Abstract

The Elmore delay is an extremely popular delay metric, particularly for RC tree analysis. The widespread usage of this metric is mainly attributable to it being the most accurate delay measure that is a simple analytical function of the circuit parameters. The only drawbacks to this delay metric are the uncertainty as to whether it is an optimistic or a pessimistic estimate, and the restriction to step response delay estimation.In this paper, we prove that the Elmore delay is an absolute upper bound on the 50% delay of an RC tree response. Moreover, we prove that this bound holds for input signals other than steps, and that the actual delay asymptotically approaches the Elmore delay as the input signal rise time increases. A lower bound on the delay is also developed using the Elmore delay and the second moment of the impulse response. The utility of this bound is for understanding the accuracy and the limitations of the Elmore delay metric as we use it for design automation.

Abstract

Process variations have a growing impact on circuit performance for today's integrated circuit (IC) technologies. The Non-Gaussian delay distributions as well as the correlations among delays make statistical timing analysis more challenging than ever. In this paper, we present an efficient block-based statistical timing analysis approach with linear complexity with respect to the circuit size, which can accurately predict Non-Gaussian delay distributions from realistic nonlinear gate and interconnect delay models. This approach accounts for all correlations, from manufacturing process dependence, to re-convergent circuit paths to produce more accurate statistical timing predictions. With this approach, circuit designers can have increased confidence in the variation estimates, at a low additional computation cost.

This paper proposes a definition of magnetic vector potential that can be used to evaluate sparse partial inductance matrices. Unlike the commonly applied procedure of discarding the smallest matrix terms, the proposed approach maintains accuracy at middle and high f r e q mcies and is guaranteed to be positive definite for any degree of sparsity (thereby producing stable circuit solutions). While the proposed technique is strictly based upon potential theory (i.e. the invariance of potential difserences on the zero potential reference choice), the technique is, nevertheless, presented and discussed in both circuit and magnetic terms. The conventional and the proposed sparse formulation techniques are contrasted in terms of eigenvalues and circuit simulation results on practical examples.$ This work was supported in part by IBM and the Semiconductor Research Corporation under contract 95-DJ-343. t Formerly Lawrence T. Pillage. As of Jan. 1996, he will be with Cam-