PRIMO: probability interpretation of moments for delay calculation

Abstract

Moments of the impulse response are widely used for interconnect delay analysis, from the explicit Elmore delay (first moment of the impulse response) expression, to moment matching methods which create reduced order transimpedance and transfer function approximations. However the Elmore delay is fast becoming ineffective for deep submicron technologies, and reduced order transfer function delays are impractical for use as early-phase design metrics or as design optimization cost functions. This paper describes an approach for fitting moments of the impulse response to probability density functions so that delays can be estimated from probability tables. For RC trees it is demonstrated that the incomplete gamma function provides a provably stable approximation. The step response delay is obtained from a one-dimensional table lookup.