An explicit RC-circuit delay approximation based on the first three moments of the impulse response

Abstract

Due to its simplicity, the ubiquitous Elmore delay, or first moment of the impulse response, has been an extremely popular delay metric for analyzing RC trees and meshes. Its inaccuracy has been noted however and it has been demonstrated that higher order moments can be mapped to dominant pole approximations (e.g. AWE) in the general case. The first three moments can be mapped to a two pole approximation, but stability is an issue and even a stable model results in a transcendental equation that must be iteratively evaluated to determine the delay. We describe an explicit delay approximation based on the first three moments of the impulse response. We begin with the development of a provably stable two pole transfer function/impedance model based on the first three moments (about s=0) of the impulse response. Then, since the model form is known, we evaluate the delay (any waveform percentage point) in terms of an analytical approximation that is consistently within a fraction of 1 percent of the "exact" solution for this model. The result is an accurate, explicit delay expression that will be an effective metric for high speed interconnect circuit models.