Q.An RC-coupled amplifier has a mid-frequency gain of 200 and a frequency response from 100Hz to 20 kHz. A negative feedback network with $\beta$=0.02 is incorporated into the amplifier circuit. Determine the new system performance.

Negative feedback lowers the gain by $(1+A\beta)$ and widens the band by the same factor: $A_f=\dfrac{A}{1+A\beta}$, $f_1'=\dfrac{f_1}{1+A\beta}$, $f_2'=f_2(1+A\beta)$, leaving the gain-bandwidth product essentially unchanged. …

[!TLDR]

With $A=200$, band 100 Hz–20 kHz and $\beta=0.02$: gain drops to $A_f=40$ while the band widens to 20 Hz–100 kHz ($BW_f\approx99.98$ kHz), the gain-bandwidth product staying constant.

Negative feedback trades gain for bandwidth: the loop gain $A\beta=200\times0.02=4$, so $1+A\beta=5$.

New gain:

Lower cut-off decreases:

Upper cut-off increases:

Bandwidth with feedback:

Check the gain-bandwidth product. Without feedback $BW = f_2-f_1 = 20\times10^{3}-100 = 19.9\text{ kHz}$, so …