Full-wave equivalent circuit of via-hole grounds in microstrip

From a rigorous study of diffraction by a via-hole modeled as a metal post in open microstrip, we derive its equivalent circuit taking into account both reactive and resistive effects due to radiation and to ohmic losses. Element values are obtained in simple form and they are easy to evaluate by a desktop computer. Comparisons are given with other theoretical full-wave analysis, with data obtained from a commercially available package, as well as with measured data.