Quasi-Static Inductance of Vertical Interconnections in Parallel-Plane Structures

Vertical interconnections between parallel planes often determine the signal- and power-integrity performance on printed-circuit-boards (PCBs). The quasi-static inductance of the port is an important parameter of the port RF impedance. In contrast to recent approaches based on a low-frequency approximation of the exact impedance solution, this letter presents a straightforward quasi-static approach. Besides the physical insight and interpretation, it establishes a general solution method, in terms of a magnetostatic boundary value problem for the quasi-static vector potential. It is found that a unique definition of the port inductance is provided by the vector potential and its average value. The result for a circular model as well as for the rectangular structure is in full agreement with the corresponding low-frequency approximations of the exact modal solution.