  
See the online filter calculators and plotters here. Prototype element values are here. Butterworth poles lie along a circle and are spaced at equal angular distances around a circle. Prototype value real and imaginary pole locations (ω=1 at the 3dB cutoff point) for Butterworth filters are presented in the table below. Pole locations are calculated as follows, where
K=1,2,...,n. n is the filter order. |  |
|
Order (N) | Re Part (-σ) | Im Part (ąjω) | 1 | 1.0000 | | 2 | 0.7071 | 0.7071 | 3 | 0.5000
1.0000 | 0.8660 | 4 | 0.9239
0.3827 | 0.3827
0.9239 | 5 | 0.8090
0.3090
1.0000 | 0.5878
0.9511 | 6 | 0.9659
0.7071
0.2588 | 0.2588
0.7071
0.9659 | 7 | 0.9010
0.6235
0.2225
1.0000 | 0.4339
0.7818
0.9749 | 8 | 0.9808
0.8315
0.5556
0.1951 | 0.1951
0.5556
0.8315
0.9808 | 9 | 0.9397
0.7660
0.5000
0.1737
1.0000 | 0.3420
0.6428
0.8660
0.9848 | 10 | 0.9877
0.8910
0.7071
0.4540
0.1564 | 0.1564
0.4540
0.7071
0.8910
0.9877 |
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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