Some convergence considerations in space-domain moment-method analysis of a class of wide-band microstrip antennas

The method of moments (MoM) analysis of probe-fed rectangular microstrip patches requires the inclusion of a probe-to-patch attachment mode-expansion function when the substrate thickness d⩾0.02λ, where λ is the free-space wavelength. The results for the input impedance showed increased divergence with measurements when the attachment mode was omitted from the full-wave analysis. The attachment mode can be expressed as an infinite eigenfunction series that increases the fill time of the impedance matrix in an MoM analysis. In an earlier investigation, the infinite eigenfunction series was reduced to a residue series that required one or two terms compared to about 55 terms for the eigenfunction series. In this paper, the convergence properties of the eigenfunction and residue series are investigated in view of rigorous MoM analysis. The relative errors resulting from replacing the eigenfunction by the residue series for the attachment mode, are compared by numerically evaluating a class of two-dimensional (2-D) spatial integrals shown to be closely related to the elements of an MoM impedance matrix. Additionally, the computation times for the evaluation of these integrals for the two forms of the attachment mode-expansion function are also included. Based on the superior convergence properties of the residue series for the attachment mode-expansion function, it is mathematically justified that this form can readily be used for analytic reduction of the spatial, reaction integrals from four to 2-D forms. This feature allows further reduction of the fill time of the MoM impedance matrix, suggesting the possibility of developing an efficient space-domain MoM technique for modeling of wide-band microstrip antennas