Synthesis of Multiport Networks Using Port Decomposition Technique and its Applications

Abstract

A systematic approach to synthesize multiport ( $N$ -port) network with desired characteristics, for a given network topology, has been proposed. The heart of the algorithm lies with a novel port decomposition technique introduced here, wherein a reduced two-port network (2PN) is obtained by short-circuiting the remaining $N-2$ ports of the original topology. This reduced network is easily analyzed in terms of its unknown design parameters and can be compared with the known characteristics to provide a subset of design equations. Iteratively proceeding with this approach, one can obtain the required synthesis equations for any multiport network, even when there exists no plane of symmetry. Utilizing this algorithm, four theorems pertaining to multiport network synthesis have been proposed. The first and second theorems establish the synthesis guidelines of an arbitrary-phased rat-race and branch-line type coupler having unequal (or equal) power division at the output ports, with a ring type topology consisting of arbitrary building blocks. The third theorem deals with the synthesis of a five-port network, and the final one provides the design equations for arbitrary phase difference coupler involving coupled lines.