Tuning-free analysis of planar radiators based on an exact numerical evaluation of the two-dimensional generalized exponential integral

It is demonstrated that it is possible to accurately calculate the two-dimensional generalized exponential integral in the method-of-moments formulation. By performing the integration in polar coordinates over the radial variable p, the singularity existing in Cartesian coordinates is removed from the integrand. This in effect means that the commonly applied introduction of an offset into the integrand and subsequent tuning of that offset can be eliminated entirely. As a result, the calculated current distribution is unambiguous and exact. A comparison between calculated and measured input impedance data of a patch antenna shows good agreement and, hence, verifies the integral evaluation, even if a simplified model of non-overlapping subsectional expansion functions is assumed. The proposed integral calculation requires minimal computational effort; only 12 points in the Gaussian quadrature are needed to achieve results accurate to better than 0.1 percent.