Method for Extracting the Effective Tensor Surface Impedance Function From Nonuniform, Anisotropic, Conductive Patterns

A patterning technique known as the point shifting method has enabled the generation of smoothly varying and highly anisotropic impedance surfaces with a wide range of patch sizes and shapes. Previously, the surface impedances of different shapes of unit cells were assumed by the impedance of similar size rectangle cells. In this paper, we study an approach to calculate the surface impedances for anisotropic polygon unit cells more accurately, based on the area moment of inertia equations. We define an alternative unit cell called the equivalent rectangle, which has the same tensor impedance properties of a general polygon unit cell in the surface impedance pattern. The size of the equivalent rectangle cell is calculated by using the moment of inertia equations between the polygon and the rectangle. The extracted surface impedance from the equivalent rectangle is compared to the surface impedance of polygon in the unit cell simulation, validating our method. We also verify the method by comparing the results between PEC patterns and impedance boundary sheets to which the extracted impedances are applied. Simulations of the patterns are verified by measurements as well.