Physics-Based Inductance Extraction for Via Arrays in Parallel Planes for Power Distribution Network Design

A systematic approach for inductance extraction for via arrays between two parallel planes is presented. Both self and mutual inductance values are obtained based on a cavity model. The physics associated with the via inductances is analyzed, and a rigorous method is developed to derive an equivalent total inductance for multiple via arrays. Analytical equations for the equivalent total inductance are derived in closed forms for simple cases. The proposed method is corroborated with measurements, and application of the method for power distribution network designs is demonstrated.