The excess capacitance of a microstrip via in a dielectric substrate

The equivalent circuit of a via that connects two semi-infinite microstrip transmission lines imbedded in a dielectric medium above a ground plane is considered. The T-type equivalent circuit consists of an excess capacitance and an excess inductance. The excess inductance of the via is the same as the one computed in the case of free space (without a substrate). The excess capacitance of the via is computed quasi-statically by the method of moments and the image method from the integral equations. Parametric plots of the excess capacitance of the via are given for reference