# Do we always take the corner frequency of a filter at exactly -3dB?

I'm doing some work on filters, but all the references I can find use a 'perfect' gain characteristic, with the trace starting at 0dB. Is the measurement for corner/cutoff frequency always taken at exactly -3dB? What if the maximum gain isn’t 0dB?

For example, see the below figure, where the maximum gain is -3dB. Surely taking the corner frequency at -3dB in this case would not be useful- instead would we take it at -6dB, which is -3dB from the actual maximum gain?

• Half power is used for all Filters, LED Beamwidth and other things. It's convenient and approximately 3 dB not exact relative to the flat gain Mar 19, 2021 at 0:49
• 20 log (1/2) = -3.01 dB Mar 19, 2021 at 1:29
• – user16324
Mar 19, 2021 at 12:36

It's not 3dB absolute, it's 3dB down from the peak, or some sort of nominal attenuation. So in your case, where the passband is -3dB, 3dB down is at -6dB.

Note that some filters (e.g. Chebychev) have significant passband ripple; if this exceeds 3dB then the "3dB down" figure loses meaning. In that case, or just if it's what matters to the system designer, a different definition of bandwidth may be chosen.

• "....down from the peak..." To me this sounds a bit misleading. Example: For Chebyshev lowpass and highpass responses we have at least one "peak" in the passband, but the cut-off is NOT defined "3 dB down from the peak".
– LvW
Mar 19, 2021 at 11:15

It is not correct that for "all filters" the corner or cut-off frequency is defined by the "-3dB point" (magnitude 3 dB down with respect to the maximum).

This is only the case for

• all first-order low- and highpass responses as well as 2nd-order bandpass filters, and

• for higher-order filters with Butterworth characteristics.

For all other filters (e.g. Chebyshev or elliptical responses) we have different definitions - depending on the allowed ripple (amplitude variations) within the passband.