Q.To an amplifier of 60dB voltage gain, a negative feedback of $\beta$ = 0.005 is applied. What would be the change in overall gain of the feedback amplifier if the internal amplifier is subjected to a gain reduction of 12%?

One of the chief merits of negative feedback is that it makes the overall gain almost constant, even though an amplifier's internal gain $A$ varies with device parameters, supply voltage, temperature and ageing.

The closed-loop gain is $A_f = \dfrac{A}{1+A\beta}$. When the loop gain is large, $A\beta \gg 1$, the $1$ in the denominator is negligible, so

The gain now depends only on $\beta$, which is fixed by stable passive components in the feedback network, and is essentially independent of the amplifier's own parameters.

The improvement can be quantified. Differentiating $A_f$ with respect to $A$ gives

$\frac{dA_f}{A_f} = \frac{dA}{A} \times \frac{1}{1 + A\beta}.$ …