Symmetry synthesis of the multiport scattering matrix as a first step in the design of electromagnetic devices and components with bianisotropic media

There is a tendency in practice of EM device design to use the highest possible symmetries because they allow one to obtain better frequency responses, to simplify calculations, tuning and regulation of the devices. Some restrictions for example technological ones, may influence on the symmetry choice. In 2D planar structures, we can usually use symmetrical solutions with planes and axes of symmetry, that is we consider the symmetry of plane figures. In the up-to-date technology, there exists a trend to use 3D structures, which provide miniaturization and an improvement of some of the parameters and characteristics. In these structures, we may investigate more sophisticated symmetries especially in those with magnetic media. In this paper, we outline a general method for symmetry synthesis of multiport devices based on magnetic group theory. This theory gives an opportunity to consider all the possible symmetry solutions to the problem of synthesis and to find an optimal one. The method is illustrated with an example of a nonreciprocal four-port divider symmetry synthesis. The full group tree for four-ports is also derived.