A domain decomposition finite-element method for signal integrity analysis of via transition

A two-dimensional finite-element method (FEM) based on domain decomposition was provided to analyze the signal integrity of via transition in power/ground planes pair of multilayer printed circuit board (PCB). The electromagnetic wave produced by the signal current on via barrel distributes in three-dimensional form, part of which propagates along axial direction of via barrel, while other part of which propagates along radial direction in power/ground planes. The region to be solved is partitioned into via domain and power/ground domain using a virtual cylindrical surface. The via domain is modeled as two-dimensional axial symmetrical problem whose dominant component is circumferential magnetic field, while the power/ground planes domain is modeled as another two-dimensional problem whose dominant component is vertical electric field. The wave impedance of the nodes at partition boundary is obtained through solving the two-dimensional power/ground planes boundary value problem, and then the wave impedances of nodes are substituted into the boundary condition at partition boundary of via domain, thereupon the S parameters of via signal can be calculated. Higher accuracy and rapid calculation for signal integrity of tiny via structure are realized by model reduction. The effectiveness and accuracy are validated through full wave electromagnetic simulation software.