Equivalent surface impedance of passive impedance loads fabricated on the basis of a two-dimensional cavity-backed hole in a screen

Four designs of impedance loads made of slots in a metal screen are considered. The loads are simulated by a unified mathematical model involving two domains coupled through one or several holes in a planar, perfectly conducting screen. The first domain is the free space, whereas the second domain is different for different designs: for the first design, it is also the free space; for the second design, it is a plane-parallel waveguide connected with the first domain through a hole in one of the planes; for the third design, it is also a plane-parallel waveguide, but connected with the first domain through the butt-end; and for the fourth design, it is a rectangular cavity. The electric and magnetic field distributions over the hole aperture, which are applied for calculating the equivalent surface impedance, are obtained from the numerical solution to the Fredholm integral equation of the first kind. The technique for calculating the integral equation kernel is discussed in detail, and in particular, the improvement of convergence of infinite series and calculation of quantities involving logarithmic singularities. Numerical results for all types of the impedance loads under study are presented in the form of the active and reactive components of the equivalent surface impedance against basic geometric dimensions.