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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02 Dec 2013
TL;DR: This paper presents a geostatistical based metamodeling technique that can accurately take into account process variation and considerably reduces the amount of time for simulation.
Abstract: The design of Analog Mixed-Signal Systems-on-Chip (AMS-SoCs) presents difficult challenges given the number of design specifications that must be met. This situation is more aggravating in the presence of process variation effects for nanoscale technologies. Existing statistical techniques heavily rely on Monte-Carlo analysis for design parameters in an effort to mitigate the effects of process variation. Such methods, while accurate are often expensive and require extensive amount of simulations. In this paper we present a geostatistical based metamodeling technique that can accurately take into account process variation and considerably reduces the amount of time for simulation. An illustration of the proposed technique is shown using a 180nm PLL design. The proposed technique achieves an accuracy of 0.7 % and 0.33% for power consumption and locking time, respectively, and improves the run time by about 10 times.
10 citations
Cites methods from "Hierarchical statistical characteri..."
...These methods include hierarchical statistical analysis, symbolic and regression based techniques [5], [3]....
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Dissertation•
01 Nov 2003
10 citations
TL;DR: The proposed methodology uses the concept of a correlation matrix, which transforms the process level information to the device and circuit level information through the BSIM model parameters, which has been successfully implemented on an advanced CMOS process.
Abstract: In this paper, we demonstrate a methodology to link process parameters to BSIM model parameters. Here, we have combined well-known statistical methods like principal component analysis (PCA), design of experiments (DOE), and response surface methodology (RSM) to bridge the missing link between process parameters and model parameters. The proposed methodology uses the concept of a correlation matrix, which transforms the process level information to the device and circuit level information through the BSIM model parameters. The proposed methodology has been successfully implemented on an advanced CMOS process. Our results show a strong linear correlation for the data obtained from two techniques namely TCAD technique and the standard HSPICE simulation technique. In both cases the process conditions were kept identical for comparison.
9 citations
Patent•
01 Oct 2008TL;DR: In this paper, a method for tuning nano-scale analog-circuit designs in order to reduce random-device mismatches and optimize said design, where nanoscale devices potentially have large-scale process variations is presented.
Abstract: The invention discloses a method for tuning nano-scale analog-circuit designs in order to reduce random-device mismatches and optimize said design, where nano-scale devices potentially have large-scale process variations. The method includes providing a tunable circuit topology, wherein each nano-scale device comprises a single component or comprises multiple parallel components. Each component is decomposed into multiple discrete sub-components, wherein each said sub-component either operates in parallel with other like components to effectively operate like one bigger component. The sub-components are subjected to a dynamic-programming process to adaptively select the sub-components to be kept operational, while configuring the nonselected sub-components to be nonoperational, based on the measurement of at least one operational parameter.
9 citations
20 Oct 2009
TL;DR: A new method is proposed to estimate the variation bounds of circuit performance, that combines response surface modeling techniques with the Cornish-Fisher expansion: process parameter variations are first mapped to circuit performance metrics by a quadratic model, then an analytical approximation of the performance distribution's quantiles enables enclosure of theperformance variations.
Abstract: The impact of process variability in nanoscale circuits has traditionally been handled with Monte Carlo analysis. In this paper, we propose a new method to estimate the variation bounds of circuit performance, that combines response surface modeling techniques with the Cornish-Fisher expansion: process parameter variations are first mapped to circuit performance metrics by a quadratic model, then an analytical approximation of the performance distribution's quantiles enables enclosure of the performance variations. The proposed method demonstrates an excellent accuracy/efficiency ratio compared to Monte Carlo-based methods.
8 citations
Cites methods from "Hierarchical statistical characteri..."
...percentiles of the performance metric’s PDF are estimated either with Monte Carlo analysis as in [ 4 ] or with CFE as explained in Section II....
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...They result in non-normal performance distributions and Monte Carlo analysis is generally applied to these non-normal meta-models to obtain the shape of the performance PDF [ 4 ]....
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...The meta-model can be a polynomial [ 4 ] or a posynomial function [5], a symbolic [6] or a Kriging model [7]....
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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
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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