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.< >