General coupling matrix synthesis methods for Chebyshev filtering functions

• Published in: IEEE transactions on microwave theory and techniques Vol. 47; no. 4; pp. 433 - 442
• Main Author: Cameron, R.J.
• Format: Journal Article
• Language: English
• Published: IEEE 01.04.1999
• Subjects: Chebyshev approximation; Couplings; Delay; Filtering; Filtering theory; Filtration; Group delay; Joining; Microwave technology; Microwave theory and techniques; Microwaves; Network synthesis; Networks; Polynomials; Space technology; Symmetric matrices; Synthesis
• ISSN: 0018-9480; 1557-9670
• DOI: 10.1109/22.754877

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.