Finite difference modeling of multiple planes in packages

Power/ground planes in electronic packaging can be a major factor for noise coupling. There can be noise coupling not only in the transversal direction between two planes, but also vertically from one plane pair to another through the apertures and via holes. Due to the large size of the power/ground planes, it is difficult to analyze them using full-wave simulators. It is known that the finite difference solution of the Helmholtz equation provides a faster approach with a comparable accuracy. This paper presents new circuit models for a single plane pair based on the finite difference method: T- and X-models. It also presents a modeling approach for multiple plane pairs that are coupled through apertures