RLC interconnect delay estimation via moments of amplitude and phase response

Abstract

A new category of moments-Amplitude and Phase moments (AP moments) are introduced for RLC interconnect delay estimation. We show that there are tight relationships between AP moments, circuit moments and central moments. The first order AP moment represents the Elmore delay while the higher order AP moments can be used to represent the error between the Elmore delay and the exact 50% delay from the view of gain and phase-shift variation. With the help of the physical meaning revealed by the AP moments, a closed-form 50% delay model-AP delay model is proposed for RLC interconnect delay estimation in terms of the first four AP moments. We also propose a new two-pole model (AP two-pole model) by matching the first two phase moments of the transfer function. The AP two-pole model can be used for more generally timing parameters estimation. The input signal's impact on delay estimation can be incorporated into these two delay models by simply combining the input signal's AP moments with the transfer function's AP moments. In our experiments these two models show significant accuracy improvement over the Elmore delay model.