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Bessel-Thompson Low Pass Filter (BTLPF)

Bessel-Thompson Low Pass Filter (BTLPF)

Properties	Description	Units	Default	Range
N	Order of filter	none	Required	³1
FC	Cutoff frequency (3dB)	Hz	Required	>0
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:

where B_n(s) 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 cutoff frequency from unity to w_c, the frequency dependence of the transfer function needs to be scaled by 1/wc, which is accomplished by replacing w by w/w_c³:

4. Range for N: 5.0 < N < 15

Netlist Form

BTLPF:NAME n1 [n2] N=val FC=val [R1=val] R2=val] [IL=val]

Netlist Example

BTLPF:1 1 2 N=13 FC=2.0

References

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

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

3. Microwave Engineering, second ed., David M. Pozar, John Wiley & Sons, Inc., 1998.

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