Question 8.6: An amplifier has an open-loop voltage amplification of A = 1...
An amplifier has an open-loop voltage amplification of A = 1000. A fraction of the output voltage is fed back in opposition to the input. If the feedback fraction is 0.01, calculate the percentage change in gain of the feedback amplifier if the amplifier gain, A gets reduced by 6 dB due to ageing.
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Gain of the feedback amplifier, A_{f}, is calculated as
A_{f}=\frac{A}{1+Aβ}=\frac{1000}{1+ 1000× 0.01} =\frac{1000}{11}=90.99Let the open-loop gain, A change to A_{1} due to ageing. This change has been expressed in dB.
Therefore, 20\log _{10}\left|\frac{A}{A_{1}} \right|=6
\log _{10}\left|\frac{A}{A_{1}} \right|=\frac{6}{20}=0.3or, \frac{A}{A_{1}}=2
or, A_{1}=\frac{A}{2}=\frac{1,000}{2}=500
Now, let A_{f_{1}}=\frac{A_{1}}{1+A_{1}β}=\frac{500}{1+500 ×0.01}=\frac{500}{6}=83.33
The percentage change in gain of the feedback amplifier is calculated as
Percentage change = \left\lgroup\frac {A_{f}-A_{f_{1}}}{A_{f}} \right\rgroup\times 100
=\left(\frac{90.99-83.33}{90.99} \right)\times 100= 8.4.