Q.Relate the bandwidth of an amplifier with and without feedback and comment on the gain-bandwidth product of the amplifier.

Negative feedback widens the bandwidth by the same factor by which it reduces the gain, so their product stays fixed. …

[!TLDR]

Bandwidth increases by $(1+A\beta)$: $BW_f = BW(1+A\beta)$; and the gain-bandwidth product stays constant, $A\cdot BW = A_f\cdot BW_f$.

Without feedback the amplifier has a lower 3 dB frequency $f_1$, an upper 3 dB frequency $f_2$, and bandwidth

When negative feedback is applied, the cut-off frequencies shift outwards:

The lower cut-off decreases and the upper cut-off increases, so the new bandwidth is

which is larger than $BW$ by the factor $(1+A\beta)$.

Comment on the gain-bandwidth product: negative feedback reduces the gain by the factor $(1+A\beta)$ ($A_f = A/(1+A\beta)$) and increases the bandwidth by the same factor. The two changes cancel, so the product of gain and bandwidth is the same with or without feedback: …