According to Marc E. Goldfarb and Robert A. Pucel  a via hole ground in microstrip is a series of a resistance and an inductance. The given model for a cylindrical via hole has been verified numerically and experimentally for a range of .
whence is the via length (substrate height) and the via's radius.
The relationship for the via resistance can be used as a close approximation and is valid independent of the ratio of the metalization thickness to the skin depth. In the formula denotes the specific resistance of the conductor material.