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General synthesis method for variable couplers, switches, bridges, and power dividers and combiners

A general method for synthesizing lossless fully matched variable couplers, switches, bridges, and power dividers and combiners is presented. The method uses lossless multiport ring-coupled resonators that are characterized by a circulant coupling matrix. Only physically realizable reactances obeying Foster's Theorem are used in the synthesis. This results in a practically feasible realization of the design based on the proposed synthesis procedure. Based on the presented analysis, it is shown that for this class of ring components, lossless matched reciprocal four-ports can only be bridges, anisotropy is needed for the synthesis of variable couplers and switches, and power dividers and combiners must be at least a five-port junction. The paper is essentially of a fundamental nature and presents a technique, which — to the best of the author's knowledge — has not been reported before. Therefore, no simulation or measurement results are included.