Systematic procedure to avoid unintended polarity mismatch in the cascade connection of multiport devices with symmetric feeding lines

The traditional cascading of generalised scattering matrices (GSMs) assumes that the modal sets at the connected ports of a cascaded network are strictly equal. This implies a careful selection of the modal polarities, or the reference systems, of every port. Usually, the connection scheme of every device is known a priori. Then, the individual GSMs are pre-processed, or auxiliary devices, which correct possible modal mismatches at the ports, are included in appropriate positions among the cascade, so that the traditional cascading-by-pairs approach can be directly applied. This scheme clearly complicates the reutilisation of previously calculated GSMs, and mixes the cascading with the solution of the individual building blocks. In this study, a systematic procedure is proposed to define the polarity of the modes at the ports of a device fed with transmission lines or waveguides showing a single or double symmetry. The modified expressions to calculate the scattering parameters of the cascade of two multiport devices, incorporating the regular modal corrections to apply when this criterion is used to define the modal polarity at the ports, is also presented in this study. This strategy is more convenient from the point of view of programming, less error-prone and easier to implement.