Nonorthogonal 2.5-D PEEC for Power Integrity Analysis of Package-Board Geometries

Design of the power ground layout of a multilayered printed circuit board (PCB) is crucial for low noise and stable power supply. 2.5-D tools are better suited for early stage power distribution network (PDN) analysis over 3-D full-wave electromagnetic solvers due to faster simulation times. For example, the multilayered finite difference method (MFDM), which is based on a 2.5-D formulation on an orthogonal mesh grid, can accurately model and analyze power planes. However, this method loses its advantage while analyzing planes with irregular shapes and holes, which require unnecessarily fine discretization at boundaries for a suitable staircase approximation in an orthogonal grid. In this paper, a nonorthogonal 2.5-D partial element equivalent circuit (PEEC) formulation is proposed, employing quadrilateral mesh elements for efficient simulation of the PDN. The individual stamps for resistance, inductance, capacitance, and conductance elements for a unit quadrilateral cell are derived. Further, the methodology is enhanced to capture coplanar coupling through the introduction of mutual inductance and capacitive terms between neighboring PEEC cell pairs. The numerical results demonstrate good accuracy compared with a 3-D full-wave commercial tool for layered PCB geometries. The efficiency of the proposed method is benchmarked against an orthogonal MFDM implementation and a commercial 2.5-D tool.