Robust and efficient method for evaluation of the non-symmetrical components of the green´s functions for microstrip structures

This study presents a robust and efficient approach for derivation of non-symmetrical closed-form Green´s functions for microstrip structures. In this method, the discrete complex image technique is used to extract the closed-form expressions for stratified Green´s functions. The surface-wave poles in these expressions are first extracted using a recursive contour integration method. The remainder is then approximated by a series of complex exponentials using either the Prony´s method or the generalised pencil-of-function (GPOF) along the extended rooftop-shaped path in k_ρ-plane. An analytical identity is subsequently employed to obtain the new spatial-domain Green´s functions. For calculation of the integral of GzxA with respect to x, it is observed that only a single approximate Green´s function can accurately represent both the near and far fields. Moreover, the method generates accurate results in the near-field region when z´´z and ρρ0. A two-part expression for the non-symmetrical potential GzxA is introduced as well. This two-part approximation is very accurate and computationally fast for the entire range of distances, especially when z=z´´0 or z´´z.