TY - JOUR

T1 - Optimal shape function for a bidirectional wire under Elmore delay model

AU - Gao, Youxin

AU - Wong, D. F.

N1 - Funding Information:
Manuscript received July 6, 1998; revised October 21, 1998. This work was supported in part by the Texas Advanced Research Program under Grant 003658288 and by a grant from Intel Corporation. This paper was recommended by Associate Editor M. Sarrafzadeh.

PY - 1999

Y1 - 1999

N2 - 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.

AB - 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.

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U2 - 10.1109/43.771180

DO - 10.1109/43.771180

M3 - Article

AN - SCOPUS:0032660942

VL - 18

SP - 994

EP - 999

JO - IEEE Transactions on Computer-Aided Design of Integrated Circuits and Systems

JF - IEEE Transactions on Computer-Aided Design of Integrated Circuits and Systems

SN - 0278-0070

IS - 7

ER -