A filter's cutoff frequency is the point where output falls to 0.707 of maximum — the half-power (−3 dB) point

By convention, a filter’s cutoff frequency is not where the signal disappears but where its amplitude has dropped to 0.707 of the maximum passband value. This specific number arises because signal power is proportional to amplitude squared, and 0.707² = 0.5 — so at cutoff the filter passes exactly half the power. For this reason the cutoff is also called the half-power point, or the −3 dB point (since 0.707 relative to 1.0 is about −3 dB). Frequencies attenuated beyond this point lie in the stopband; those passed lie in the passband. For a bandpass filter, the difference between its upper and lower cutoff (−3 dB) frequencies defines its bandwidth. A common misconception is that ‘cutoff’ means a hard edge where sound stops — real filters roll off gradually through a transition band, and even at the labelled cutoff, half the power still passes.

Examples

A lowpass labelled ‘cutoff 1 kHz’ still passes a 1 kHz tone at 0.707 (−3 dB) of full level; the tone is only strongly attenuated well above 1 kHz. A bandpass with −3 dB points at 1800 and 2200 Hz has a 400 Hz bandwidth.

Assessment

A datasheet lists a lowpass filter’s cutoff at 2 kHz. Explain what fraction of the signal amplitude and power passes at exactly 2 kHz, and why engineers also call this the −3 dB point.