Transient striction and skin effects on voltage drop across flat conductors

Closed formulas for computing the time-domain voltage between the contact points of a ground plane produced by conducted currents are presented. The approach takes into account realistic effects such as the transient skin effect and the confinement of current lines at the contacts, known as the transient striction or constriction effect. The contribution of external inductance depends on the geometry and relative position of the return conductor and is not addressed in the present paper. Calculated results are presented for various parameters, such as the dimensions of the ground plane and contacts and the type of current time-function. Using a simple geometrical model, computed results show that the ground voltage may become non-negligible when short rise-time signals are considered.