For a first order passive filter (RC circuit), we often reach for a the familiar 10X rule. If the -3dB corner frequency is f, then "ideal" frequency response starts at 10f.

What similar factor can be used for a second order Sallen-Key filter which is critically damped (C2 = 2C1)?

If, say, the -3dB roll-off of such a low-pass filter is at 25Khz, until where do we consider the frequency response to be as flat as we would by the 10X rule for RC filter for the same corner frequency?


There's many ways to answer that, here are some to throw out ideas:

1) since it is a second order filter with 2X slope per octave then you can argue that it should be sqrt(10) X.

2) typically though that measurement might also take into account the ripple and constrain it so that a fixed factor may not be apropos. In your case of critically damped this doesn't hold, but in a more general sense perhaps a simple factor isn't the right criteria.

3) Since I work with S&H system and switched cap we don't use a 10X but how many time periods until settled to within the error budget of the system (so it's variable depending upon what is being designed).

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  • \$\begingroup\$ I'm going to accept this. I think the sqrt(10) has intuitive appeal and looking at graphs qualitatively seems to bear it out. It is sensitive to Q. If we have a high Q, then we have overshoot, so in fact we can tune it so that there is even a boost at the corner frequency. That's why I was interested in the critically damped case. Critical damping seems to optimally "tuck" the curve into the angle formed by the asymptotes (flat level and roll-off line). Any more Q, and we go above the horizontal. But less Q pulls the curve out of the corner and gives it earlier roll-off. \$\endgroup\$ – Kaz Nov 27 '12 at 21:27

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