A provably passive and cost-efficient model for inductive interconnects

To reduce the model complexity for inductive interconnects, the vector potential equivalent circuit (VPEC) model was introduced recently and a localized VPEC model was developed based on geometry integration. In this paper, the authors show that the localized VPEC model is not accurate for interconnects with nontrivial sizes. They derive an accurate VPEC model by inverting the inductance matrix under the partial element equivalent circuit (PEEC) model and prove that the effective resistance matrix under the resulting full VPEC model is passive and strictly diagonal dominant. This diagonal dominance enables truncating small-valued off-diagonal elements to obtain a sparsified VPEC model named truncated VPEC (tVPEC) model with guaranteed passivity. To avoid inverting the entire inductance matrix, the authors further present another sparsified VPEC model with preserved passivity, the windowed VPEC (wVPEC) model, based on inverting a number of inductance submatrices. Both full and sparsified VPEC models are SPICE compatible. Experiments show that the full VPEC model is as accurate as the full PEEC model but consumes less simulation time than the full PEEC model does. Moreover, the sparsified VPEC model is orders of magnitude (1000×) faster and produces a waveform with small errors (3%) compared to the full PEEC model, and wVPEC uses less (up to 90×) model building time yet is more accurate compared to the tVPEC model.