Q.An amplifier has a mid-frequency gain of 400 and lower and upper 3dB frequencies are 100Hz and 10 kHz. A negative feedback network with $\beta$=0.01 is incorporated into the amplifier circuit. Calculate a) gain with feedback b) new bandwidth

The bandwidth of an amplifier is the span between its two $3\text{ dB}$ (0.707 of maximum) cut-off frequencies — the lower cut-off $f_1$ and the upper cut-off $f_2$:

When negative feedback is applied, the response flattens and widens: the lower cut-off decreases and the upper cut-off increases, each by the factor $(1+A\beta)$,

so the new bandwidth is

The passband therefore grows by the same factor $(1+A\beta)$ by which the gain shrank. On a gain-versus-frequency graph the "after feedback" curve sits lower (peak $A_{f,max} < A_{max}$) but stretches wider on both sides.

Because the mid-band gain falls by exactly the factor that the bandwidth rises, the two changes cancel and the gain-bandwidth product stays constant:

This is the key trade-off of negative feedback: it lets a designer exchange gain for bandwidth in exact proportion, but it cannot increase both at once. For a given amplifier the gain-bandwidth product is a fixed figure of merit, and feedback simply redistributes it between gain and bandwidth.