Skip to main content Accessibility help
×
Home

The maximum voltage drop in an on-chip power distribution network: analysis of square, triangular and hexagonal power pad arrangements

  • TOM CARROLL (a1) and JOAQUIM ORTEGA-CERDÀ (a2)

Abstract

A mathematical model of the voltage drop which arises in on-chip power distribution networks is used to compare the maximum voltage drop in the case of different geometric arrangements of the pads supplying power to the chip. These include the square or Manhattan power pad arrangement, which currently predominates, as well as equilateral triangular and hexagonal arrangements. In agreement with the findings in the literature and with physical and SPICE models, the equilateral triangular power pad arrangement is found to minimize the maximum voltage drop. This headline finding is a consequence of relatively simple formulas for the voltage drop, with explicit error bounds, which are established using complex analysis techniques, and elliptic functions in particular.

Copyright

References

Hide All
[1]Abramowitz, M. and Stegun, I. A. (eds.) (1992) Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables, Dover, New York, NY, xiv+1046 pp (reprint of the 1972 edition).
[2]Aguareles, M., Haro, J., Rius, J. and Solà-Morales, J. (2012) On an asymptotic formula for the maximum voltage drop in a on-chip power distribution network. Euro. J. Appl. Math. 23 (2), 245265.
[3]Chen, H., Cheng, C.-K., Kahng, A. B., Mandoiu, I., Wang, Q. and Yao, B. (2003) The Y-architecture for on-chip interconnect: Analysis and methodology. In: Proceedings of the 2003 IEEE/ACM International Conference on Computer-Aided Design, 9–13 November, 13 pp.
[4]Gröchenig, K. and Lyubarskii, Y. (2009) Gabor (super) frames with Hermite functions. Math. Ann. 345, 267286.
[5]Hayman, W. K. (1974) The local growth of the power series: A survey of the Wiman-Valiron method. Canad. Math. Bull. 17 (3), 317358.
[6]Hille, E. (1949) Analytic Function Theory, Ginn and Co., Oxford, UK.
[7]Lin, C.-S. and Chin-Lung, W. (2010) Elliptic functions, Green functions and the mean field equations on tori. Ann. Math. 172 (2), 911954.
[8]Sandier, E. and Serfaty, S. (2012) From the Ginzburg–Landau Model to vortex lattice problems. Comm. Math. Phys. 313, 635743.
[9]Shakeri, K. and Meindl, J. D. (2005) Compact physical IR-drop models for chip/package co-design of gigascale integration (GSI). IEEE Trans. Electron Devices 52 (6), 10871096.

Keywords

Metrics

Altmetric attention score

Full text views

Total number of HTML views: 0
Total number of PDF views: 0 *
Loading metrics...

Abstract views

Total abstract views: 0 *
Loading metrics...

* Views captured on Cambridge Core between <date>. This data will be updated every 24 hours.

Usage data cannot currently be displayed