A simple metric for slew rate of RC circuits based on two circuit moments

In this paper, we introduce a simple metric for the slew rate of an RC circuit based on the first two circuit moments. Metrics focusing on 50% delay of RC circuits have been proposed recently that greatly improve the accuracy of the traditional Elmore delay model. However, these new models have not been applied to the determination of transition time or slew rates (e.g., 10-90% of V/sub dd/). We study how well existing approaches to 50% delay modeling translate to slew-rate modeling. We first describe a new metric called slew with two moments (S2M) that is based on Elmore's observation that the transition time of a step response is proportional to the standard deviation of the corresponding impulse response. The S2M metric modifies Elmore's original formulation by deriving a new constant of proportionality. This new constant is shown to be more accurate for general RC circuits. Next, we show that metrics relying on a simple constant multiplied by standard deviation such as S2M and Elmore do not work well for near-end nodes. To address this issue, we propose a new slew metric called scaled S2M that provides high accuracy across all types of nodes, while maintaining the advantage of a simple closed-form expression. Scaled S2M is shown to be very accurate for both near and far-end nodes. The average error for scaled S2M is approximately 2% with 96% of all nodes showing less than 5% error from a large set of industrial 0.18-/spl mu/m microprocessor nets.