Optimisation of driving-point immittance with equiripple magnitude

Abstract

A simple procedure for the design of a Chebyshev rational function is presented. Extremes of the equiripple magnitude function are defined by the accepted orthogonal polynomial, the ‘ minimum property’ of which guarantees a good group delay characteristic and small transient overshoot. A single parameter allows us to compromise between a broad bandwidth and a good group delay characteristic without changing the magnitude of the ripples. When compared with the published maximally flat approximations, the presented function proved superior in both the frequency and time domains.One of the possible applications of such rational functions, in the design of equalisers to cancel the effects of parasitic reactances, is discussed.