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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01 Oct 2007
TL;DR: The methodology combines statistical techniques with direct investigation of circuit behavior, and achieves model simplification and computational efficiency while ensuring sufficient accuracy, and ensures fast convergence to the global optimal design.
Abstract: A methodology for constructing circuit-level mismatch models and performing yield optimization is presented for CMOS analog circuits. The methodology combines statistical techniques with direct investigation of circuit behavior, and achieves model simplification and computational efficiency while ensuring sufficient accuracy. The circuit-level mismatch model can be used in performance characterization and yield estimation, both important in providing information for circuit reliability analysis. The proposed yield optimization technique consists of constructing and refining a yield model over the designable parameters, and ensures fast convergence to the global optimal design. The experimental results on two representative circuits confirm the efficiency and effectiveness of the proposed method.
2 citations
TL;DR: This paper builds on the scaled sigma sampling (SSS) foundation presented earlier and develops a formalism for efficient assessment of circuit yield exposure to low probability tails, including estimation of its confidence interval and optimization of process sigma scale factors and sample sizes used for the SPICE simulations.
Abstract: Spiraling costs of a product revision demand that we mitigate risks to product yield due to unintended disconnects between SPICE models used for design and production silicon, and intentional process retargeting for product performance optimization. This often necessitates product robustness to about +/−4.0-sigmas or about 60 ppm. However, the computational costs of even the most advanced simulation techniques are so prohibitive for many of the large circuit design problems that one often cannot obtain visibility to circuit behavior below about 5000 ppm. In this paper, we build on the scaled sigma sampling (SSS) foundation presented earlier and develop a formalism for efficient assessment of circuit yield exposure to low probability tails, including estimation of its confidence interval and optimization of process sigma scale factors and sample sizes used for the SPICE simulations. We illustrate the efficacy of SSS through an extended suite of circuit yield estimation examples including one that investigates the yield dependencies of a normality capable metric on process shifts and multiplicity.
2 citations
Patent•
IBM1
TL;DR: In this article, a first level integration solver is used to obtain a first probability distribution function modeling variations within a chip and to perform a discontinuous first-level integration with the first distribution function.
Abstract: Systems and methods for determining a chip yield are disclosed. One system includes a first level integration solver and a second level integration solver. The first level integration solver is configured to obtain a first probability distribution function modeling variations within a chip and to perform a discontinuous first level integration with the first probability distribution function. In addition, the second level integration solver is implemented by a hardware processor and is configured to perform a continuous second level integration based on a second probability distribution function modeling variations between dies to determine the chip yield.
2 citations
TL;DR: Experiments showed that ALAMO method is more accurate than Monte Carlo analysis and @s-space method, and scales well even for analog circuits involving hundreds of fingered MOSFETs.
2 citations
TL;DR: A new method to estimate the variation bounds of analog circuit performance is proposed, which combines design of experiment techniques with the Cornish-Fisher expansion and demonstrates a better accuracy/efficiency ratio than Monte-Carlo-based methods.
Abstract: In nanoscale integrated circuit technologies, process parameter fluctuations gain increasingly in importance. Efficient methods are thus required during the design phase to evaluate the resulting variability. In this letter, we propose a new method to estimate the variation bounds of analog circuit performance. This method combines design of experiment techniques with the Cornish-Fisher expansion: process parameter variations are first mapped to circuit performance metrics by a quadratic model, and then an analytical approximation of the performance distribution's quantiles enables the enclosure of the performance variations. The proposed method demonstrates a better accuracy/efficiency ratio than Monte-Carlo-based methods.
2 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