Driving-point immittance with equiripple magnitude

Abstract

Reccurrence relations of the Ln polynomials of class L filters are derived. Using them, it is found that the ratio of the two consecutive odd order monotonic Ln polynomials form a Chebyshev rational function, whose maxima and minima coincide with the zeros of the tabulated orthogonal Legendre polynomials and their derivatives.One of the possible applications of such rational functions, in the design of equalisers for parasitic reactances, is discussed. The network has a larger gain-bandwidth product and a smaller step response overshoot than other known networks with maximally flat magnitudes.