Vector potential equivalent circuit based on PEEC inversion

The geometry-integration based vector potential equivalent circuit (VPEC) was introduced to obtain a localized circuit model for inductive interconnects in A. Pacelli (2002). In this paper, we show that the method in A. Pacelli (2002) is accurate only for two-body problem. We derive N-body VPEC models based on geometry integration and inversion of the inductance matrix under the PEEC model, respectively. Both VPEC models are derived from first principles and are accurate compared to the full PEEC model. The resulting circuit matrix G^ˆ can be analyzed directly by existing simulation tools such as SPICE, and the simulation time of VPEC model is 47X less than that for PEEC model for a bus structure with 256 wires. It is also passive and strictly diagonal dominant, which leads to efficient circuit sparsification methods such as numerical and geometry based sparsifications. Compared to the full PEEC model, the sparsified VPEC models are orders of magnitude faster and produce waveforms with very small error.