Surface Impedance Boundary Conditions under Transmit and Receive Conditions

Abstract

For an impedance boundary condition (IBC) to accurately model a physical electromagnetic problem, it becomes imperative to consider the surface impedance variation as the excitation source location is changed. Using the rigorous Green's function field solution for the grounded dielectric slab, it is shown that the surface impedance varies as the excitation source location is changed. For the transmit problem (source close to the slab surface), a Sommerfeld integral is numerically evaluated in the complex $w$ plane, which allows one to compute the exact surface impedance at any surface point, including points near the source. The surface impedance from the exact solution is shown to agree with a numerical electromagnetic full-wave (COMSOL) solution. For the IBC to have the same field as the original grounded slab, the surface impedance should match the actual slab- and it is not a constant, but varies, especially near the source. An IBC Green's function is only possible when the surface impedance is constant. When the impedance is not constant, we obtain an exact solution by using radiation integrals on the infinite aperture. We decompose the true aperture fields from the true grounded slab problem into geometrical optics (GO) field part and the surface wave field part. This in turn allows one to compute the field solution by solving the radiation integrals over an infinite aperture. The field solution is compared with COMSOL. The results show that for a transmitting antenna the surface impedance is a relatively complicated function, compared to the receiving case. It is therefore incorrect to assume that surface impedance is simply a number, when considering transmitting antennas.