Stochastic Behavioral Modeling and Analysis for Analog/Mixed-Signal Circuits

It has become increasingly challenging to model the stochastic behavior of analog/mixed-signal (AMS) circuits under large-scale process variations. In this paper, a novel moment-matching-based method has been proposed to accurately extract the probabilistic behavioral distributions of AMS circuits. This method first utilizes Latin hypercube sampling coupling with a correlation control technique to generate a few samples (e.g., sample size is linear with number of variable parameters) and further analytically evaluate the high-order moments of the circuit behavior with high accuracy. In this way, the arbitrary probabilistic distributions of the circuit behavior can be extracted using moment-matching method. More importantly, the proposed method has been successfully applied to high-dimensional problems with linear complexity. The experiments demonstrate that the proposed method can provide up to 1666X speedup over crude Monte Carlo method for the same accuracy.

[1]  C. C. McAndrew,et al.  Understanding MOSFET mismatch for analog design , 2003 .

[2]  Hao Yu,et al.  Stochastic analog circuit behavior modeling by point estimation method , 2011, ISPD '11.

[3]  Mark Denny,et al.  Introduction to importance sampling in rare-event simulations , 2001 .

[4]  Y-G Zhao,et al.  NEW POINT ESTIMATES FOR PROBABILITY MOMENTS. TECHNICAL NOTE , 2000 .

[5]  Jian Wang,et al.  SRAM parametric failure analysis , 2009, 2009 46th ACM/IEEE Design Automation Conference.

[6]  Sani R. Nassif,et al.  Modeling and analysis of manufacturing variations , 2001, Proceedings of the IEEE 2001 Custom Integrated Circuits Conference (Cat. No.01CH37169).

[7]  R. Iman,et al.  A distribution-free approach to inducing rank correlation among input variables , 1982 .

[8]  Xin Li,et al.  Finding Deterministic Solution From Underdetermined Equation: Large-Scale Performance Variability Modeling of Analog/RF Circuits , 2010, IEEE Transactions on Computer-Aided Design of Integrated Circuits and Systems.

[9]  E. Rosenblueth.  Point estimates for probability moments. , 1975, Proceedings of the National Academy of Sciences of the United States of America.

[10]  Hao Yu,et al.  PiCAP: A parallel and incremental capacitance extraction considering stochastic process variation , 2009, 2009 46th ACM/IEEE Design Automation Conference.

[11]  W. J. Conover,et al.  Practical Nonparametric Statistics , 1972 .

[12]  James D. Meindl,et al.  Impact of die-to-die and within-die parameter fluctuations on the maximum clock frequency distribution for gigascale integration , 2002, IEEE J. Solid State Circuits.

[13]  Yiyu Shi,et al.  QuickYield: An efficient global-search based parametric yield estimation with performance constraints , 2010, Design Automation Conference.

[14]  Ronald L. Wasserstein,et al.  Monte Carlo: Concepts, Algorithms, and Applications , 1997 .

[15]  M. Stein.  Large sample properties of simulations using latin hypercube sampling , 1987 .

[16]  D. Schmitt-Landsiedel,et al.  The impact of intra-die device parameter variations on path delays and on the design for yield of low voltage digital circuits , 1996, Proceedings of 1996 International Symposium on Low Power Electronics and Design.

[17]  Dongbin Xiu,et al.  The Wiener-Askey Polynomial Chaos for Stochastic Differential Equations , 2002, SIAM J. Sci. Comput..

[18]  Yan-Gang Zhao,et al.  New Point Estimates for Probability Moments , 2000 .

[19]  Trevor Hastie,et al.  The Elements of Statistical Learning , 2001 .

[20]  Sarma B. K. Vrudhula,et al.  Hermite Polynomial Based Interconnect Analysis in the Presence of Process Variations , 2006, IEEE Transactions on Computer-Aided Design of Integrated Circuits and Systems.

[21]  Hao Yu,et al.  A fast analog mismatch analysis by an incremental and stochastic trajectory piecewise linear macromodel , 2010, 2010 15th Asia and South Pacific Design Automation Conference (ASP-DAC).

[22]  Doris Schmitt-Landsiedel,et al.  The impact of intra-die device parameter variations on path delays and on the design for yield of low voltage digital circuits , 1996, ISLPED '96.

[23]  Yu Cao,et al.  Modeling the electrical effects of metal dishing due to CMP for on-chip interconnect optimization , 2004, IEEE Transactions on Electron Devices.

[24]  Lawrence T. Pileggi,et al.  Quadratic Statistical $MAX$ Approximation for Parametric Yield Estimation of Analog/RF Integrated Circuits , 2008, IEEE Transactions on Computer-Aided Design of Integrated Circuits and Systems.

[25]  M. Degroot,et al.  Probability and Statistics , 2021, Examining an Operational Approach to Teaching Probability.

[26]  Richard D. Deveaux,et al.  Applied Smoothing Techniques for Data Analysis , 1999, Technometrics.

[27]  L. Pileggi,et al.  Asymptotic probability extraction for non-normal distributions of circuit performance , 2004, ICCAD 2004.

[28]  Lawrence T. Pileggi,et al.  Asymptotic waveform evaluation for timing analysis , 1990, IEEE Trans. Comput. Aided Des. Integr. Circuits Syst..

[29]  John G. Proakis,et al.  Probability, random variables and stochastic processes , 1985, IEEE Trans. Acoust. Speech Signal Process..

[30]  Xin Li,et al.  Statistical regression for efficient high-dimensional modeling of analog and mixed-signal performance variations , 2008, 2008 45th ACM/IEEE Design Automation Conference.