question_answer

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 onewith transconductance 0.02 mho and current gain 20, the voltage gain will

A)  \[\frac{2}{3}G\]

B)  \[1.5\,G\]

C)  \[\frac{1}{3}G\]

D)  \[\frac{5}{4}G\]

Correct Answer: A

Solution :

 As \[{{A}_{v}}=\beta \frac{{{R}_{L}}}{{{R}_{i}}}\] or \[G=\left( \frac{\beta }{{{R}_{i}}} \right){{R}_{L}}\]  \[\left[ \because \,{{g}_{m}}=\frac{\beta }{{{R}_{i}}} \right]\] \[\Rightarrow \] \[G={{g}_{m}}{{R}_{L}}\] \[\Rightarrow \] \[G\propto {{g}_{m}}\] \[\therefore \] \[\frac{{{G}_{2}}}{{{G}_{1}}}=\frac{{{g}_{{{m}_{1}}}}}{{{g}_{{{m}_{2}}}}}\] \[\Rightarrow \] \[{{G}_{2}}=\frac{0.02}{0.03}\times G\] \[\therefore \] Voltage gain \[{{G}_{2}}=\frac{2}{3}G\]