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 ( ) by Gaussian quadrature; b) on the range ( ) by a pole extraction technique c) on the range ( ) by a Romberg algorithm and d) on the range ( ) 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).