Analysis of finite tolerance effect of critical pole on characteristics of selective RC active special Gegenbauer filters

Abstract

A precise analytical method for finding the explicit expression for the characteristic function of special Gegenbauer filters applicable to the design of RC active filters is suggested in this paper. The adverse parasite effects of limited finite gain-bandwidth product of operational amplifiers are decreased by using filters with the low pass-band attenuation. The new class of continual filter functions generated by analytical method by extremal Christoffel-Darboux formula for orthogonal Gegenbauer polynomials has two parameters. One is the filter order, n, and the second one is real free parameter, v, which provides a wide range of the amplitude responses. In this paper, a detailed analysis of attenuation and insertion loss in the bandwidth and around the stop-band cutoff frequency,  cs , are carried out using 3D plots and using examples of the effect of finite tolerance of quality factor module, Q, of critical conjugate-complex poles of considered RC active filter functions.