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Chebyshev Lowpass Filter Poles
See the online filter calculators and plotters here.
Chebyshev poles lie along an ellipse, rather than a circle like the Butterworth and Bessel. Prototype value real and imaginary pole locations (ω=1 at the ripple attenuation cutoff point) for Bessel filters are presented in the table below.
Pole locations are calculated as follows, where K=1,2,...,n. n is the filter order.
0.01 dB Ripple
Order (N)
Re Part (-σ)
Im Part (ąjω)
1
20.82774
2
2.22776
2.33729
3
0.79469 1.58937
1.62621
4
0.41087 0.99192
1.35553 0.56148
5
0.25251 0.66109 0.81715
1.22820 0.75907
6
0.17147 0.46845 0.63992
1.15867 0.84820 0.31046
7
0.12426 0.34818 0.50313 0.55844
1.11664 0.89548 0.49695
8
0.09429 0.26852 0.40187 0.47404
1.08934 0.92350 0.61706 0.21668
9
0.07405 0.21321 0.32665 0.40070 0.42641
1.07060 0.94147 0.69879 0.37182
10
0.05971 0.17329 0.26991 0.34011 0.37701
1.05720 0.95371 0.75687 0.48594 0.16744
0.10 dB Ripple
Order (N)
Re Part (-σ)
Im Part (ąjω)
1
6.55220
2
1.18618
1.38095
3
0.48470 0.96941
1.20616
4
0.26416 0.63773
1.12261 0.46500
5
0.16653 0.43599 0.53891
1.08037 0.66771
6
0.11469 0.31335 0.42804
1.05652 0.77343 0.28309
7
0.08384 0.23492 0.33947 0.37678
1.04183 0.83549 0.46366
8
0.06398 0.18220 0.27268 0.32165
1.03218 0.87504 0.58468 0.20531
9
0.05044 0.14523 0.22251 0.27294 0.29046
1.02551 0.90182 0.66935 0.35616
10
0.04079 0.11837 0.18437 0.23232 0.25753
1.02071 0.92080 0.73075 0.46917 0.16166
0.25 dB Ripple
Order (N)
Re Part (-σ)
Im Part (ąjω)
1
4.10811
2
0.89834
1.14325
3
0.38361 0.76722
1.09155
4
0.21252 0.51306
1.05678 0.43773
5
0.13503 0.35350 0.43695
1.03788 0.64145
6
0.09339 0.25515 0.34854
1.02689 0.75173 0.27515
7
0.06845 0.19178 0.27714 0.30760
1.02001 0.81798 0.45395
8
0.05232 0.14900 0.22299 0.26304
1.01545 0.86085 0.57520 0.20198
9
0.04130 0.11890 0.18217 0.22347 0.23781
1.01227 0.89018 0.66071 0.35156
10
0.03342 0.09700 0.15108 0.19037 0.21102
1.00998 0.91112 0.72307 0.46424 0.15997
0.50 dB Ripple
Order (N)
Re Part (-σ)
Im Part (ąjω)
1
2.86278
2
0.71281
1.00404
3
0.31323 0.62646
1.02193
4
0.17535 0.42334
1.01625 0.42095
5
0.11196 0.29312 0.36232
1.01156 0.62518
6
0.07765 0.21214 0.28979
1.00846 0.73824 0.27022
7
0.05700 0.15972 0.23080 0.25617
1.00641 0.80708 0.44789
8
0.04362 0.12422 0.18591 0.21929
1.00500 0.85200 0.56929 0.19991
9
0.03445 0.09920 0.15199 0.18644 0.19841
1.00400 0.88291 0.65532 0.34869
10
0.02790 0.08097 0.12611 0.15891 0.17615
1.00327 0.90507 0.71826 0.46115 0.15890
1.0 dB Ripple
Order (N)
Re Part (-σ)
Im Part (ąjω)
1
1.96523
2
0.54887
0.89513
3
0.24709 0.49417
0.96600
4
0.13954 0.33687
0.98338 0.40733
5
0.08946 0.23421 0.28949
0.99011 0.61192
6
0.06218 0.16988 0.23206
0.99341 0.72723 0.26618
7
0.04571 0.12807 0.18507 0.20541
0.99528 0.79816 0.44294
8
0.03501 0.09970 0.14920 0.17600
0.99645 0.84475 0.56444 0.19821
9
0.02767 0.07967 0.12205 0.14972 0.15933
0.99723 0.87695 0.65090 0.34633
10
0.02241 0.06505 0.10132 0.12767 0.14152
0.99778 0.90011 0.71433 0.45863 0.15803
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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