Advanced coupling matrix synthesis techniques for microwave filters

TLDR

The N+2 transversal network coupling matrix enables multiple input/output couplings and direct source‑load coupling, allowing folded matrices to realize microwave bandpass filters across technologies, though some require awkward cross‑couplings. This work presents a general method for synthesizing folded‑configuration coupling matrices for arbitrary Chebyshev or other filtering functions, including fully canonical cases, and introduces two procedures that transform these matrices into novel network configurations to realize advanced bandpass filters without complex inter‑resonator couplings. The authors first describe a direct construction of the transversal coupling matrix, then outline a simple non‑optimization conversion to the N+2 folded matrix, and finally provide two procedures that transform the transversal and folded matrices into novel configurations for advanced microwave bandpass filters.

Abstract

A general method is presented for the synthesis of the folded-configuration coupling matrix for Chebyshev or other filtering functions of the most general kind, including the fully canonical case, i.e., N prescribed finite-position transmission zeros in an Nth-degree network. The method is based on the "N+2" transversal network coupling matrix, which is able to accommodate multiple input/output couplings, as well as the direct source-load coupling needed for the fully canonical cases. Firstly, the direct method for building up the coupling matrix for the transversal network is described. A simple non-optimization process is then outlined for the conversion of the transversal matrix to the equivalent "N+2" folded-configuration coupling matrix. The folded matrix may be used directly to realize microwave bandpass filters in a variety of technologies, but some of these could require awkward-to-realize cross-couplings. This paper concludes with a description of two simple procedures for transforming the transversal and folded matrices into two novel network configurations, which enable the realization of advanced microwave bandpass filters without the need for complex inter-resonator coupling elements.