question_answer

Output characteristics of an n-p-n transistor in CE configuration is shown in the below figure. Determine :

(i) DC current gain.

(ii) Dynamic output resistance.

(iii) AC current gain at an operating point,

\[{{V}_{CE}}=10V,\,\,when\,\,{{I}_{B}}=30\mu A.\]

 

Answer:

 (i) According to the question, \[{{I}_{B}}=30\mu A,\] \[{{V}_{CE}}=10\,V\] and \[{{I}_{C}}=3.5mA\] DC current gain             \[{{\beta }_{DC}}=\frac{{{I}_{C}}}{{{I}_{B}}}=\frac{3.5\,mA}{0.030\,mA}=117\] (ii) Dynamic output resistance is given by             \[{{r}_{0}}=\left( \frac{\Delta \,{{V}_{CE}}}{\Delta {{I}_{c}}} \right)\] For \[{{I}_{B}}=30\mu A,\] \[\Delta {{V}_{CE}}=12-8=4\,V,\] \[\Delta {{I}_{C}}=3.6-3.4=0.2\,mA.\] \[\therefore \]      \[{{r}_{0}}=\frac{4\,V}{0.2\,mA}=\frac{4}{0.2\times {{10}^{-3}}}=2\times {{10}^{4}}\Omega \] (iii) AC current gain, \[{{\beta }_{AC}}={{\left( \frac{\Delta {{I}_{C}}}{\Delta {{I}_{B}}} \right)}_{{{V}_{CE}}}}\] At \[{{V}_{CE}}=10\,V,\] \[\Delta {{I}_{C}}=(3.5-2.5)\,mA=1mA\] and \[\Delta {{I}_{B}}=30\mu A-20\mu A=10\mu A\] \[\therefore \] \[{{\beta }_{AC}}=\frac{1\,mA}{10\,\mu A}=100\]