## Butterworth Lowpass Filter PolesThe 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 s _{1} and s_{n}. The polynomials are normalized by setting ω_{c}
= 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. Related Pages on RF Cafe- Filter Transfer Functions - Filter Equivalent Noise Bandwidth - Filter Prototype Denormalization - Filter Design Resources - Filter Design Books - Bessel Filter Poles - Bessel Filter Prototype Element Values - Butterworth Lowpass Filter Poles - Butterworth Filter Prototype Element Values - Chebyshev Lowpass Filter Poles - Chebyshev Filter Prototype Element Values - Monolithic Ceramic Block Combline Bandpass Filters Design - Coupled Microstrip Filters: Simple Methodologies for Improved Characteristics
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