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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
- Filter Transfer Functions
- Filter Equivalent Noise Bandwidth
- Filter Prototype Denormalization
- Filter Design Resources
- 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