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Proceedings ArticleDOI

Hierarchical statistical characterization of mixed-signal circuits using behavioral modeling

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.

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Citations
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Proceedings ArticleDOI
02 Oct 2009
TL;DR: A piecewise modeling algorithm is proposed that optimally partitions the parameter space into several regions and, on each of them, fits a linear or a quadratic function to the performance metrics.
Abstract: In nano-scale IC technologies, analog performance metrics are highly non-linear and cannot be accurately captured by traditional response surface models. In this paper, we propose a piecewise modeling algorithm that optimally partitions the parameter space into several regions and, on each of them, fits a linear or a quadratic function to the performance metrics. This piecewise modeling strategy efficiently combines good global and local approximation properties.

4 citations


Cites methods from "Hierarchical statistical characteri..."

  • ...This model can be a polynomial [ 1 ] or a posynomial function [2], a Kriging model [3] or based on neural network [4]....

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  • ...parameter space (14 parameters) Wi∈ [ 1 , 25] (µm) Li∈ [1, 5] (µm)...

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  • ...parameter space (14 parameters) Wi∈ [1, 25] (µm) Li∈ [ 1 , 5] (µm)...

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Journal ArticleDOI
TL;DR: A cluster-based delta-QMC technique is proposed in this paper to reduce the delta change in each sample that can increase speed by two orders of magnitude with almost the same accuracy and significantly improves the efficiency of yield analysis.

4 citations

Proceedings ArticleDOI
18 May 2008
TL;DR: A method for enabling accurate statistical analysis of a low noise amplifier and its differential version is proposed and relies on application of the RS (Response Surface) methodology to the y-parameters of both the circuit and the inductors independently and expressing the eventual performance measures through a suitable combination of these y- parameters.
Abstract: With continuing trends towards miniaturization of circuits and inclusion of multiple, complex functionalities on a single chip, the effect of process variations on circuit performance is assuming critical importance. In view of increasing frequency of operation, accurate variability analysis of RF/Microwave circuits would require modeling of the variability in the passive elements through a field solver. In this paper, a method for enabling accurate statistical analysis of a low noise amplifier and its differential version is proposed. The on-chip spiral inductors are modeled through an EM (Electromagnetic) solver, while the circuit part is modeled through SPICE. The proposed approach relies on application of the RS (Response Surface) methodology to the y-parameters of both the circuit and the inductors independently and expressing the eventual performance measures through a suitable combination of these y-parameters. The eventual performance measures are expressed through a hierarchical approach in terms of the underlying Gaussian random variables representing both the circuit and EM process parameters. An RSMC (Rapid Response Surface Monte Carlo) analysis on these derived response surfaces furnishes the PDFs and can also be used to predict the yield based on different qualifying criteria and objective functions. Several advantages of this method are outlined.

3 citations

Proceedings ArticleDOI
01 Sep 2007
TL;DR: An accurate behavioral Monte Carlo simulation (BMCS) approach to analyze PLL designs under process variation is developed by building a bottom-up behavioral modeling approach with an efficient extraction process to provide accurate enough results with less regression cost.
Abstract: Hierarchical statistical analysis using the regression-based approach is often used to improve the extremely expensive HSPICE Monte Carlo (MC) analysis. However, accurately fitting the regression equations requires many simulation samples. In this paper, an accurate behavioral Monte Carlo simulation (BMCS) approach to analyze PLL designs under process variation is developed by building a bottom-up behavioral modeling approach with an efficient extraction process. Using the accurate model, we also develop a modified sensitivity analysis for process variation effects to provide accurate enough results with less regression cost. As shown in the experimental results, we reduce the simulation time of HSPICE MC analysis from several weeks to several hours and still retain similar statistical results as in HSPICE MC simulation.

3 citations

Journal ArticleDOI
TL;DR: This article proposes a fast heuristic approach that tries to finish all iteration steps of the yield enhancement flow at behavior level, and using the obtained behavioral parameters as the sizing targets of each subblock, the device sizing time is significantly reduced.
Abstract: In traditional yield enhancement approaches, a lot of computation efforts have to be paid first to find the feasible regions and the Pareto fronts, which will become a heavy cost for large analog circuits. In order to reduce the computation efforts, this article proposes a fast heuristic approach that tries to finish all iteration steps of the yield enhancement flow at behavior level. First, a novel force-directed Nominal Point Moving (NPM) algorithm is proposed to find a better nominal point without building the feasible regions. Then, an equation-based behavior-level sizing approach is proposed to map the NPM results at performance level to behavior-level parameters. A fast behavior-level Monte Carlo simulation is also proposed to shorten the iterative yield enhancement flow. Finally, using the obtained behavioral parameters as the sizing targets of each subblock, the device sizing time is significantly reduced instead of sizing from the system-level specifications directly. As demonstrated on several analog circuits, this heuristic approach could be another efficient methodology to help designers improve their analog circuits toward better yield.

3 citations

References
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Book
29 Aug 1995
TL;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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Journal ArticleDOI

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
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
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