Optimal shape function for a bi-directional wire under Elmore delay model

Youxin Gao; D. F. Wong

doi:10.1109/ICCAD.1997.643603

Optimal shape function for a bi-directional wire under Elmore delay model

Youxin Gao, D. F. Wong

Office of the Provost

Research output: Chapter in book/report/conference proceeding › Chapter › peer-review

16 Citations (Scopus)

Abstract

In this paper, we determine the optimal shape function for a bi-directional wire under the Elmore delay model. Given a bi-directional wire of length L, let f(x) be the width of the wire at position x, 0≤x≤L. Let T_DR be the right-to-left delay. Let T_DL be the left-to-right delay. Let T_BD = αT_DR+βT_DL 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 T_BD 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) = -c_f/2c₀(1/W(-ae^-bx)+1), where c_f 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 uni-directional wire.

Original language	English
Title of host publication	1997 IEEE International Conference on Computer Aided Design, ICCAD 1997
Publisher	IEEE
Pages	622-627
Number of pages	6
ISBN (Print)	0818682000
DOIs	https://doi.org/10.1109/ICCAD.1997.643603
Publication status	Published - Nov 1997
Event	1997 IEEE/ACM International Conference on Computer-Aided Design, ICCAD 1997 - San Jose, United States Duration: 9 Nov 1997 → 13 Nov 1997 https://ieeexplore.ieee.org/xpl/conhome/5191/proceeding (Link to conference proceedings)

Publication series

Name	Proceedings of IEEE International Conference on Computer Aided Design
Publisher	IEEE

Conference

Conference	1997 IEEE/ACM International Conference on Computer-Aided Design, ICCAD 1997
Country/Territory	United States
City	San Jose
Period	9/11/97 → 13/11/97
Internet address	https://ieeexplore.ieee.org/xpl/conhome/5191/proceeding (Link to conference proceedings)

Scopus Subject Areas

Software
Computer Science Applications
Computer Graphics and Computer-Aided Design

Access to Document

10.1109/ICCAD.1997.643603

Cite this

@inbook{27301200f69c4b4fb57300f5ef01e801,

title = "Optimal shape function for a bi-directional wire under Elmore delay model",

abstract = "In this paper, we determine the optimal shape function for a bi-directional wire under the Elmore delay model. Given a bi-directional 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 uni-directional wire.",

author = "Youxin Gao and Wong, {D. F.}",

note = "Publisher Copyright: {\textcopyright} 1997 IEEE; 1997 IEEE/ACM International Conference on Computer-Aided Design, ICCAD 1997 ; Conference date: 09-11-1997 Through 13-11-1997",

year = "1997",

month = nov,

doi = "10.1109/ICCAD.1997.643603",

language = "English",

isbn = "0818682000",

series = "Proceedings of IEEE International Conference on Computer Aided Design",

publisher = "IEEE",

pages = "622--627",

booktitle = "1997 IEEE International Conference on Computer Aided Design, ICCAD 1997",

address = "United States",

url = "https://ieeexplore.ieee.org/xpl/conhome/5191/proceeding",

}

Gao, Y & Wong, DF 1997, Optimal shape function for a bi-directional wire under Elmore delay model. in 1997 IEEE International Conference on Computer Aided Design, ICCAD 1997. Proceedings of IEEE International Conference on Computer Aided Design, IEEE, pp. 622-627, 1997 IEEE/ACM International Conference on Computer-Aided Design, ICCAD 1997, San Jose, California, United States, 9/11/97. https://doi.org/10.1109/ICCAD.1997.643603

TY - CHAP

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

AU - Gao, Youxin

AU - Wong, D. F.

PY - 1997/11

Y1 - 1997/11

N2 - In this paper, we determine the optimal shape function for a bi-directional wire under the Elmore delay model. Given a bi-directional 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 uni-directional wire.

AB - In this paper, we determine the optimal shape function for a bi-directional wire under the Elmore delay model. Given a bi-directional 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 uni-directional wire.

UR - http://www.scopus.com/inward/record.url?scp=0031336426&partnerID=8YFLogxK

U2 - 10.1109/ICCAD.1997.643603

DO - 10.1109/ICCAD.1997.643603

M3 - Chapter

AN - SCOPUS:0031336426

SN - 0818682000

T3 - Proceedings of IEEE International Conference on Computer Aided Design

SP - 622

EP - 627

BT - 1997 IEEE International Conference on Computer Aided Design, ICCAD 1997

PB - IEEE

T2 - 1997 IEEE/ACM International Conference on Computer-Aided Design, ICCAD 1997

Y2 - 9 November 1997 through 13 November 1997

ER -

Optimal shape function for a bi-directional wire under Elmore delay model

Abstract

Publication series

Conference

Scopus Subject Areas

Access to Document

Other files and links

Fingerprint

Cite this