Utilizing time-domain waveform to synthesize scalable SPICE-compatible macro-models of interconnectors

A novel time-domain approach is proposed to synthesize the scalable macro-model of the interconnectors based on time-domain reflected waveforms either measured by TDR or simulated by FDTD method. The step responses of the interconnectors are solved in terms of rational functions by the generalized Pencil-of-Matrix (GPOM) method. The macro- model in terms of the rational functions pairs is obtained through microwave matrix transformation. The equivalent lumped circuits of the macro-model are synthesized by a lumped circuit extraction method (LCEM). The regression analysis is utilized to construct scalable regression equations from equivalent lumped circuits of the macro-model. The stability of the extracted models can be preserved based on this time-domain approach and the macro-model topology. Two examples, one is an un-uniform transmission line in two-layer FR4 board and the other is a through via in four-layer FR4 PCB, are used to demonstrate the accuracy of the scalable equivalent lumped circuits of the macro-model.