Application of recursive convolution to transient simulation of interconnects using a hybrid phase-pole macromodel

A hybrid phase-pole macromodel (HPPM), which explicitly includes phase shifts (time delays) in addition to the system poles, was recently developed for modeling interconnects. In this paper, the HPPM is applied to the transient simulation of interconnects. First, the time-domain source waveform is expanded in terms of triangular expansion functions. Knowledge of the triangle impulse response (TIR) for an interconnect, which is represented in the form of an HPPM, then allows for the time domain simulation of the interconnect. A recursive convolution algorithm is adopted to carry out the required convolutions efficiently in the transient simulator. Combining this transient simulator with an HPPM extractor yields a transient interconnect signal analysis tool.