Network synthesis using Tchebycheff polynomial series

A general method is developed for finding functions of frequency which approximate assigned gain or phase characteristics, within the special class of functions which can he realized exactly as the gain or phase of finite networks of linear lumped elements. The method is based upon manipulations of two Tchebycheff polynomial series, one of which represents the assigned characteristic, and the other the approximating network function, The wide range of applicability is illustrated with a number of examples.