In this paper, we determine the optimal shape function for a bidirectional wire under the Elmore delay model. Given a bidirectional wire of length L, let f(x) be the width of the wire at position x, 0 ≤ x ≤ L. Let TDR be the right-to-left delay. Let TDL be the left-to-right delay. Let TBD = αTDR + βTDL be the total weighted delay where α ≥ 0 and β ≥ 0 are given weights such that α + β = 1. We determine f(x) so that TBD is minimized. Our study shows that, if α = β, the optimal shape function is f(x) = c, for some constant c; if α ≠ β, the optimal shape function can be expressed in terms of the Lambert's W function as f(x) = -cf/2c0((1/W(-ae-bx))+1), where cf is the unit length fringing capacitance, c0 is the unit area capacitance, a and b are constants in terms of the given circuit parameters. If α = 0 or β = 0, our result gives the optimal shape function for a unidirectional wire.
|Original language||English (US)|
|Number of pages||6|
|Journal||IEEE Transactions on Computer-Aided Design of Integrated Circuits and Systems|
|State||Published - 1999|
ASJC Scopus subject areas
- Computer Graphics and Computer-Aided Design
- Electrical and Electronic Engineering