A CLOSED-FORM SPATIAL GREENS-FUNCTION FOR THE THICK MICROSTRIP SUBSTRATE

The spatial Green's function for the open microstrip structure, especially with a thick substrate, is generally represented by time-consuming Sommerfeld integrals. In this paper, through the Sommerfeld identity, a closed-form spatial Green's function of a few terms is found from the quasi-dynamic images, the complex images, and the surface waves. With the numerical integration of the Sommerfeld integrals thus avoided, this closed-form Green's function is computationally very efficient. Numerical examples show that the closed-form Green's function gives less than 1% error for all substrates and source-to-field distances.