Q.The loop gain of a negative feedback amplifier is 10 and bandwidth before feedback is 50 kHz. Find the bandwidth of an amplifier with feedback.

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. …