Weibull-based analytical waveform model

Current complimentary metal-oxide-semiconductor technologies are characterized by interconnect lines with increased relative resistance with respect to driver output resistance. Designs generate signal waveshapes that are very difficult to model using a single-parameter model such as the transition time. In this paper, we present a simple and robust two-parameter analytical expression for waveform modeling based on the Weibull cumulative distribution function. The Weibull model accurately captures the variety of waveshapes without introducing significant runtime overhead and produces results with less than 5% error. We also present a fast and simple algorithm to convert waveforms obtained by circuit simulation to the Weibull model. A methodology for characterizing gates for the new model is also presented. Simulation results for many single- and multiple-input gates show errors well below 5%. Our model can be used in a mixed environment where some signals may still be characterized by a single parameter.