Frequency-dependent via inductances for accurate power distribution network modeling

In power distribution network (PDN) modeling, interconnection inductance can play a critical role. It often determines the effectiveness of a component, such as a decoupling capacitor. This paper studies a typical one-plane-pair PDN structure with parallel power and ground planes and vertical vias in between. This work improves the conventional lumped circuit model for the PDN by introducing a model for the inductance of each via that is frequency-dependent. This frequency dependency is obtained from a rigorous cavity model formulation. The improved lumped circuit model is validated with the cavity model and the HFSS full-wave model. Further, the frequency-dependent mutual inductance between two vias can have either a positive or a negative value depending on via locations in the PDN structure, which is an interesting property that has not been reported.