Question

A common emitter amplifier has a voltage gain of 50, an input impedance of $\text{100 }\!\!\Omega\!\!\text{ }$ and an output impedance of $\text{200 }\!\!\Omega\!\!\text{ }$. The power gain of the amplifier is:
A. 100
B. 500
C. 1000
D. 1250

Answer 1

Hint: We must know that power gain of an amplifier is given as the ratio of output power to the input power. Also, power is given as the product of voltage and current. For a common emitter configuration, input will be through the base and output will be through the collector. We will also need ohm’s law to find the current gain.
Formula used:
$\begin{align}
  & \text{Power Gain}=\dfrac{\text{Output Power}}{\text{Input Power}} \\
 & P=VI \\
 & I=\dfrac{V}{R} \\
\end{align}$

Complete answer:
Let us consider the voltage of the input as $V$ .
So, it is given that the voltage gain is 50. By voltage gain, we mean that it is the ratio of output voltage to the input voltage.
Now, to find the current gain, we will find the resistance gain and divide it with the voltage gain.

So, to find the resistance gain, the input impedance is given as $\text{100 }\!\!\Omega\!\!\text{ }$ and the output impedance is given as $\text{200 }\!\!\Omega\!\!\text{ }$.
Then, the resistance gain will be,
$\text{R=}\dfrac{\text{200 }\!\!\Omega\!\!\text{ }}{100\Omega }=2$
Now, we will find the current gain using ohm’s law. i.e.
$I=\dfrac{V}{R}$
Voltage gain is given as 50 and resistance gain is 2.
$\Rightarrow I=\dfrac{V}{R}=\dfrac{50}{2}=25$
Therefore, current gain is found to be 25.
Now, the power gain of the amplifier is given as,
$\text{Power Gain}=\dfrac{\text{Output Power}}{\text{Input Power}}$
But, we know $P=VI$.
Therefore,
\[\begin{align}
  & \text{Power Gain = Voltage gain }\times \text{ Current Gain} \\
 & \text{Power Gain }=\left( \dfrac{{{V}_{out}}}{{{V}_{in}}} \right)\times \left( \dfrac{{{I}_{out}}}{{{I}_{in}}} \right) \\
 & \text{Power Gain }=50\times 25=1250 \\
\end{align}\]
Hence, the power gain of the amplifier is 1250.

So, the correct answer is “Option D”.

Note:
A Common Emitter Amplifier is mainly used because of the advantage of moderate current and voltage gain. A Common Emitter Amplifier is also used in frequency generation circuits in order to increase the strength of the input signal. In fans, motors and time circuits it is used to increase the speed.