research-article

An efficient method for statistical circuit simulation

Author:

Frank LiuAuthors Info & Claims

ICCAD '07: Proceedings of the 2007 IEEE/ACM international conference on Computer-aided design

Pages 719 - 724

Published: 05 November 2007 Publication History

Abstract

The dynamic behavior of a VLSI circuit can be described by a system of differential-algebraic equations. When some circuit elements are affected by process variations, the dynamic behavior of the circuit will deviate from its nominal trajectory. Monte-Carlo-type random sampling methods are widely used to estimate the trajectory deviation. However they can be quite time-consuming when the dimension of the parameter space is large. This paper offers an alternative solution by casting the problem into the theoretic frame work of non-linear non-Gaussian filtering. To estimate the mean and variance of the time-dependent circuit trajectory, we develop a method based on unscented transformation, which is an efficient Bayesian analysis sampling technique. Theoretically the method has linear runtime complexity. Experimental results show that compared to traditional Monte-Carlo methods, the new method can achieve over 10x speedup with less than 2% error.

References

[1]

K. Agarwal, F. Liu, C. McDowell, et al. A test structure for characterizing local device mismatches. In Proceedings of 2006 Symposium on VLSI circuits, July 2006.

[2]

H. Chang and S. Sapatnekar. Statistical timing analysis considering spatial correlation using a single PERT-like traversal. In Proceedings of IEEE/ACM Intl. Conference on Computer-Aided Design, Nov. 2003.

Digital Library

[3]

M. Chen, W. Zhao, F. Liu, and Y. Cao. Fast statistical circuit analysis with finite-point based transistor model. In Proceedings of the Design, Automation and Test Conference in Europe, Apr. 2007.

Digital Library

[4]

L. Daldoss, P. Gubian, and M. Quarantelli. Multiparameter time-domain sensitivity computation. IEEE Transactions on VLSI Systems, 48:1296--1307, Nov. 1999.

[5]

G. Evensen. Sequential data assimilation with nonlinear quasi-geostrophic model using monte carlo methods to forecast error statistics. Journal of Geophysical Research, 9, May 1994.

[6]

C. W. Gear. Numerical initial value problems in ordinary differential equations. Prentice-Hall, Englewood Cliffs, NJ, 1971.

Digital Library

[7]

A. H. Jazwinski. Stochastic process and filtering theory. Academic Press, New York and London, 1970.

[8]

S. Julier and J. K. Uhlmann. A general method for approximating nonlinear transformations of probability distributions. Available online http://citeseer.ist.psu.edu/julier96general.html, 1996.

[9]

S. Julier and J. K. Uhlmann. A new extension of the Kalman Filter to nonlinear systems. Available online http://citeseer.ist.psu.edu/julier97new.html, 1997.

[10]

R. E. Kalman. A new approach to linear filtering and prediction problems. Transaction of the ASME, Journal of Basic Engineering, 82, Mar. 1960.

[11]

R. Kanj, R. Joshi, and S. R. Nassif. Mixture importance sampling and its application on the analysis of SRAM designs in the presence of rare failure events. In Proceedings of the ACM/IEEE Design Automation Conference, pages 69--72, July 2006.

Digital Library

[12]

P. E. Kloeden and E. Platen. Numerical solution of stochastic differential equations. Springer-Verlag, 1992.

[13]

L. T. Pang and B. Nikolic. Impact of layout on 90nm cmos process parameter flucturations. In Proceedings of 2006 Symposium on VLSI circuits, July 2006.

[14]

C. Visweswariah, K. Ravinder, et al. First-order incremental block-based statistical timing analysis. IEEE Transactions on Computer-Aided Design of Integrated Circuits and Systems, 25:2170--2180, Oct. 2006.

Digital Library

[15]

S. F. Wojtkiewicz and L. A. Bergman. Numerical solution of high dimensional Fokker-Planck equations. In The 8th ASCE specialty conference on probablistic mechanics and structural reliability, July 2000.

[16]

Y. Zhan, A. J. Strojwas, et al. Correlation-aware statistical timing analysis with non-Gaussian delay distributions. In Proceedings of the ACM/IEEE Design Automation Conference, pages 77--82, June 2005.

Digital Library

Cited By

Srinivasan RCarter HLombardi FBhanja SMassoud YBahar R(2009)A taylor series methodology for analyzing the effects of process variation on circuit operationProceedings of the 19th ACM Great Lakes symposium on VLSI10.1145/1531542.1531593(203-208)Online publication date: 10-May-2009
https://dl.acm.org/doi/10.1145/1531542.1531593

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Published In

cover image ACM Conferences

ICCAD '07: Proceedings of the 2007 IEEE/ACM international conference on Computer-aided design

November 2007

933 pages

ISBN:1424413826

General Chair:
Georges Gielen
ESAT-MICAS, Katholieke Univ. Leuven, Leuven, Belgium

Sponsors

CEDA: Council on Electronic Design Automation
SIGDA: ACM Special Interest Group on Design Automation
IEEE CASS/CANDE
IEEE-CS\DATC: IEEE Computer Society

Publisher

IEEE Press

Publication History

Published: 05 November 2007

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ICCAD07

Sponsor:

CEDA
SIGDA
IEEE-CS\DATC

ICCAD07: The International Conference on Computer-Aided Design 2007

November 5 - 8, 2007

California, San Jose

Acceptance Rates

ICCAD '07 Paper Acceptance Rate 139 of 510 submissions, 27%;

Overall Acceptance Rate 457 of 1,762 submissions, 26%

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Cited By

Srinivasan RCarter HLombardi FBhanja SMassoud YBahar R(2009)A taylor series methodology for analyzing the effects of process variation on circuit operationProceedings of the 19th ACM Great Lakes symposium on VLSI10.1145/1531542.1531593(203-208)Online publication date: 10-May-2009
https://dl.acm.org/doi/10.1145/1531542.1531593

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