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Bessel-Thompson Band Pass Filter (BTBPF)

Bessel-Thompson Band Pass Filter (BTBPF)

Properties	Description	Units	Default	Range
N	Order of filter	none	Required	³1
FL	Lower cutoff frequency (3dB)	Hz	Required	>0
FU	Upper cutoff frequency (3dB)	Hz	Required	>FL
R1	Reference resistance at node 1	Ohm	50.	³0
R2	Reference resistance at node 2	Ohm	50	³0
IL	Insertion loss in dB		0	³0

Notes

1. Bessel-Thompson filters are derived from a maximally flat delay criterion (the first n derivatives of the delay are zero at the origin). As a result, they exhibit very good group delay characteristics, but at the cost of a poor attenuation performance in the stopband.

2. The transfer function of the Bessel filter is given by¹ (low-pass prototype):

where B_n(jw) is the n^th order Bessel polynomial, and b₀=B_n(0).

3. The normalized low-pass prototype filter is designed for a cutoff frequency w_c=1. To change the response of the filter to a bandpass, a frequency transformation must take place, where w is substituted by:

where w₀ is the geometric mean of the edge frequencies, w_L and w_H, of the passband:

4. Range for N is: 4.0 < N < 15

Netlist Form

BTBPF:NAME n1 [n2] N=val FL=val FU=val [R1=val] [R2=val] [IL=val]

Netlist Example

BTBPF:1 1 2 N=8 FL=1.0 FL=3.0 FU=5.0

References

1. Approximation methods for Electronic Filter Design, Richard W. Daniels, McGraw-Hill Book Co.

2. Handbook of Filter Synthesis, Anatol I. Zverev, John Wiley & Sons, Inc, 1967.

3. Microwave Engineering, Second Edition, David M. Pozar, John Wiley & Sons, Inc., 1998.

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