6
\$\begingroup\$

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?

Thanks for your help.

Gain plot where the greatest value of gain = ~-3dB

\$\endgroup\$
3
  • \$\begingroup\$ 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 \$\endgroup\$ Mar 19, 2021 at 0:49
  • \$\begingroup\$ 20 log (1/2) = -3.01 dB \$\endgroup\$ Mar 19, 2021 at 1:29
  • \$\begingroup\$ Related : electronics.stackexchange.com/questions/200944/… \$\endgroup\$
    – user16324
    Mar 19, 2021 at 12:36

2 Answers 2

8
\$\begingroup\$

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.

\$\endgroup\$
1
  • 2
    \$\begingroup\$ "....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". \$\endgroup\$
    – LvW
    Mar 19, 2021 at 11:15
6
\$\begingroup\$

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.

\$\endgroup\$

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service and acknowledge you have read our privacy policy.

Not the answer you're looking for? Browse other questions tagged or ask your own question.