Closed-Form Crosstalk Noise Delay Metrics

In this paper we present efficient closed-form formulas to estimate capacitive coupling-induced delay in distributed RC coupling networks. The efficiency of our approach stems from the fact that only five basic operations are used in the expressions: addition (x + y), subtraction (x − y), multiplication (x × y), division (x / y) and square root (\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document} $$\left( {\sqrt x } \right)$$ \end{document}). The formulas do not require exponent computation or numerical iterations. Our estimates, though conservative, achieve acceptable accuracy. They are simple enough to be used in the inner loops of performance optimization or as cost functions for a router. The delay expressions capture the dependency on coupling direction and coupling location (near-driver and near-receiver).