A novel time-domain method for synthesizing broadband macro-π models of differential via

A novel time-domain approach is proposed to synthesize the broadband equivalent model of the differential via based on time-domain reflected (TDR)/transmitted waveforms either measured by TDR or simulated by finite-difference time-domain (FDTD) method. The step responses of the differential via are solved in terms of rational functions by the generalized pencil-of-matrix (GPOM) method. According to the step responses, the broadband macro-π model with each element represented by the optimum pole-residue forms is derived to model the differential via. 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 frequencyand time-domain.