PERI: a technique for extending delay and slew metrics to ramp inputs

Recent years have seen significant research in finding closed-form formulae for the delay of an RC circuit that improves upon the Elmore delay model. However, several of these formulae assume a step excitation, leaving it to the reader to find a suitable extension to ramp inputs. The few works that do consider ramp inputs do not present a closed-form formula that works for a wide range of possible input slews. We propose a new technique, PERI (Probability distribution function Extension for Ramp Inputs), that extends delay metrics for step inputs to the more general and realistic non-step (such as a saturated ramp) inputs. Although there has been little work done in finding good slew (which is also referred as signal transition time) metrics, we also show how one can extend a slew metric for step inputs to the non-step case. We validate the efficacy of our approach through experimental results from several hundred RC dominated nets extracted from an industry ASIC design.