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Copyright: 1996 - 2024

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    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...

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Bessel Filter Poles

Order

(N)

Re Part

(-σ)

Im Part

(±jω)

1 1.0000  
2 1.1030 0.6368
3 1.0509

1.3270

1.0025
4 1.3596

0.9877

0.4071

1.2476

5 1.3851

0.9606

1.5069

0.7201

1.4756

6 1.5735

1.3836

0.9318

0.3213

0.9727

1.6640

7 1.6130

1.3797

0.9104

1.6853

0.5896

1.1923

1.8375

8 1.7627

0.8955

1.3780

1.6419

0.2737

2.0044

1.3926

0.8253

9 1.8081

1.6532

1.3683

0.8788

1.8575

0.5126

1.0319

1.5685

2.1509

10 1.9335

0.8684

1.8478

1.6669

1.3649

0.2424

2.2996

0.7295

1.2248

1.7388

Bessel poles lie along a circle similar to the Butterworth filter, but are spaced approximately equal distances apart relative to the real axis rather than at equal angular distances. Prototype value real and imaginary pole locations (ω=1 at the 3dB cutoff point) for Bessel filters are presented in the table below.

4th-order lowpass Bessel filter pole-zero diagram - RF Cafe

This pole-zero diagram shows the location of poles for a 4th-order Bessel lowpass filter.

Bessel filter prototype element values are here.

Bessel function plots can be found here.

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

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