Electronics World articles Popular Electronics articles QST articles Radio & TV News articles Radio-Craft articles Radio-Electronics articles Short Wave Craft articles Wireless World articles Google Search of RF Cafe website Sitemap Electronics Equations Mathematics Equations Equations physics Manufacturers & distributors Engineer Jobs LinkedIn Crosswords Engineering Humor Kirt's Cogitations RF Engineering Quizzes Notable Quotes Calculators Education Engineering Magazine Articles Engineering software RF Cafe Archives RF Cascade Workbook 2018 RF Symbols for Visio - Word Advertising Magazine Sponsor RF Cafe RF Electronics Symbols for Visio RF Electronics Symbols for Office Word RF Electronics Stencils for Visio Sponsor Links Saturday Evening Post NEETS EW Radar Handbook Microwave Museum About RF Cafe Aegis Power Systems Anritsu Alliance Test Equipment Amplifier Solutions Anatech Electronics Axiom Test Equipment Berkeley Nucleonics Centric RF Conduct RF Copper Mountain Technologies Empower RF everything RF Exodus Advanced Communications Innovative Power Products ISOTEC KR Filters Lotus Systems PCB Directory Rigol San Francisco Circuits Reactel RFCT TotalTemp Technologies Triad RF Systems Windfreak Technologies Withwave LadyBug Technologies Wireless Telecom Group Sponsorship Rates RF Cafe Software Resources Vintage Magazines Thank you for visiting RF Cafe!
Windfreak Technologies SynthHD PRO - RF Cafe

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.

Related Pages on RF Cafe

- How to Use Filter Equations in a Spreadsheet

- Filter Transfer Functions

- Filter Equivalent Noise Bandwidth

- Filter Prototype Denormalization

- 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

Berkeley Nucleonics Vector Signal Generators Radar Simulations - RF Cafe
KR Electronics (RF Filters) - RF Cafe		 Triad RF Systems Amplifiers - RF Cafe
Anatech Electronics RF Microwave Filters - RF Cafe

Please Support RF Cafe by purchasing my  ridiculously low−priced products, all of which I created.

These Are Available for Free
 

About RF Cafe

Kirt Blattenberger - RF Cafe Webmaster

Copyright: 1996 - 2024

Webmaster:

    Kirt Blattenberger,

    BSEE - KB3UON

RF Cafe began life in 1996 as "RF Tools" in an AOL screen name web space totaling 2 MB. Its primary purpose was to provide me with ready access to commonly needed formulas and reference material while performing my work as an RF system and circuit design engineer. The World Wide Web (Internet) was largely an unknown entity at the time and bandwidth was a scarce commodity. Dial-up modems blazed along at 14.4 kbps while tying up your telephone line, and a nice lady's voice announced "You've Got Mail" when a new message arrived...

All trademarks, copyrights, patents, and other rights of ownership to images and text used on the RF Cafe website are hereby acknowledged.

My Hobby Website:

AirplanesAndRockets.com