Incorporating vertical discontinuities in power-bus modeling using a mixed-potential integral equation and circuit extraction formulation

Noise on the DC power-bus attributed to device switching is among the primary sources of EMI and signal integrity problems. A mixed-potential integral equation formulation with circuit extraction approach is used to model the planar multi-layer power-bus geometry, which can also include arbitrary shaped power regions on multiple layers. Incorporating vertical discontinuities, e.g. decoupling capacitor interconnects, is a critical aspect of the modeling, and must be done properly since they are included as a lumped element model and not as a part of the MPIE formulation. Agreement with experimental results verifies the validity of the present approach.