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Determine the order of a Butterworth low-pass filter satisfying the following specifications: fp=0.10 Hz fs=0.15 Hz αp=0.5 dB

Determine the order of a Butterworth low-pass filter satisfying the following specifications: fp=0.10 Hz fs=0.15 Hz αp=0.5 dB αs=15 dB;f=1 Hz

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Solution:

The type of transformation is not specified. Let us use bilinear transformation,

Ω2Ω1=2Ttanω222Ttanω12=21tan0.3π221tan0.2π2=1.0190.649=1.57

N12log{[1A221]/[1A211]}log(Ω2Ω1)12log{[10.17721]/[10.94421]}log(1.57)6.167

So the order of the low-pass Butterworth filter is N = 7.

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