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

Abstract

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 ε, and we deal with the singular limit ε → 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 ε 15 . 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 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 of the Gauss constant G.

Derivation of the maximum voltage drop in power grids of integrated circuits with an array bonding package

“…Such pads, as it will be described in the following section, can be manufactured in different shapes, although squared pads are the most commonly produced pads. The aim in this paper is to extend the results in Aguareles et al [3] to provide a formula for the maximum voltage drop in a power distribution network when the pads are small squares of side 2ε. The same problem with circular pads was tackled in [14], where the authors claimed that the maximum voltage drop could be approximated by 1 2π…”

“…+ o(1), (1.1) where ε is the radius of the pads. However, in [3] it is shown that the actual formula should be given by…”

“…It is precisely in this inner region where the shape of the pads comes into the play. This same idea was already used in [3] to solve the problem of circular pads. However, in the present case the inner solution is not so simple and a conformal mapping technique should be used, which implies that the inner solution for square pads is now a composition of the one for circular pads with a conformal map that sends the exterior of the disc to the exterior of the square.…”

“…

Link to this article: http://journals.cambridge.org/abstract_S0956792512000277How to cite this article: M. AGUARELES and J. de HARO (2012). Derivation of the maximum voltage drop in power grids of integrated circuits with an array bonding package.

In this work we derive a formula for the maximum value of the voltage drop that takes place in power grids of integrated circuits with an array bonding package.

…”

“…How to cite this article: M. AGUARELES and J. de HARO (2012). Derivation of the maximum voltage drop in power grids of integrated circuits with an array bonding package.…”