Modeling and Analysis of Printed-Circuit Tensor Impedance Surfaces

Analysis of a printed-circuit tensor impedance surface (PCTIS) is presented. The surface consists of a periodic, subwavelength-patterned metallic cladding printed over a grounded dielectric substrate. First, the dispersion equation for an idealized tensor impedance boundary condition is derived by expressing the field in terms of TE and TM waves. A similar method is then used to find the dispersion equation of the PCTIS consisting of a tensor sheet impedance, which models the metallic cladding, over a grounded dielectric substrate. In addition, a method for extracting the tensor sheet impedance of a periodic, metallic cladding printed over a grounded dielectric substrate, is reported. It involves performing two normal-incidence scattering simulations using a full-wave electromagnetic solver. The method is strictly valid when the ground plane is sufficiently far from the metallic cladding to avoid evanescent-wave interactions. By combining the tensor sheet extraction method with the dispersion equation, the full dispersion characteristics of the PCTIS are analytically predicted in the homogenous limit. The results are verified through full-wave eigenmode simulations.