Closed-form expressions for extending step delay and slew metrics to ramp inputs for RC trees

Recent years have seen significant research in finding closed form expressions 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-we always refer to saturated ramps in this paper-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 the PERI (probability distribution function extension for ramp inputs) technique, that extends delay metrics for step inputs to the more general and realistic non-step (such as a 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 application specific integrated circuit design.