3 db bandwidth

the answer is simple the amplifier gain at lower cut off and upper cut off frequency is 1/ root 2 times the actual gain in the mid frequency region

the 20(log(1/root2)) is -3 dB

so we use it for drawing the line

check this out frequency response of lower frequency region

Av=1/(1+j(f/f1))
where f= frequency of the signal
f1= lower cut off frequency

when f=f1
|Av|=1/root(2)

this is also true for higher frequency respone


PS: refer electronic circuits and devices by S. Salivahanan for more info

i took this from there