Closed-form crosstalk noise metrics for physical design applications

In this paper we present efficient closed-form formulas to estimate capacitive coupling-induced crosstalk noise for distributed RC coupling trees. The efficiency of our approach stems from the fact that only the five basic operations are used in the expressions: addition (x+y), subtraction (x-y), multiplication (x/spl times/y), division (x/y) and square root (/spl radic/x). The formulas do not require exponent computation or numerical iterations. We have developed closed-form expressions for the peak crosstalk noise amplitude, the peak noise occurring time and the width of the noise waveform. Our approximations are conservative and yet achieve acceptable accuracy. The formulas are simple enough to be used in the inner loops of performance optimization algorithms or as cost functions to guide routers. They capture the influence of coupling direction (near-end and far-end coupling) and coupling location (near-driver and near-receiver).