Question

In a common emitter (CE) amplifier having a voltage gain G, the transducer used has transconductance 0.03 mho and current gain 25. If the above transistor is replaced with another one with transconductance 2.02 mho and current gain 20, the voltage gain will be.
A. $\dfrac{2}{3}$ G
B. 1.5 G
C. $\dfrac{1}{3}$ G
D. $\dfrac{5}{4}$G

Answer 1

In this question we have been asked to calculate the voltage gain for the transistor under the given conditions. We have been given the transconductance and current gain of the transistor. Therefore, we shall be using the formula for voltage gain which is given as collector voltage or output voltage over the base voltage or input voltage. Therefore, we shall calculate the output voltage from given data and thus calculate the voltage gain.

Formula used: ${{V}_{g}}=\dfrac{{{V}_{c}}}{{{V}_{b}}}$
Where,
${{V}_{g}}$ is the voltage gain
${{V}_{c}}$is the output voltage
${{V}_{b}}$ is the input voltage

Complete step by step answer:
We know that for a transistor the voltage gain is given by,
${{V}_{g}}=\dfrac{{{V}_{c}}}{{{V}_{b}}}$
Now, from ohms law we can say that
${{V}_{c}}={{I}_{c}}{{R}_{c}}$
Therefore, we can say,
${{V}_{g}}=\dfrac{{{I}_{c}}{{R}_{c}}}{{{V}_{b}}}$ ……………………. (1)
Now, we know that for transconductance (g) of a transistor,
$g=\dfrac{{{I}_{c}}}{{{V}_{b}}}$
Substituting above value in equation (1)
We get,
${{V}_{g}}=g{{R}_{c}}$
Now, for the first transistor we have been given that voltage gain is G
We can say that
$G={{g}_{1}}{{R}_{c}}$ …………… (2)
Similarly, for second transistor let the voltage gain be ${{G}_{2}}$
Therefore, we can say that,
${{G}_{2}}={{g}_{2}}{{R}_{c}}$ ………………. (3)
From (2) and (3)
We can say that,
$\dfrac{G}{{{G}_{2}}}=\dfrac{{{g}_{1}}{{R}_{c}}}{{{g}_{2}}{{R}_{c}}}$
On solving,
$\dfrac{G}{{{G}_{2}}}=\dfrac{{{g}_{1}}}{{{g}_{2}}}$
After substituting the given values of transconductance
We get,
${{G}_{2}}=\dfrac{{{g}_{2}}}{{{g}_{1}}}G$
Therefore,
${{G}_{2}}=\dfrac{0.02}{0.03}G$
On solving,
${{G}_{2}}=\dfrac{2}{3}G$

So, the correct answer is “Option A”.

Note: Transconductance also referred to as mutual conductance is an electrical characteristic which relates the current through output of device to the voltage across the input of device. The conductance is usually the reciprocal of resistance. Transconductance is given as the ratio of current change at output to voltage change at input port.