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 pa tches requires the inclusion of a probe-to-patch attachment mode-expansion function when the substrate thickness d greater than or equal to 0.02 lambd a, where lambda is the free-space wavelength, The results for the input imp edance showed increased divergence with measurements when the attachment mo de was omitted from the full-wave analysis. The attachment mode can be expr essed as an infinite eigenfunction series that increases the fill time of t he impedance matrix in an MoM analysis. In an earlier investigation, the in finite eigenfunction series was reduced to a residue series that required o ne or two terms compared to about 55 terms for the eigenfunction series. In this paper, the convergence properties of the eigenfunction and residue se ries are investigated in view of rigorous MoM analysis. The relative errors resulting from replacing the eigenfunction by the residue series for the a ttachment mode, are compared by numerically evaluating a class of two-dimen sional (2-D) spatial integrals shown to be closely related to the elements of an MoM impedance matrix. Additionally, the computation times for the eva luation of these integrals, for the two forms of the attachment mode-expans ion function-are also included, Based on the superior convergence propertie s of the residue series for the attachment mode-expansion function, it is m athematically justified that this form can readily be used for analytic red uction of the spatial, reaction integrals from four to 2-D forms. This feat ure allows further reduction of the till time of the MoM impedance matrix, suggesting the possibility of developing an efficient space-domain MoM tech nique for modeling of wide-band microstrip antennas.