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

Published online by Cambridge University Press:  19 October 2011

MARIA AGUARELES
Affiliation:
IMA, UdG, Campus Montilivi, EPS-Ed. P4, E-17071 Girona, Spain email: maria.aguareles@udg.edu
JAUME HARO
Affiliation:
MA1, UPC, ETSEIB, Av. Diagonal 647, E-08028 Barcelona, Spain email: jaime.haro@upc.edu, jc.sola-morales@upc.edu
JOSEP RIUS
Affiliation:
EE, UPC, ETSEIB, Av. Diagonal 647, E-08028 Barcelona, Spain email: rius@eel.upc.edu
J. SOLÀ-MORALES
Affiliation:
MA1, UPC, ETSEIB, Av. Diagonal 647, E-08028 Barcelona, Spain email: jaime.haro@upc.edu, jc.sola-morales@upc.edu

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 the Poisson's equation in an infinite planar domain whose boundary is an array of circular pads of radius ϵ, and we deal with the singular limit ϵ → 0 case. In comparison with approximations that appear in the electronics engineering literature, our formula is more complete, since we have obtained terms up to order ϵ15. A procedure will be presented to compute all the successive terms, which can be interpreted by using multipole solutions of equations involving spatial derivatives of δ-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 the Gauss constant G.

Type
Papers
Copyright
Copyright © Cambridge University Press 2011

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