An Improved Multiple Scattering Method for Via Structures With Axially Isotropic Modes in an Irregular Plate Pair

Abstract

An improved multiple scattering method is developed for an irregular plate pair where via pad/antipad radius is electrically small and the spacing between any two vias is relatively large so that the axially anisotropic parallel plate modes can be neglected. The plate-pair impedance matrix, widely used as an important parameter in power integrity analysis and also a critical part for via coupling in the intrinsic and the physics-based via models, is found to be related to the addition theorems of the zero-order axially isotropic propagating modes. As the impedance matrix of an irregular plate pair can be calculated by many analytical and numerical methods, the relationship between the plate-pair impedance matrix and the addition theorems of the zero-order axially isotropic propagating modes enables the handling of both the mutual coupling among vias and the reflection from plate-pair edges. Thus, the conventional multiple scattering method, restricted to either an infinitely large or a finite circular plate pair, can be extended to irregular plates for the via structures described earlier. The assumptions of the method are discussed and several numerical examples are provided to validate the proposed improved method.