Question

What is the voltage gain in the common emitter amplifier where input resistance is $3\,\Omega$ and load resistance is $24\,\Omega$ and current gain is $\beta = 6$ ?

Answer 1

An amplifier is a device that increases the amplitude of the voltage or current inputs. The common emitter configuration is represented as

A common emitter configuration has the emitter common to both input and output circuits. The input signal is collected at the base and output received from the collector. It has both current and voltage gain. This configuration is more commonly used as a voltage amplifier.

Formula used: The voltage gain in a common emitter amplifier is given as $v = \beta \dfrac{{{R_L}}}{{{R_i}}}$ .
Here $v$ is the voltage gain, $\beta$ is the current gain, ${R_L}$ is the load resistance and ${R_i}$ is the input resistance.

Complete step by step solution:
We are given that the configuration is the common emitter so we shall apply the formula $v = \beta \dfrac{{{R_L}}}{{{R_i}}}$ where $v$ is the voltage gain, $\beta$ is the current gain, ${R_L}$ is the load resistance and ${R_i}$ is the input resistance.
Given that the current gain, $\beta = 6$ .
Also, the ${R_L} = 24\,\Omega$ is the load resistance and ${R_i} = 3\,\Omega$ is the input resistance.
Substituting these values in the formula,
$v = 6 \times \dfrac{{24}}{3}$
Further solving this we get,
$v = 48$
So, the voltage gain in this situation is 48.

Note: In a common emitter configuration, it is both PNP and NPN transistor arrangements that are available but more frequently designed and widely used is the NPN transistor arrangement. Capacitors can also be a part of amplifier arrangements. At low and very high frequencies, the voltage gain drops. But when the frequencies are mid-level ranging, it is a constant value for the given circuit parameters.