Why 3 dB is taken in frequency response curve

3db is the power level, its the frequency at which the power is at 3db below the maximum value and 3db means in normal unit its half the maximum power so 3db frequency means the frequency at which the power is half the maximum value so its decided the cuttoff frequency. actually the frequency corresponding to 3dB magnitude is considered as bandwidth of the signal or of the system. This is taken as a standard reference frequency beyond which the response is not very important from the system analysis point of view.The -3dB point is at the start of the attenuation.

Frequencies beyond that are attenuated at a 20 dB per decade of frequency (per pole) beyond the -3dB frequency.

The -3dB, come from 20 Log (0.707) or 10 Log (0.5).

to determine the bandwidth of signal, when decrease the voltage from maximum to 0.707Max or decreasing the power from max to half power.

The -3dB point is also known as the "half power" point. In voltage it may not make not make tons of sense as to why we use (2–√

$2/2$), but lets look at an example of what it means in the sense of power.

First, P=V^2/R, but lets assume R is a constant 1 Ω

Ω

$\Omega$. Because of the constant 1 ohm, we can remove it from the equation all together.

Lets say you have a signal at 6 V, its power would then be (6 V)^2=36 W.

Now I take the -3dB point, 6 V(√2/2)=4.2426 V.

Now lets get the power at the -3dB point, 4.2426 V^2 = 18 W.

So originally we had 36 W, now we have 18 W (which of course is half of 36 W).