Multipole Expansion of Radiation From Patch Antenna Using Quasi-Static Surface Currents

Abstract

In this letter, the multipole expansion of the fields radiated from a rectangular microstrip patch antenna on an infinite ground plane is presented. Such multipole expansion allows calculating the fields at any distance (near and far fields) from the antenna. It is shown that the coefficients of the expansion can be obtained from the quasi-static fields due to the quasi-static currents on the edges of the patch. The static fields are calculated on a spherical surface enclosing the patch and its image in the infinite perfect electric conductor (PEC) ground plane by applying the duals of Coulomb's and Biot–Savart's laws. Using only the radial components of the fields on the enclosing sphere, the multipole coefficients and, hence, the fields outside the sphere are calculated. The field distributions obtained using such multipole expansion match well with the corresponding analytical approximations in the far-field and HFSS simulation results. The spatial evolution of the field components with distance from near field to far field for the patch is presented. The minor deviations of the obtained results from that of simulations and the limitations of the proposed method are discussed.