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Butterworth Filter Prototype Element Values
poles lie along a circle and are spaced at equal angular distances around a circle. It is designed to have a
frequency response which is as flat as mathematically possible in the passband, and is often referred to as a
'maximally flat magnitude' filter. Prototype value real and imaginary pole locations (ω=1 at the 3 dB cutoff
point) for Butterworth filters are presented in the table below.
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.
table below lists prototype element values for the normalized lowpass function, which assumes a cutoff frequency
of 1 rad/sec and source and load impedances of 1 Ω. Either an input capacitor
(top reference line in table) or an input inductor (bottom line in table) can
Convert Butterworth prototype values to other cutoff frequencies, impedances, and to highpass, bandpass or
bandstop using the equations here.
See my online Butterworth
filter calculators and plotters here.