Analytical technique to evaluate the asymptotic part of the impedance matrix of sommerfeld-type integrals

The integral transform method with the asymptotic extraction technique is formulated for calculating a Sommerfeldtype integral problem. This formulation allows the infinite double integral of the asymptotic part of the impedance matrix to be transformed into a finite one-dimensional (1-D) integral. This finite 1-D integral contains a spherical Legendre function and can be easily evaluated numerically after the singular part of the integral is performed analytically. It is shown that the proposed method dramatically reduces the computation time and improves the accuracy over the conventional method to evaluate the asymptotic part of impedance matrix.