A uniform asymptotic expansion for the Green´s functions used in microstrip calculations

A uniform asymptotic approximation is developed in the limit of small substrate thickness for the Green´s functions used in microstrip-type problems. The author develops an approximation which is uniformly valid for all distances from the source in the limit where the substrate region is thin, which is typically the case of interest for microstrip problems. The approximation is valid for a single-layer substrate. The expansions agree with previously published near and far-field results. The approximation is compared with numerical evaluations of the exact integral solution available for the problem.