Derivation of closed-form Green´s functions for a general microstrip geometry

The derivation of the closed-form spatial domain Green´s functions for the vector and scalar potentials is presented for a microstrip geometry with a substrate and a superstrate, whose thicknesses can be arbitrary. The spatial domain Green´s functions for printed circuits are typically expressed as Sommerfeld integrals, which are inverse Hankel transforms of the corresponding spectral domain Green´s functions and are time-consuming to evaluate. Closed-form representations of these Green´s functions in the spatial domains can only be obtained if the integrands are approximated by a linear combination of functions that are analytically integrable. This is accomplished here by approximating the spectral domain Green´s functions in terms of complex exponentials by using the least square Prony´s method