A hybrid formulation for the probe-to-patch attachment-mode current for rectangular microstrip antennas

In this paper, we present a hybrid representation for the attachment-mode current existing on the suirface of a coaxially fed rectangular microstrip patch antenna. The hybrid representation consists of a one- or two-term residue anid an eigenfunction series which gives the attachment-mode curirent at all points on the patch surface, including the probe-to-patch junction. It is numerically demonstrated that the residue and eigenfunction series blend smoothly in the close vicinity of the Stokes region which includes the probe-to-patch junction. The Stokles region is a very narrow region over which the attachment-mode current changes rapidly. The residue and eigenfunction series are used outside and within this Stokes region, respectively. This hybrid representation can be used in either spectral- or space-domain techniques for a full-wave solution to the microstrip antenna problem. The residue series is obtained by using an equivalent contour integral representation of the infinite eigenfunction series, which subsequently reduces to the Watson transform under the assumption of a slightly lossy substrate. At or near the Stokes regions the residue series is inadequate, as it cannot model the rapidly varying junction currents there. Examination of the residue series shows that the attachment mode is a superposition of exponentially attenuated, leaky, surface-traveling modes. This hybrid representation is expected to provide the optimum trade-off between speed and accuracy for computationis involving electrically large finite arrays.