Abstract
In this chapter, we present a stochastic method for analyzing the voltage drop variations of on-chip power grid networks with log-normal leakage current variations, which is called StoEKS and which still applies the spectral-stochastic-method to solve for the variational responses. But different from the existing spectral-stochastic-based simulation method, the EKS method [191, 177] is employed to compute variational responses using the augmented matrices consisting of the coefficients of Hermite polynomials. Our work is inspired by recent spectral-stochastic-based model order reduction method 2[214]. We apply this work to the variational analysis of on-chip power grid networks considering the variational leakage currents with the log-normal distribution.
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References
Y. Cao, Y. Lee, T. Chen, and C. C. Chen, “HiPRIME: hierarchical and passivity reserved interconnect macromodeling engine for RLKC power delivery,” in Proc. Design Automation Conf. (DAC), 2002, pp. 379–384.
C. Chiang and J. Kawa, Design for Manufacturability. Springer, 2007.
P. Ghanta, S. Vrudhula, R. Panda, and J. Wang, “Stochastic power grid analysis considering process variations,” in Proc. Design, Automation and Test In Europe. (DATE), vol. 2, 2005, pp. 964–969.
Y. S. Kumar, J. Li, C. Talarico, and J. Wang, “A probabilistic collocation method based statistical gate delay model considering process variations and multiple input switching,” in Proc. Design, Automation and Test In Europe. (DATE), 2005, pp. 770–775.
Y. Lee, Y. Cao, T. Chen, J. Wang, and C. Chen, “HiPRIME: Hierarchical and passivity preserved interconnect macromodeling engine for RLKC power delivery,” IEEE Trans. on Computer-Aided Design of Integrated Circuits and Systems, vol. 24, no. 6, pp. 797–806, 2005.
D. Li, S. X.-D. Tan, and B. McGaughy, “ETBR: Extended truncated balanced realization method for on-chip power grid network analysis,” in Proc. Design, Automation and Test In Europe. (DATE), 2008, pp. 432–437.
N. Mi, J. Fan, and S. X.-D. Tan, “Simulation of power grid networks considering wires and lognormal leakage current variations,” in Proc. IEEE International Workshop on Behavioral Modeling and Simulation (BMAS), Sept. 2006, pp. 73–78.
N. Mi, J. Fan, and S. X.-D. Tan, “Statistical analysis of power grid networks considering lognormal leakage current variations with spatial correlation,” in Proc. IEEE Int. Conf. on Computer Design (ICCD), 2006, pp. 56–62.
N. Mi, S. X.-D. Tan, Y. Cai, and X. Hong, “Fast variational analysis of on-chip power grids by stochastic extended krylov subspace method,” IEEE Trans. on Computer-Aided Design of Integrated Circuits and Systems, vol. 27, no. 11, pp. 1996–2006, 2008.
N. Mi, S. X.-D. Tan, P. Liu, J. Cui, Y. Cai, and X. Hong, “Stochastic extended Krylov subspace method for variational analysis of on-chip power grid networks,” in Proc. Int. Conf. on Computer Aided Design (ICCAD), 2007, pp. 48–53.
L. T. Pillage and R. A. Rohrer, “Asymptotic waveform evaluation for timing analysis,” IEEE Trans. on Computer-Aided Design of Integrated Circuits and Systems, pp. 352–366, April 1990.
S. X.-D. Tan and L. He, Advanced Model Order Reduction Techniques in VLSI Design. Cambridge University Press, 2007.
“Umfpack,” http://www.cise.ufl.edu/research/sparse/umfpack/.
J. M. Wang and T. V. Nguyen, “Extended Krylov subspace method for reduced order analysis of linear circuit with multiple sources,” in Proc. IEEE/ACM Design Automation Conference (DAC), 2000, pp. 247–252.
Y. Zou, Y. Cai, Q. Zhou, X. Hong, S. X.-D. Tan, and L. Kang, “Practical implementation of stochastic parameterized model order reduction via hermite polynomial chaos,” in Proc. Asia South Pacific Design Automation Conf. (ASPDAC), Jan 2007, pp. 367–372.
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Shen, R., Tan, S.XD., Yu, H. (2012). Statistical Power Grid Analysis by Stochastic Extended Krylov Subspace Method. In: Statistical Performance Analysis and Modeling Techniques for Nanometer VLSI Designs. Springer, Boston, MA. https://doi.org/10.1007/978-1-4614-0788-1_9
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DOI: https://doi.org/10.1007/978-1-4614-0788-1_9
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