Q.Explain the effect of negative feedback on stability of the gain.

Gain stability means the amplifier's overall gain stays constant even when its internal gain changes; negative feedback provides this by tying the gain to a stable passive network. …

[!TLDR]

Negative feedback makes $A_f \approx 1/\beta$ and reduces any fractional change in gain by $(1+A\beta)$, so the overall gain stays almost constant.

The voltage gain of a transistor amplifier varies with device parameters, supply voltage, temperature and ageing, so the open-loop gain $A$ is not constant. Negative feedback stabilises the overall gain.

Gain depends only on $\beta$. The closed-loop gain is

When the loop gain is large, $A\beta \gg 1$, the '1' is negligible:

Now the gain is fixed by $\beta$, which is set by stable passive components (resistors, capacitors, inductors), and is essentially independent of the amplifier's own parameters.

Quantitative measure of stability. Differentiate $A_f$ with respect to $A$:

Multiplying and dividing the right-hand side by $A$ and using $A_f = A/(1+A\beta)$:

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