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Asymptotic probability extraction for non-normal distributions of circuit performance

Publication ,  Conference
Li, X; Le, J; Gopalakrishnan, P; Pileggi, LT
Published in: IEEE/ACM International Conference on Computer-Aided Design, Digest of Technical Papers, ICCAD
December 1, 2004

While process variations are becoming more significant with each new IC technology generation, they are often modeled via linear regression models so that the resulting performance variations can be captured via Normal distributions. Nonlinear (e.g. quadratic) response surface models can be utilized to capture larger scale process variations; however, such models result in non-Normal distributions for circuit performance which are difficult to capture since the distribution model is unknown. In this paper we propose an asymptotic probability extraction method, APEX, for estimating the unknown random distribution when using nonlinear response surface modeling. APEX first uses a novel binomial moment evaluation to efficiently compute the high order moments of the unknown distribution, and then applies moment matching to approximate the characteristic function of the random circuit performance by an efficient rational function. A simple statistical timing example and an analog circuit example demonstrate that APEX can provide better accuracy than Monte Carlo simulation with 104 samples and achieve orders of magnitude more efficiency. We also show the error incurred by the popular Normal modeling assumption using standard IC technologies. ©2004 IEEE.

Duke Scholars

Published In

IEEE/ACM International Conference on Computer-Aided Design, Digest of Technical Papers, ICCAD

ISSN

1092-3152

Publication Date

December 1, 2004

Start / End Page

2 / 9
 

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Li, X., Le, J., Gopalakrishnan, P., & Pileggi, L. T. (2004). Asymptotic probability extraction for non-normal distributions of circuit performance. In IEEE/ACM International Conference on Computer-Aided Design, Digest of Technical Papers, ICCAD (pp. 2–9).
Li, X., J. Le, P. Gopalakrishnan, and L. T. Pileggi. “Asymptotic probability extraction for non-normal distributions of circuit performance.” In IEEE/ACM International Conference on Computer-Aided Design, Digest of Technical Papers, ICCAD, 2–9, 2004.
Li X, Le J, Gopalakrishnan P, Pileggi LT. Asymptotic probability extraction for non-normal distributions of circuit performance. In: IEEE/ACM International Conference on Computer-Aided Design, Digest of Technical Papers, ICCAD. 2004. p. 2–9.
Li, X., et al. “Asymptotic probability extraction for non-normal distributions of circuit performance.” IEEE/ACM International Conference on Computer-Aided Design, Digest of Technical Papers, ICCAD, 2004, pp. 2–9.
Li X, Le J, Gopalakrishnan P, Pileggi LT. Asymptotic probability extraction for non-normal distributions of circuit performance. IEEE/ACM International Conference on Computer-Aided Design, Digest of Technical Papers, ICCAD. 2004. p. 2–9.

Published In

IEEE/ACM International Conference on Computer-Aided Design, Digest of Technical Papers, ICCAD

ISSN

1092-3152

Publication Date

December 1, 2004

Start / End Page

2 / 9