Q.Find the bandwidth and gain at 3dB line for an amplifier having mid-band gain of 600 having 3dB frequencies 100Hz and 300kHz.

An amplifier does not amplify all frequencies equally. The frequency response is a plot of voltage gain against frequency. It is flat at a maximum value (the mid-band gain, $A_m$) over a middle range, and rolls off at both the low and high ends.

At low frequencies the coupling and bypass capacitors have a large reactance $X_C = 1/(2\pi f C)$; in series with the signal path this attenuates the input and the gain falls. At high frequencies the small junction and stray capacitances have a low reactance; shunting the signal, they again reduce the gain. In the mid-band both effects are negligible, so the gain stays almost constant.

The edges of the useful range are the lower and upper cut-off frequencies $f_L$ and $f_H$, where the voltage gain has dropped to $1/\sqrt{2} = 0.707$ (70.7%) of its maximum. These are the half-power or 3 dB frequencies: because power varies as the square of voltage, the power there is exactly half its maximum, i.e. 3 dB down. The frequencies below 70.7% gain are considered too weak to be useful, so the bandwidth is taken as

For distortionless amplification the whole signal's frequency range must lie inside this bandwidth.