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# When the negative feedback is applied to an amplifier of gain 50, the gain after feedback falls to 25. Calculate the feedback ratio.

Last updated date: 15th Aug 2024
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Hint: In the above question, we are given that the amplifier gain is $50$ , which is denoted by $A$. We are also given that the gain after feedback falls to $25$ , which is denoted by ${A_f}$ . We also know that Voltage gain after feedback is ${A_f} = \dfrac{A}{{1 + A\beta }}$ . Where, $\beta$ is the feedback ratio. Now, By substituting the values of amplifier gain and voltage gain after feedback falls, we will get our answer.

Formula used:
Voltage gain after feedback falls, ${A_f} = \dfrac{A}{{1 + A\beta }}$.
Where, $\beta$ is the feedback ratio and $A$ is amplifier gain.

Complete step by step solution:
From the above question, we know that
Here, amplifier gain is $A = 50$ and Voltage gain after feedback falls is ${A_f} = 25$
Now, we know that
Formula used for voltage gain after feedback falls is ${A_f} = \dfrac{A}{{1 + A\beta }}$
Here, we have the values of amplifier gain and voltage gain after feedback falls,
Now, substituting the values of amplifier gain and voltage gain after feedback falls, which is $A = 50$ and ${A_f} = 25$ respectively in the above formula,
We get,
$\Rightarrow {A_f} = \dfrac{A}{{1 + A\beta }} \\ \Rightarrow 25 = \dfrac{{50}}{{1 + 50\beta }} \\$
Now, simplifying the above equation,
$\Rightarrow 25\left( {1 + 50\beta } \right) = 50 \\ \Rightarrow 1 + 50\beta = 2 \\ \Rightarrow \beta = \dfrac{1}{{50}} \\ \Rightarrow \beta = 0.02 \\$
Hence, The feedback ratio is $\beta = 0.02$.