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
More filters
TL;DR: A simple, yet reliable methodology to expedite yield estimation and optimization of microwave structures by exploiting the almost linear dependence of the feature points on the designable parameters of the structure.
Abstract: In this paper, we propose a simple, yet reliable methodology to expedite yield estimation and optimization of microwave structures. In our approach, the analysis of the entire response of the structure at hand (e.g., $S$ -parameters as a function of frequency) is replaced by response surface modeling of suitably selected feature points. On the one hand, this is sufficient to determine whether a design satisfies given performance specifications. On the other, by exploiting the almost linear dependence of the feature points on the designable parameters of the structure, reliable yield estimates can be realized at low computational cost. Our methodology is verified using two examples of waveguide filters and one microstrip hairpin filter and compared with conventional Monte Carlo analysis based on repetitive electromagnetic simulations, as well as with statistical analysis exploiting linear response expansions around the nominal design. Finally, we perform yield-driven design optimizations on these filters.
134 citations
TL;DR: This paper develops an efficient analysis of variance-based stochastic circuit/microelectromechanical systems simulator to efficiently extract the surrogate models at the low level and employs tensor-train decomposition at the high level to construct the basis functions and Gauss quadrature points.
Abstract: Hierarchical uncertainty quantification can reduce the computational cost of stochastic circuit simulation by employing spectral methods at different levels. This paper presents an efficient framework to simulate hierarchically some challenging stochastic circuits/systems that include high-dimensional subsystems. Due to the high parameter dimensionality, it is challenging to both extract surrogate models at the low level of the design hierarchy and to handle them in the high-level simulation. In this paper, we develop an efficient analysis of variance-based stochastic circuit/microelectromechanical systems simulator to efficiently extract the surrogate models at the low level. In order to avoid the curse of dimensionality, we employ tensor-train decomposition at the high level to construct the basis functions and Gauss quadrature points. As a demonstration, we verify our algorithm on a stochastic oscillator with four MEMS capacitors and 184 random parameters. This challenging example is efficiently simulated by our simulator at the cost of only 10min in MATLAB on a regular personal computer.
126 citations
Cites methods from "Hierarchical statistical characteri..."
...1 stochastic testing [15] Method 1 [32] Monte Carlo Monte Carlo Method 2 Alg....
[...]
...If Method 1 [32] is used, Monte Carlo has to be repeatedly used for each MEMS capacitor, leading to extremely long CPU time due to the slow convergence....
[...]
...In our preliminary conference paper [1], this method was employed to simulate a low-dimensional stochastic oscillator with 9 random parameters, achieving250× speedup over the hierarchical Monte-Carlo method proposed in [32]....
[...]
...In Method 1, both low-level and high-level simulations use Monte Carlo, as suggested by [32]....
[...]
...In such example, our method is over 92× faster than the hierarchical Monte Carlo method developed in [32], and is about 14× faster than the method that uses ANOVA-based solver at the low level and Monte Carlo at the high level....
[...]
07 Nov 2004
TL;DR: An asymptotic probability extraction method, APEX, for estimating the unknown random distribution when using nonlinear response surface modeling, which uses a binomial moment evaluation to efficiently compute the high order moments of the unknown distribution and applies moment matching to approximate the characteristic function of the random circuit performance by an efficient rational function.
Abstract: While process variations are becoming more significant with each new IC technology generation, they are often modeled via linear regression models so that the resulting performance variations can be captured via normal distributions. Nonlinear (e.g. quadratic) response surface models can be utilized to capture larger scale process variations; however, such models result in non-normal distributions for circuit performance which are difficult to capture since the distribution model is unknown. In this paper we propose an asymptotic probability extraction method, APEX, for estimating the unknown random distribution when using nonlinear response surface modeling. APEX first uses a binomial moment evaluation to efficiently compute the high order moments of the unknown distribution, and then applies moment matching to approximate the characteristic function of the random circuit performance by an efficient rational function. A simple statistical timing example and an analog circuit example demonstrate that APEX can provide better accuracy than Monte Carlo simulation with 10 samples and achieve orders of magnitude more efficiency. We also show the error incurred by the popular normal modeling assumption using standard IC technologies.
110 citations
TL;DR: The APEX begins by efficiently computing the high-order moments of the unknown distribution and then applies moment matching to approximate the characteristic function of the random distribution by an efficient rational function, and is proven that such a moment-matching approach is asymptotically convergent when applied to quadratic response surface models.
Abstract: While process variations are becoming more significant with each new IC technology generation, they are often modeled via linear regression models so that the resulting performance variations can be captured via normal distributions. Nonlinear response surface models (e.g., quadratic polynomials) can be utilized to capture larger scale process variations; however, such models result in nonnormal distributions for circuit performance. These performance distributions are difficult to capture efficiently since the distribution model is unknown. In this paper, an asymptotic-probability-extraction (APEX) method for estimating the unknown random distribution when using a nonlinear response surface modeling is proposed. The APEX begins by efficiently computing the high-order moments of the unknown distribution and then applies moment matching to approximate the characteristic function of the random distribution by an efficient rational function. It is proven that such a moment-matching approach is asymptotically convergent when applied to quadratic response surface models. In addition, a number of novel algorithms and methods, including binomial moment evaluation, PDF/CDF shifting, nonlinear companding and reverse evaluation, are proposed to improve the computation efficiency and/or approximation accuracy. Several circuit examples from both digital and analog applications demonstrate that APEX can provide better accuracy than a Monte Carlo simulation with 104 samples and achieve up to 10times more efficiency. The error, incurred by the popular normal modeling assumption for several circuit examples designed in standard IC technologies, is also shown
84 citations
TL;DR: In this article, a methodology is presented for the expedient statistical analysis of the electromagnetic attributes of passive microwave structures exhibiting manufacturing uncertainty in geometric and material parameters, which leads to an expedient estimation of production yield by means of the crossentropy algorithm, which provides for fast calculation of the failure probability for a given functionality criterion.
Abstract: A methodology is presented for the expedient statistical analysis of the electromagnetic attributes of passive microwave structures exhibiting manufacturing uncertainty in geometric and material parameters. In the proposed approach, the computational complexity stemming from the high dimensionality of the random space that describes the uncertainty in the electromagnetic analysis of the structure is mitigated by employing a principal component analysis with sensitivity assessment in combination with an adaptive sparse grid collocation scheme. The method exploits the inherent dependencies between random parameters to reduce the number of simulations needed to extract the statistics of the desired output response. This leads to the expedient estimation of production yield by means of the cross-entropy algorithm, which provides for fast calculation of the failure probability for a given functionality criterion. The proposed methodology is demonstrated through its application to the analysis of crosstalk in coupled microstrip lines exhibiting manufacturing variability and the investigation of the variation the bandwidth characteristics of a bandpass filter in the presence of uncertainty in geometric and/or material parameters.
80 citations
References
More filters
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]....
[...]
[...]
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]....
[...]
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]....
[...]
...Note that for any given coefficients in a quadratic equation, A is uniquely determined [13]....
[...]
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