Methods for modeling interactions between massively coupled multiple vias in multilayered electronic packaging structures

摘要

Analyzing interactions between vias in multilayered electronic packages that include at least two spaced-apart conducting planes, and multiple vias that connect signal traces on different layers. Voltages at active via ports are represented as magnetic ring current sources, which generate electromagnetic modes inside the plane structure. Substantial electromagnetic coupling between vias occurs. A full-wave solution of multiple scattering among cylindrical vias in planar waveguides is derived using Foldy-Lax equations. By using the equivalence principle, the coupling is decomposed into interior and exterior problems. For the interior problem, the dyadic Green's function is expressed in terms of vector cylindrical waves and waveguide modes. The Foldy-Lax equations for multiple scattering among the cylindrical vias are applied, and waveguide modes are decoupled in the Foldy-Lax equations. The scattering matrix of coupling among vias is then calculated for use in determining signal reflection, transmission, and/or coupling in the electronics package.