Nonsingular Green’s Functions for Multi-Layer Homogeneous Microstrip Lines

In this article, three new green's functions are presented for a narrow strip line (not a thin wire) inside or on a homogeneous dielectric, supposing quasi-TEM dominant mode. These functions have no singularity in contrast to so far presented ones, so that they can be used easily to determine the capacitance matrix of multi-layer and single-layer homogeneous coupled microstrip lines. To obtain the green’s functions, the Laplace’s equation is solved analytically in Fourier integral or Fourier series expressions, taking into account the boundary conditions including the narrow strip. The validity and accuracy of three presented green’s functions are verified by some examples.