what is 3db frequency .why it is 3db not 1 db?

Answer 1

The 3dB frequency, or more precisely the -3dB frequency, is the frequency at which the amplitude power has dropped by 1/2. Every time the frequency increases passed one additional pole of the circuit, the Bode plot (a plot of power or gain in dB steps versus frequency in decade steps) changes its straight-line trend. A transition between two straight-line slopes follows a relatively extended smooth curve; so it is easier to project the two trend lines to find a sharp intersect point to represent the smooth segment. That sharp point is the -3dB point.

The 1 dB point, incidentally, is used in specifying gain compression. As the input signal of an amplifier keeps increasing its output power will start to drop down from the constant gain line. The output power point at which the gain drops by 1 dB from its straight line is called the 1 dB gain compression point.

Answer 2

Power value for a signal to be considered faithful = 1/2 the max power for that signal
=> Pacceptable/Pmax = 1/2 = -3 db ( log10(1/2)=-3)
To calculate BW (bandwidth) , this figure is used.