Effect of substrate on the efficiency of an arbitrarily shaped microstrip patch antenna

A general approach is presented for the determination of power radiated via the space wave and surface wave from the aperture of an arbitrarily shaped microstrip antenna. The magnetic current model is used for this, and the analysis is carried out in the Fourier domain to determine the effect of the substrate. It has been shown that, in the Fourier domain, the longitudinal components of electric and magnetic displacement vectors follow the transmission line equation and can be solved by inspection. An expression for total radiated power has been derived. The singularities of the integral for power radiation indicate the presence of surface wave modes, and the associated power has been obtained using a singularity extraction technique. The effect of the substrate on space wave power has also been determined. This theory has been applied to a rectangular patch antenna. The results are in conformity with those reported in the literature. It has been found that for the frequency range (
h/\lambda, < 0.02
), the effect of dielectric substrate can be neglected.