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Chebyshev Lowpass Filter Poles

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 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

where    Chebyshev pole equation sinh 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

 

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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