Novel design methodology of matching networks based on the use of symmetry operators

In this paper we present a novel design methodology of matching networks. The functionality of a matching network is two-fold: first to decouple the antennas of a particular antenna array and secondly to match the resultant ports. The benefits of using a matching network are several: the antenna elements of a particularly antenna array can be closely spaced thus producing compact array designs (but at the expenses of narrower bandwidth), and it can be shown that the produced set of radiation patterns/polarization are orthogonal among each other (assuming an ideal NLOS scenario), thus producing maximum diversity gains when employed in MIMO systems. Several methods to design matching networks exist in the literature. Most of these designs methods, do not provide a general procedure to derive such networks for any number of antenna elements, topologies or antenna spacing. Instead, the proposed methodology is valid for any number of antenna elements, array topology, and antenna spacing. It is based on the use of the Takagi factorization, which allows us to produce reciprocal lossless designs. To compute this factorization we make use of the symmetry operators Theory to simply derive these networks from a physical inspection of the symmetry properties of the antenna array.