Question 8.14: The open-loop gain of an amplifier changes by 20 per cent du...

The open-loop gain of an amplifier changes by 20 per cent due to ageing, temperature effect, etc. A negative feedback of 20 dB is used to have a reasonably stable closed-loop gain. Calculate the percentage change in the gain of the negative feedback amplifier for an open-loop gain change of 20 per cent.

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The amount of feedback expressed in decibels is

20 \log _{10}\left|\frac{A_{f}}{A} \right| =-20

or,                     \log _{10}\left|\frac{A_{f}}{A} \right| =-1

A_{f}=\frac{A}{1+βA}.

\frac{A_{f}}{A}=\frac{1}{1+βA}.

Therefore,

\log _{10}\frac{1}{1+βA}=-1

\log _{10}(1+βA)=1

(1+βA)=10

Again,

A_{f}=\frac{A}{1+βA}

 

\frac{dA_{f}}{A_{f}}=\frac{dA}{A} ×\frac{1}{1+βA}

 

=20 × \frac{1}{10}

or, v                                  \frac{dA_{f}}{A_{f}}=2  per cent.

The change in gain with negative feedback is reduced to 2 per cent only.

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