gain (i.e \$\frac{v_o}{v_i}\$) based on \$R_s, R_c, I_c, V_A\$ and β.

So I draw the small signal model as below:

simulate this circuit – Schematic created using CircuitLab

So, for \$A_v\$ we have:

\$v_o = g_m v_{be} (r_o || R_c)\$

\$v_{be} = v_i \frac{rπ}{(rπ + Rs)}\$

so:

\$A_v = \frac{v_o}{v_i} = g_m \frac{r_π}{R_s + r_π} (r_o || R_c)\$

I think everything is okay so far! Am I right?

In the next part of question, I have been asked to find the value of \$I_c\$
which we have maximum \$A_v\$ for it. I have been stuck in this point.

Would you please give me some hints?