Simple algorithms for elliptic filters and generalizations thereof

Abstract

Described herein are some applications of previously published work [1] on choosing the coefficients in a polynomial, which can be part of a more complicated function, for a Chebyshev approximation to a given function. Here, the applications are to rational functions of frequency describing filters or filterlike circuits. Algorithms are derived for critical frequencies and poles of elliptic filters and a generalization thereof, simple enough for HP65 calculators. Also described briefly are a generalization of Chebyshev polynomials and the addition of a second terminal shunt C to an impedance transforming ladder circuit.