A network based approach to the hybrid electromagnetic/circuit modeling of the power grid of multifunctional planar integrated circuits

A methodology is presented for the development of a numerical model for the power distribution network of the multi-functional, hybrid planar, integrated circuits. The discrete model of the structure of interest is developed in terms of two-dimensional finite element models for the domains between the closely spaced, adjacent power/ground planes and frequency-dependent multi-port network descriptions of the various three-dimensional features (e.g., pins, vias, metallization voids, and plan edges). Passive rational function fits of these network matrices allow for the development of a state-space model for the entire structure. A specific type of a network macromodel used for vias is described. Also included is a rational function model for the skin effect impedance of the metallization. A novel alternating direction implicit time-domain update scheme is used for the unconditionally stable integration of the state-space model under arbitrary current switching waveforms exciting the power distribution network.