An Efficient Hybrid Finite-Element Analysis of Multiple Vias Sharing the Same Anti-Pad in an Arbitrarily Shaped Parallel-Plate Pair

A hybrid 3-D and equivalent 2-D finite-element method (FEM) is proposed for signal/power integrity analysis of multiple vias in a shared anti-pad in an arbitrarily shaped parallel-plate pair. The entire domain of the plate pair is decomposed into via-domains and plate domains by virtual interfaces. Complicated fields in via-domains, due to mode conversions from transverse electromagnetic modes in anti-pads or via-holes to parallel-plate modes, are described by a 3-D FEM while in plate domains, only the zeroth-order parallel-plate modes are assumed to exist a little far away from anti-pads. Triangular prism elements are utilized in both via-domains and plate domains. It is proven that the 3-D triangular prism element can be reduced to an equivalent 2-D triangle element by a novel edge numbering process and the boundary conditions along the interfaces of via-domains and plate domains can be automatically satisfied. The accuracy of the hybrid method has been validated by comparison with other numerical methods, and its flexibility, as well as efficiency, are also demonstrated.