Roots of Equiripple Insertion-Loss Functions for Commensurate Line Filters

A technique is presented to find the roots of low-pass equiripple insertion-loss functions realizable by commensurate line filters containing stubs as well as the unit elements. The technique is akin to closed form solution in that the roundoff errors of one root do not affect the rest of the roots. Results of a numerical example illustrate the practical advantage of this technique.