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In a common emitter (CE) amplifier having a voltage gain $G$, the transistor used has transconductance 0.03 mho and current gain 25. If the above transistor is replaced with another one with transconductance $0.02 \mathrm{mho}$ and current gain 20 , the voltage gain will
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Verified Answer
The correct answer is:
$\frac{2}{3} G$
$\mathrm{As} A_v=\beta \frac{R_L}{R_j} \quad\left[\because g_m=\frac{\Delta_C}{\Delta V_B}=\frac{\Delta_C}{\Delta /_B R_j}\right]$
or
$$
G=\left(\frac{\beta}{R_i}\right) R_L \quad\left[\because g_m=\frac{\beta}{R_i}\right]
$$
$$
\begin{array}{ll}
\Rightarrow & G=g_m R_i \\
\Rightarrow & G \propto g_m
\end{array}
$$
$\begin{aligned} & \therefore \quad \frac{G_2}{G_1}=\frac{g_{m_1}}{g_{m_2}} \\ & \Rightarrow \quad G_2=\frac{0.02}{0.03} \times G \\ & \therefore \text { Voltage gain } G_2=\frac{2}{3} G\end{aligned}$
or
$$
G=\left(\frac{\beta}{R_i}\right) R_L \quad\left[\because g_m=\frac{\beta}{R_i}\right]
$$
$$
\begin{array}{ll}
\Rightarrow & G=g_m R_i \\
\Rightarrow & G \propto g_m
\end{array}
$$
$\begin{aligned} & \therefore \quad \frac{G_2}{G_1}=\frac{g_{m_1}}{g_{m_2}} \\ & \Rightarrow \quad G_2=\frac{0.02}{0.03} \times G \\ & \therefore \text { Voltage gain } G_2=\frac{2}{3} G\end{aligned}$
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