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

The propagation of electromagnetic waves in a grounded dielectric slab has numerous applications in printed antenna technology and in the analysis of microwave- and millimeter-wave integrated circuits. For the accurate analysis of microstrip dipoles and circuits based on the moment of method (MoM), a crucial step is the precise evaluation of the impedance matrix elements which contain the integration of Sommerfeld-type integrals. The integral transform method with the asymptotic extraction technique is formulated for calculating a Sommerfeld-type 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.