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      Filtronetics INC • 6010 Parretta Drive • Kansas City, Missouri (USA) 64120
               Tel: 816-231-7375 • Fax: 816-241-0368 • Email: filtro@filtro.net

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Comparison of Group Delay and Amplitude Characteristics in the
Frequency Domain of Bessel, Gaussian, Chebychev, and
Butterworth Filters of the Second degree.


















Several observations can be made from the above graph of second order bandpass
filters of Bessel, Butterworth, Gaussian, and Chebychev shape.
The group delay of the Bessel is flat in the passband; whereas the Gaussian group
delay is “bullet” shaped. The group delays of the Butterworth and Chebychev
have more variation and have a somewhat inverse shape in the Passband relative
to the Gaussian. They also have peeks near their cutoff frequencies.

The amplitude response of the Chebychev is better than the Butterworth, which is
better than the Bessel. Note that the graph does not depict this, because the 3 dB
bandwidths are not equal. The Bessel and Gaussian filters are also more sensitive to
load variations which may seriously affect the good group delay or phase shift
response of these filters. In conclusion, the better the group delay response of the filter
the worse the amplitude response.

Filtronetics, Inc. can custom design a filter using design techniques that optimized
amplitude, return loss, group delay, phase linearity and ringing characteristics.

References
A. Zeverev, Handbook of Filter Synthesis, John Wiley, New York, 1967, p. 73