Question

In the figure, an $n-p-n$ transistor is shown in common emitter configuration. If $V_{B B}=10\, V , V_{C C}=20\, V , R_{E}=2 \,k \,\Omega, V_{i}=2 \sin \omega\, t$ in milli-volts, then find the maximum voltage gain of the transistor. Assume that $\beta$ is very large.

Answer 1

$A_{V}=\text { Voltage gain }=\frac{\beta R_{C}}{R_{\text {in }}+(\beta+1) R_{E}} \cong \frac{R_{C}}{R_{E}}=\frac{R_{C}}{2}$
For proper biasing, $V_{C}>V_{B}$
$\Rightarrow 20-\frac{2 A_{V}}{1000}>10+\frac{2}{1000} $
$\Rightarrow \frac{2 A_{V}}{1000}< 10-\frac{2}{1000} $
$\Rightarrow 2 A_{V}< 1000$
$\Rightarrow A_{V}< 5000 $
$\Rightarrow A_{V \max }=5000$