Butterworth Lowpass Filter Poles
The Butterworth type filter was first described by the British engineer Stephen Butterworth in his paper "On the Theory of Filter Amplifiers", Wireless Engineer (also called Experimental Wireless and the Wireless Engineer), vol. 7, 1930, pp. 536-541.
See my online filter calculators and plotters here.
Butterworth filter prototype element values are here.
Pole locations are calculated as follows, where K=1,2,...,n. n is the filter order.
The Butterworth polynomials may be written in complex form as above, but are usually written with real coefficients by multiplying pole pairs which are complex conjugates, such as s1 and sn. The polynomials are normalized by setting ωc = 1.
The normalized Butterworth polynomial equations have the general form:
Data taken from "Filter Design," by Steve Winder, Newnes Press, 1998. This is a great filter design book, and I recommend you purchase a copy of it.
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