过孔转换信号完整性分析的区域分解有限元法

提出了一种基于区域分解的二维有限元法分析多层印制电路板电源/地平面中过孔转换结构的信号完整性.过孔电流产生的电磁场呈三维结构，其中，一部分电磁波沿过孔轴向传输，另一部分电磁波在电源/地平面间沿径向传播.采用一虚拟柱面将求解区域分割为过孔区和电源/地平面区.将过孔区建模为以周向磁场为主分量的二维轴对称问题，而将电源/地平面区建为以垂直电场为主分量的二维模型.首先求解电源/地平面区的二维边值问题获得分割边界上节点的波阻抗，然后将该波阻抗代入过孔区模型中分割边界节点的边界条件，从而计算出过孔信号传输的S参数.所提方法通过模型缩减可实现对微细过孔结构信号完整性的精确快速计算，且采用全波电磁场分析软件对算法的有效性和准确性进行了验证.

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.