Question

Output characteristics of an $n-p-n$ transistor in $CE$ configuration is shown in the figure. Determine:
(i) dynamic output resistance
(ii) dc current gain and
(iii) ac current gain at an operating point $V_{CE}=10V$, when $I_B=30\mu A$.

Answer 1

1. Dynamic output resistance
   $r_o=\frac{\Delta V_{CE}}{\Delta I_C}$
   $I_C=$ constant
   $=\frac{(12-8)V}{(4.8-4.6)\left(mA\right)}=\frac{4V}{0.2mA}$
   $=\frac{4\times {10}^3}{2\times {10}^{-1}}$
   $=2\times {10}^4$
   $=20k\omega$
   
2. dc current gain
   $\beta =\frac{I_C}{I_B}$
   $\beta =\frac{3.5mA}{30\mu A}$
   $=\frac{3.5\times {10}^3}{30}=116.67$
   
3. ac current gain
   ${\beta }_{a.c}={\left(\frac{\Delta I_C}{\Delta I_B}\right)}_{V_{CE}=constant}$
   $=\frac{(5.7-3.5)mA}{(40-30)\mu A}$
   $=\frac{2.2mA}{10\mu A}=\frac{2.2}{10}\times {10}^3$
   $=\frac{22}{100}\times {10}^3$
   $=220$