Synthesizing SPICE-compatible models of power delivery networks with resonance effect by time-domain waveforms

A novel time-domain approach is proposed to synthesize the broadband equivalent circuit model of the power delivery network based on time-domain reflected (TDR)/transmitted (TDT) waveforms either through time-domain reflectometry measurement or finite-difference time-domain (FDTD) simulation. The step responses of the power delivery network are represented in terms of rational functions by the generalized Pencil-of-Matrix (GPOM) method. According to the step responses, the macro-π model with each element represented by the optimum pole-residue forms is derived to model the power delivery networks. The equivalent circuits of the macro-π model are synthesized by a systematic lumped-model extraction technique. The accuracy of this approach is demonstrated both in frequency- and time-domain.