Electrical – Nth order Butterworth filter transfer function for a given roll-off frequency

active-filterlow pass

I want to plot a fourth order low pass Butterworth for any given cut off freq. But I'm lacking the correct transfer function. I saw some polynomial transfer functions in s domain. But their cutoff is 1rad/s. Here is a table I found for wc=1rad/s:

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Is there a quick way to modify for example the 4th order filter transfer function above for a different wc other than 1rad/s? Is there a quick way to obtain or is there a lookup table designated for filter transfer functions?

Best Answer

The given set of functions is normalized to wc=1rad/sec. That means: The frequency variables in all expressions are to be interpreted as S=s/wc (capital letter S).

Therefore, you have nothing to do than to select different cut-off frequencies wc and to rescale the variable. Example: For wc=10rad/ses you must set S=s/10.

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