Advanced coupling matrix synthesis techniques for microwave filters

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.