General coupling matrix synthesis methods for Chebyshev filtering functions

TLDR

The paper introduces universal methods for generating transfer polynomials and directly synthesizing coupling matrices for general Chebyshev filtering functions, to aid the design of high‑performance microwave filters for space and terrestrial communication systems. The authors present a recursion‑based algorithm for constructing Chebyshev polynomials with prescribed zeros or group‑delay equalization, synthesize the corresponding coupling matrix for single‑ or double‑terminated networks, and propose a direct, non‑optimization technique to reconfigure the matrix into a practical form for microwave resonator realization.

Abstract

Methods are presented for the generation of the transfer polynomials, and then the direct synthesis of the corresponding canonical network coupling matrices for Chebyshev (i.e., prescribed-equiripple) filtering functions of the most general kind. A simple recursion technique is described for the generation of the polynomials for even- or odd-degree Chebyshev filtering functions with symmetrically or asymmetrically prescribed transmission zeros and/or group delay equalization zero pairs. The method for the synthesis of the coupling matrix for the corresponding single- or double-terminated network is then given. Finally, a novel direct technique, not involving optimization, for reconfiguring the matrix into a practical form suitable for realization with microwave resonator technology is introduced. These universal methods will be useful for the design of efficient high-performance microwave filters in a wide variety of technologies for application in space and terrestrial communication systems.