General coupling matrix synthesis methods for Chebyshev filtering functions

Methods are presented for the generation of the transfer polynomials, and t hen the direct synthesis of the corresponding canonical network coupling ma trices for Chebyshev (i.e., prescribed-equiripple) filtering functions of t he most general kind. A simple recursion technique is described for the gen eration of the polynomials for even- or odd-degree Chebyshev filtering func tions with symmetrically or asymmetrically prescribed transmission zeros an d/or group delay equalization zero pairs. The method for the synthesis of t he coupling matrix for the corresponding single- or double-terminated netwo rk is then given. Finally, a novel direct technique, not involving optimiza tion, for reconfiguring the matrix into a practical form suitable for reali zation with microwave resonator technology is introduced. These universal m ethods will be useful for the design of efficient highperformance microwave filters in a wide variety of technologies for application in space and ter restrial communication systems.