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Chebyshev Lowpass Filter Poles

Visit the Anatech Electronics websiteChebyshev 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 Chebyshev filters are presented in the table below.

See the online filter calculators and plotters here.

Pole locations are calculated as follows, where
K=1,2,...,n. n is the filter order.
 

Chebyshev pole locations - RF Cafe
    Chebyshev pole sinh arguement - RF Cafe      Chebyshev pole cosh arguement - RF Cafe



0.01 dB Ripple
Order (N) Re Part (-σ) Im Part (±jω)
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 (±jω)
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 (±jω)
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 (±jω)
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 (±jω)
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
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

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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