Coupling Matrix Synthesis for a New Class of Microwave Filter Configuration

In this paper a new approach to the synthesis of coupling matrices for microwave filters is presented. The new approach represents an advance on existing direct and optimization methods for coupling matrix synthesis in that it will exhaustively discover all possible coupling matrix solutions for a network if more than one exists. This enables a selection to be made of the set of coupling values, resonator frequency offsets, parasitic coupling tolerance etc that will be best suited to the technology it is intended to realize the microwave filter with. To demonstrate the use of the method, the case of the recently – introduced ‘extended box’ (EB) coupling matrix configuration is taken. The EB represents a new class of filter configuration featuring a number of important advantages, one of which is the existence of multiple coupling matrix solutions for each prototype filtering function, eg 16 for 8 degree cases. This case is taken as an example to demonstrate the use of the synthesis method – yielding one solution suitable for dual-mode realization and one where some couplings are small enough to neglect. Index Terms — Coupling matrix, filter synthesis, Groebner basis, inverted characteristic, multiple solutions.