Efficient analytical evaluation of the asymptotic part of Sommerfeld type reaction integrals in microstrip/slot structures

An asymptotic extraction technique has been developed for the efficient evaluation of infinite 2D spectral integrals of the method of moments matrix. Analytical, closed form expressions for the asymptotic part of the xx submatrix elements are obtained by evaluating the spectral integrals in the space domain. The xy, submatrix is expressed in the form of smooth, 1D finite integrals. These expressions allow fast evaluation with improved accuracy and reliability of the asymptotic contribution for piecewise sinusoidal expansion and test functions. The input impedance of an aperture-coupled microstrip patch antenna is presented, to determine the speed-up factor associated with efficient evaluation of integrals. The technique presented can be used for other expansion functions also if they can be expressed as a polynomial function (e.g. spline functions)