Hierarchical statistical characterization of mixed-signal circuits using behavioral modeling
10 Nov 1996-pp 374-380
TL;DR: A methodology for hierarchical statistical circuit characterization which does not rely upon circuit-level Monte Carlo simulation is presented and permits the statistical characterization of large analog and mixed-signal systems.
Abstract: A methodology for hierarchical statistical circuit characterization which does not rely upon circuit-level Monte Carlo simulation is presented. The methodology uses principal component analysis, response surface methodology, and statistics to directly calculate the statistical distributions of higher-level parameters from the distributions of lower-level parameters. We have used the methodology to characterize a folded cascode operational amplifier and a phase-locked loop. This methodology permits the statistical characterization of large analog and mixed-signal systems, many of which are extremely time-consuming or impossible to characterize using existing methods.
Citations
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06 Nov 2014
TL;DR: In this article, a hierarchical stochastic spectral simulator was developed to simulate a complex circuit or system consisting of several blocks, and a fast simulation approach based on anchored ANOVA (analysis of variance) for some design problems with many process variations.
Abstract: Process variations are a major concern in today’s chip design since they can significantly degrade chip performance. To predict such degradation, existing circuit and MEMS simulators rely on Monte Carlo algorithms, which are typically too slow. Therefore, novel fast stochastic simulators are highly desired. This paper first reviews our recently developed stochastic testing simulator that can achieve speedup factors of hundreds to thousands over Monte Carlo. Then, we develop a fast hierarchical stochastic spectral simulator to simulate a complex circuit or system consisting of several blocks. We further present a fast simulation approach based on anchored ANOVA (analysis of variance) for some design problems with many process variations. This approach can reduce the simulation cost and can identify which variation sources have strong impacts on the circuit’s performance. The simulation results of some circuit and MEMS examples are reported to show the effectiveness of our simulator.
33 citations
Patent•
29 Sep 2000TL;DR: In this paper, a computer implemented method for statistical modeling and simulation of the impact of global variation and local mismatch on the performance of integrated circuits, comprises the steps of estimating a representation of component mismatch from device performance measurements in a form suitable for circuit simulation.
Abstract: A computer implemented method for statistical modeling and simulation of the impact of global variation and local mismatch on the performance of integrated circuits, comprises the steps of: estimating a representation of component mismatch from device performance measurements in a form suitable for circuit simulation; reducing the complexity of statistical simulation by performing a first level principal component or principal factor decomposition of global variation, including screening; further reducing the complexity of statistical simulation by performing a second level principal component decomposition including screening for each factor retained in the first level principal component decomposition step to represent local mismatch; and performing statistical simulation with the joint representation of global variation and local mismatch obtained in the second level principal component decomposition step.
29 citations
TL;DR: A conceptually simple and accurate approach of direct sampling that treats the extracted SPICE parameter sets and their physical locations as an inseparable set and thus bypasses the dangerous stage of statistical inferences is proposed.
Abstract: The continued scaling of CMOS technologies introduces new difficulties to statistical circuit analysis and invalidates many of the methodologies developed earlier. The analysis of device parameter distributions reveals multiple sources of parameter correlations, some of which exhibit mutually opposing trends. We found that applying principal component analysis (PCA) to such heterogeneous statistical data may lead to confounding of data and result in underestimation of the total parameter variance. This imposes considerable constraints on the use of several methods of statistical circuit analysis based on PCA. Also the highly nonlinear relationships between the device parameters become more pronounced and cannot be approximated as linear even in the differential range. As a result, the response surface models based on the linear expansion of the performance variable around the nominal point of the device model parameters may lead to significant prediction errors. To address these difficulties, we propose a conceptually simple and accurate approach of direct sampling that treats the extracted SPICE parameter sets and their physical locations as an inseparable set and thus bypasses the dangerous stage of statistical inferences. We illustrate the methodology by applying it to the statistical analysis of a production CMOS process.
29 citations
Cites methods from "Hierarchical statistical characteri..."
...As a way to alleviate this problem, it has been proposed to utilize the methods of multivariate statistics such as principal component analysis (PCA) and factor analysis (FA) [4], [ 6 ], [7]....
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TL;DR: An efficient numerical algorithm for estimating the parametric yield of analog/RF circuits, considering large-scale process variations, which is particularly developed to handle multiple correlated nonnormal performance distributions, thereby providing better accuracy than the traditional techniques.
Abstract: In this paper, we propose an efficient numerical algorithm for estimating the parametric yield of analog/RF circuits, considering large-scale process variations. Unlike many traditional approaches that assume normal performance distributions, the proposed approach is particularly developed to handle multiple correlated nonnormal performance distributions, thereby providing better accuracy than the traditional techniques. Starting from a set of quadratic performance models, the proposed parametric yield estimation conceptually maps multiple correlated performance constraints to a single auxiliary constraint by using a MAX operator. As such, the parametric yield is uniquely determined by the probability distribution of the auxiliary constraint and, therefore, can easily be computed. In addition, two novel numerical algorithms are derived from moment matching and statistical Taylor expansion, respectively, to facilitate efficient quadratic statistical MAX approximation. We prove that these two algorithms are mathematically equivalent if the performance distributions are normal. Our numerical examples demonstrate that the proposed algorithm provides an error reduction of 6.5 times compared to a normal-distribution-based method while achieving a runtime speedup of 10-20 times over the Monte Carlo analysis with 103 samples.
28 citations
05 Nov 2007
TL;DR: A novel post-silicon timing methodology to reduce random mismatches for analog circuits in sub-90 nm CMOS is proposed and a novel dynamic programming algorithm is incorporated into a fast Monte Carlo simulation flow for statistical analysis and optimization of the proposed tunable analog circuits.
Abstract: The well-known Pelgrom model (S. Ray and B. Song, 2006) has demonstrated that the variation between two devices on the same die due to random mismatch is inversely proportional to the square root of the device area: sigma ~ 1/sqrt(Area). Based on the Pelgrom model, analog devices are sized to be large enough to werage out random variations. Importantly, with CMOS scaling, variations due to random doping fluctuations are making it exceedingly difficult to control device mismatches by sizing alone; namely, the devices have to be made so large that the benefits of CMOS scaling are not realized for analog and RF circuits. In this paper we propose a novel post-silicon timing methodology to reduce random mismatches for analog circuits in sub-90 nm CMOS. A novel dynamic programming algorithm is incorporated into a fast Monte Carlo simulation flow for statistical analysis and optimization of the proposed tunable analog circuits. We apply the proposed post-silicon tuning methodology to several commonly-used analog circuit blocks. We demonstrate that with the post-silicon tuning, device mismatch exponentially decreases as area increases: sigma-exp(-alpha-Area).
27 citations
References
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Book•
29 Aug 1995TL;DR: Using a practical approach, this book discusses two-level factorial and fractional factorial designs, several aspects of empirical modeling with regression techniques, focusing on response surface methodology, mixture experiments and robust design techniques.
Abstract: From the Publisher:
Using a practical approach, it discusses two-level factorial and fractional factorial designs, several aspects of empirical modeling with regression techniques, focusing on response surface methodology, mixture experiments and robust design techniques. Features numerous authentic application examples and problems. Illustrates how computers can be a useful aid in problem solving. Includes a disk containing computer programs for a response surface methodology simulation exercise and concerning mixtures.
10,104 citations
"Hierarchical statistical characteri..." refers methods in this paper
...The non-Monte Carlo techniques described in this paper utilize response surface methodology (RSM) [6]....
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3,788 citations
"Hierarchical statistical characteri..." refers methods in this paper
...The most widely used technique for performing statistical characterization is Monte Carlo analysis [1, 2]....
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Book•
13 Mar 1991
TL;DR: In this paper, the authors present a directory of Symbols and Definitions for PCA, as well as some classic examples of PCA applications, such as: linear models, regression PCA of predictor variables, and analysis of variance PCA for Response Variables.
Abstract: Preface.Introduction.1. Getting Started.2. PCA with More Than Two Variables.3. Scaling of Data.4. Inferential Procedures.5. Putting It All Together-Hearing Loss I.6. Operations with Group Data.7. Vector Interpretation I : Simplifications and Inferential Techniques.8. Vector Interpretation II: Rotation.9. A Case History-Hearing Loss II.10. Singular Value Decomposition: Multidimensional Scaling I.11. Distance Models: Multidimensional Scaling II.12. Linear Models I : Regression PCA of Predictor Variables.13. Linear Models II: Analysis of Variance PCA of Response Variables.14. Other Applications of PCA.15. Flatland: Special Procedures for Two Dimensions.16. Odds and Ends.17. What is Factor Analysis Anyhow?18. Other Competitors.Conclusion.Appendix A. Matrix Properties.Appendix B. Matrix Algebra Associated with Principal Component Analysis.Appendix C. Computational Methods.Appendix D. A Directory of Symbols and Definitions for PCA.Appendix E. Some Classic Examples.Appendix F. Data Sets Used in This Book.Appendix G. Tables.Bibliography.Author Index.Subject Index.
3,534 citations
Book•
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01 Jan 1971
3,429 citations
"Hierarchical statistical characteri..." refers background or methods in this paper
...6 is used to compute cov yi; yj [13]....
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...Note that for any given coefficients in a quadratic equation, A is uniquely determined [13]....
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Book•
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01 Jan 1964
TL;DR: The general nature of Monte Carlo methods can be found in this paper, where a short resume of statistical terms is given, including random, pseudorandom, and quasirandom numbers.
Abstract: 1 The general nature of Monte Carlo methods.- 2 Short resume of statistical terms.- 3 Random, pseudorandom, and quasirandom numbers.- 4 Direct simulation.- 5 General principles of the Monte Carlo method.- 6 Conditional Monte Carlo.- 7 Solution of linear operator equations.- 8 Radiation shielding and reactor criticality.- 9 Problems in statistical mechanics.- 10 Long polymer molecules.- 11 Percolation processes.- 12 Multivariable problems.- References.
3,226 citations