Design of Multi-Port With Desired Reference Impedances Using Y-Matrix and Matching Networks

Two synthesis algorithms of multiport network with desired unequal complex port-impedances are developed considering the multiport network as an interconnection of two-port networks (TPNs). The first one is direct-synthesis using Y-matrix, and the second one is port-impedance transformation method. The techniques are single-frequency methods, as the scattering parameters of known multiport networks are defined at the design frequency. In direct-synthesis, the desired S- matrix of the multiport network is converted into the desired Y-matrix, considering the reference port-impedance matrix. Then the multiport network structure or topology can be predicted using the non-zero off-diagonal entries of Y-matrix. The Y-matrix of the predicted multiport is calculated in terms of unknown design parameters or sub-network parameters. Finally, by equating the predicted Y-matrix with the desired Y- matrix, the design equations are obtained. In the port impedance transformation method, a core network with intermediate port-impedances is designed using the direct-synthesis method. Then the intermediate port-impedances are converted into desired port impedances using external matching networks. The impedance matching networks are designed using the desired phased impedance matching theory. Two different designs of a four-port network are provided to validate the proposed concepts. Two pseudocodes or algorithms are developed considering lumped Π networks as building blocks.