Radiation by a yagi-uda array in a substrate

The radiation properties of a Yagi-Uda array covered by a dielectric substrate is considered. The exciter is a monopole on a ground plane radiating through the suhstrate while the reflector and directors are monopoles shorted to the ground plane. Initially, the problem of a monopole probe radiating through a dielectric substrate is analyzed by considering a method of moments solution to the Pocklington integral equation for the antenna current distribution. A real axis integration is adopted to evaluate the Sommerfeld-type integrals involved in the Green's function to this problem and substrate surface wave effects are taken into account accurately. The integration along the real axis is carried out over four intervals a) on the range (
0,k_{0}
) by Gaussian quadrature; b) on the range (
k_{0},k
) by a pole extraction technique c) on the range (
k,\lambda_{L}
) by a Romberg algorithm and d) on the range (
\lambda_{L},x
) by an analytic-numeric technique. In the characterization of the exciter element, the method of moments includes the interaction of the monopole and the equivalent magnetic current ring at it's base (the contribution of the magnetic current ring in interactions with the reflector and director elements is omitted because it is negligible).