# What is the difference of cutoff frequency to -3dB frequency in an active filter?

This table shows the K values of a particular Q value on a Sallen-Key active filter:

Why is the $$\K_c\$$ value (cutoff value) different from $$\K_3\$$ value (-3dB value) on all Q's (except 0.707 which is a butterworth approx) ?

I mean, isn't the cutoff frequency pertains to the -3dB frequency? What is the difference of a cutoff frequency to -3dB frequency?

I mean, isn't the cutoff frequency pertains to the -3dB frequency?

To some degree you are correct, but this article points out that simple rules do not apply to under-dampening (peaking) or over-dampening, they will make those 2 values not equal.

This is from Wikipedia

In electronics, cutoff frequency or corner frequency is the frequency either above or below which the power output of a circuit, such as a line, amplifier, or electronic filter has fallen to a given proportion of the power in the passband. Most frequently this proportion is one half the passband power, also referred to as the 3 dB point since a fall of 3 dB corresponds approximately to half power. As a voltage ratio this is a fall to $$\{\displaystyle \scriptstyle {\sqrt {1/2}}\ > \approx \ 0.707}\scriptstyle\$$ of the passband voltage. Other ratios besides the 3 dB point may also be relevant.

Chebyshev filters

Sometimes other ratios are more convenient than the 3 dB point. For instance, in the case of the Chebyshev filter it is usual to define the cutoff frequency as the point after the last peak in the frequency response at which the level has fallen to the design value of the passband ripple. The amount of ripple in this class of filter can be set by the designer to any desired value, hence the ratio used could be any value.

• Quote:...."simple rules do not apply to non-linear filters..". Chebyshev and other "non-Butterworth" functions are, of course, linear. Non-linearity has nothing to do with the proble under discussion. – LvW Aug 2 at 8:50
• @LvW Fixed the nonlinear bug. Thx – VTNCaGNtdDVNalUy Aug 2 at 9:49
• You could generalize that, usually, the 3 dB cutoff (or the inflexion point of the phase) applies to: Gaussian, Bessel, Butterworth, transitional, Halpern, Papoulis, inverse Pascal, inverse Chebyshev, or any other filter that has a monotonically non-increasing passband, unless stated otherwise. I mention this because too often there seem to be over-simplifications as if Butterworth and Chebyshev are the only two types of filters. – a concerned citizen Aug 2 at 10:17
• Yes - good comment. More than this, for Bessel responses, often the passband is defined in the time domain (group delay) rather than frequency domain. – LvW Aug 2 at 11:08