A novel asymptotic extraction technique for the efficient evaluation of a class of double Sommerfeld integrals

When the Galerkin method of moments (MoM) is used in the numerical analysis of microwave microstrip networks, elements of a network impedance matrix are required. Two dimensional (2D) Sommerfeld (spectral) integrals must be evaluated in such cases. When semi-infinite circuit feed lines are used, certain specific types of Sommerfeld integrals arise whose integrands oscillate rapidly and present serious numerical difficulties for their evaluation. In this paper, a novel, accurate, and much more efficient asymptotic extraction technique (AET) is developed that involves extracting an inner asymptotic angular integral, which is then evaluated analytically before evaluating the outer integral numerically.