A moment-based effective characterization waveform for static timing analysis

Abstract

Static timing analysis of VLSI circuits relies on tabular models of logic gates obtained during library characterization. At characterization time logic gates are simulated at the circuit level with a range of input waveforms (e.g., saturated ramps with different slews) and various output loads. At timing analysis time the same gates are driven by input waveforms that differ from the class of characterization waveforms. This paper proposes a method for mapping the waveforms that arise in static timing analysis to members of the class of waveforms used to characterize gate timing performance during library characterization. The method is based on the moments of the input waveform, which describe concisely the salient features of the waveform. The mapping between the input waveform and the effective characterization waveform is accomplished by positing functional relationships between the input waveform's moments and the parameters of the characterization waveform. The unknown coefficients of this functional relationship are determined by minimizing the worst case error of the output waveform over a representative set of input waveforms and gate loads. The technique requires no change to the library characterization procedure, and minimal change to the static timing tool with little to no additional computational burden on the timer. Copyright 2009 ACM.