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On an asymptotic formula for the maximum voltage drop in a on-chip power distribution network

We present a new asymptotic formula for the maximum static voltage in a simplified model for on-chip power distribution networks of array bonded integrated circuits. In this model the voltage is the solution of a Poisson equation in an infinite planar domain whose boundary is an array of circular pads of radius ", and we deal with the singular limit Ɛ → 0 case. In comparison with approximations that appear in the electronic engineering literature, our formula is more complete since we have obtained terms up to order Ɛ15. A procedure will be presented to compute all the successive terms, which can be interpreted as using multipole solutions of equations involving spatial derivatives of functions. To deduce the formula we use the method of matched asymptotic expansions. Our results are completely analytical and we make an extensive use of special functions and of the Gauss constant G

© European Journal of Applied Mathematics, 2011, vol. 23, núm. 2, p.245-265

Cambridge University Press (CUP)

Author: Aguareles Carrero, Maria
Haro, Jaume
Rius, Josep
Solà-Morales i Rubió, Joan de
Date: 2011
Abstract: We present a new asymptotic formula for the maximum static voltage in a simplified model for on-chip power distribution networks of array bonded integrated circuits. In this model the voltage is the solution of a Poisson equation in an infinite planar domain whose boundary is an array of circular pads of radius ", and we deal with the singular limit Ɛ → 0 case. In comparison with approximations that appear in the electronic engineering literature, our formula is more complete since we have obtained terms up to order Ɛ15. A procedure will be presented to compute all the successive terms, which can be interpreted as using multipole solutions of equations involving spatial derivatives of functions. To deduce the formula we use the method of matched asymptotic expansions. Our results are completely analytical and we make an extensive use of special functions and of the Gauss constant G
Format: application/pdf
ISSN: 0956-7925 (versió paper)
1469-4425 (versió electrònica)
Document access: http://hdl.handle.net/10256/8986
Language: eng
Publisher: Cambridge University Press (CUP)
Collection: Reproducció digital del document publicat a: http://journals.cambridge.org/action/displayAbstract?fromPage=online&aid=8509585
Articles publicats (D-IMA)
Is part of: © European Journal of Applied Mathematics, 2011, vol. 23, núm. 2, p.245-265
Rights: Tots els drets reservats
Subject: Funcions el·líptiques
Elliptic functions
Constants matemàtiques
Mathematical constants
Title: On an asymptotic formula for the maximum voltage drop in a on-chip power distribution network
Type: info:eu-repo/semantics/article
Repository: DUGiDocs

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