Question

Consider the circuit shown in the figure below:

\(\text{The amplifier has common emitter input resistance equal to }r_\pi\text{ and current gain }'\beta' \text{ of the output resistance }R_{\text{out }}\text{ is equal to}\)
ouw t

• A. $R_L$
• B. $R_L||\left(\frac{r_{\pi }}{\beta +1}\right)$
• C. ${\left(\frac{1}{R_L}||\frac{1}{r_{\pi }}\right)}^{-1}$
• D. $R_L||r_{\pi }$

Answer 1

The correct option is B $R_L||\left(\frac{r_{\pi }}{\beta +1}\right)$


$I_a=\frac{V_o}{r_{\pi }}+\frac{V_o}{R_L}-\beta I_b$

$\text{and}{I}_b=-\frac{V_o}{r_{\pi }}$

$\therefore I_a=\frac{V_o}{r_{\pi }}+\frac{V_o}{R_L}+\frac{\beta V_o}{r_{\pi }}$

$\therefore R_s=\frac{V_o}{I_a}=R_L||\frac{R_{\pi }}{(\beta +1)}$