Nomographs for Designing Elliptic-Function Filters

Abstract

The elliptic-function filter is of considerable importance because of its ability to provide simultaneously small pass band ripple, large stop band attenuation, and very sharp cutoff, with equal-ripple behavior in both the pass band and the stop band. The fundamental design parameters are the pass band ripple, the stop band attenuation, the transition bandwidth, and the number of poles required. They are interrelated in a rather complicated way involving certain elliptic functions, so that determination of a compatible set of parameters is both tedious and difficult. Two nomographs relating these parameters have been devised, by means of which suitable values can be determined easily and quickly. The ranges covered are: pass band ripple, from less than 0.05 up to 3 db; stop band attenuation, from 3 to 40 db (extendable to any value above 40 db simply by renumbering certain scales); transition bandwidth, 0.001 to 1 times the cutoff frequency, and number of poles, 1 to 20. Once a compatible set of parameters has been determined, the approximation function can be obtained in a straightforward manner. The necessary formulas are given, and the procedure for evaluating them is described briefly.