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.
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01 Jan 2014
TL;DR: The most profound reason for the future increase in parameter variability is that the technology is approaching the regime of fundamental randomness in the behavior of silicon structures where device operation must be described as a stochastic process as mentioned in this paper.
Abstract: One of the most notable features of nanometer scale CMOS technology is the increasing magnitude of variability of the key parameters affecting performance of integrated circuits [1]. Although scaling made controlling extrinsic variability more complex, nonetheless, the most profound reason for the future increase in parameter variability is that the technology is approaching the regime of fundamental randomness in the behavior of silicon structures where device operation must be described as a stochastic process. Electric noise due to the trapping and de-trapping of electrons in lattice defects may result in large current fluctuations, and those may be different for each device within a circuit.
5 citations
TL;DR: A hierarchical technique to perform statistical analysis of RF circuits based on y-parameter representation for the circuit and the passive element parts is proposed, which obviates the need for optimization steps to derive the equivalent-circuit parameters for the electromagnetic objects and the need to compute the correlation matrix between the circuit equivalent elements, while maintaining accuracy.
Abstract: Spectral domain statistical analysis of RF circuits, combining a circuit simulator, which models the circuit part and a full-wave field solver, which models the passive elements, is presented in this paper. This paper first illustrates the importance of the knowledge of correlation information in accurately modeling the probability density functions (PDFs) of eventual objective functions using a simple transmission line paradigm. Next, this paper looks at the statistical study of on-chip RF passives using the spiral inductor as an example. It is shown that larger process variations necessitate modeling by means of a quadratic response surface to preserve accuracy. This results in nonindependent non-Gaussian nonclosed-form PDFs for the equivalent-circuit parameters of the passives. This paper then proposes a hierarchical technique to perform statistical analysis of RF circuits based on y-parameter representation for the circuit and the passive element parts. The proposed technique obviates the need for optimization steps to derive the equivalent-circuit parameters for the electromagnetic objects and the need to compute the correlation matrix between the circuit equivalent elements, while maintaining accuracy. The proposed approach is illustrated for the statistical analysis of an RF amplifier and its differential version operating at 15.78 GHz. PDFs of various quantities of interest are derived and yield measures are computed.
5 citations
TL;DR: A supervised learning artificial neural network (ANN) is proposed as a means by which to define an AMS regression model that allows for rapid searches of complex design dimensions, including variations in performance metrics caused by process–voltage–temperature (PVT) changes.
Abstract: An analog and mixed-signal (AMS) circuit that draws on machine learning while using a regression model differs in terms of the design compared to more sophisticated circuit designs. Technology structures that are more advanced than conventional CMOS processes, specifically the fin field-effect transistor (FinFET) and silicon-on-insulator (SOI), have been proposed to provide the higher computation performance required to meet various design specifications. As a result, the latest research on AMS design optimization has enabled enormous resource savings in AMS design procedures but remains limited with regard to reflecting the intended operating conditions in the design parameters. Hereby, we propose what is termed a supervised learning artificial neural network (ANN) as a means by which to define an AMS regression model. This approach allows for rapid searches of complex design dimensions, including variations in performance metrics caused by process–voltage–temperature (PVT) changes. The method also reduces the considerable computation expense compared to that of simulation-program-with-integrated-circuit-emphasis (SPICE) simulations. Hence, the proposed AMS circuit design flow generates highly promising output to meet target requirements while showing an excellent ability to match the design target performance. To verify the potential and promise of our design flow, a successive approximation register analog-to-digital converter (SAR ADC) is designed with a 14 nm process design kit. In order to show the maximum single ADC performance (6-bit∼8-bit resolution and few GS/s conversion speed), we have set three different ADC performance targets. Under all SS/TT/FF corners, ±6.25% supply voltage variation, and temperature variation from −40 ∘C to 80 ∘C, the designed SAR ADC using our proposed AMS circuit optimization flow yields remarkable figure-of-merit energy efficiency (approximately 15 fJ/conversion step).
5 citations
03 Mar 2014
TL;DR: A novel technique for fast and accurate process variation analysis of nanoscale circuits by combining traditional Kriging with an artificial neural network (ANN) to achieve the objective.
Abstract: Speeding up the design optimization process of Analog/Mixed-Signal circuits has been a subject of active research. Techniques such as metamodeling, artificial neural networks, and optimization over SPICE netlists have been used. While the results are accurate and promising, the effects of process variation on design space exploration still persist. Metamodels created by existing techniques are still not variation aware. This paper presents a novel technique for fast and accurate process variation analysis of nanoscale circuits. The technique combines traditional Kriging with an artificial neural network (ANN) to achieve the objective. Kriging captures correlated process variations of the circuits and accurately trains the ANN to generate the metamodels. The proposed technique uses Kriging to bootstrap target samples used for the ANN training. This introduces Kriging characteristics, which account for correlation effects between design parameters, to the ANN. As a case study of the proposed method, Kriging bootstrapped trained ANN metamodels are presented for an 180 nm Phase-Locked Loop (PLL) circuit design.
4 citations
05 Nov 2007
TL;DR: This work shows through field-solver simulations that larger process variations lead to non-Gaussian PDFs (probability density functions) for the circuit equivalent parameters of distributed passives and a method for accurate statistical analysis of coupled circuit-EM (Electromagnetic) systems without computing the equivalent circuit parameters of EM-modeled objects is demonstrated.
Abstract: As technologies continue to shrink in size, modeling the effect of process variations on circuit performance is assuming profound significance. Process variations affect the on-chip performance of both active and passive components. This necessitates the inclusion of the effect of these variations on distributed interconnect structures in modeling overall circuit performance. In this work, first it is shown through field-solver simulations that larger process variations lead to non-Gaussian PDFs (probability density functions) for the circuit equivalent parameters of distributed passives. Next, a method for accurate statistical analysis of coupled circuit-EM (Electromagnetic) systems without computing the equivalent circuit parameters of EM-modeled objects is demonstrated. This method also obviates the need to generate random variables representing the equivalent circuit parameters, from distributions which are correlated, non-Gaussian and non-closed-form. The proposed approach relies on application of the response surface (RS) methodology to the y-parameters of both the circuit and the distributed structures independently and expressing the eventual performance measures through a suitable combination of the y-parameters. The eventual performance measures are expressed through a hierarchical approach in terms of the underlying Gaussian random variables representing the process parameters. A rapid response surface Monte Carlo (RSMC) 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.
4 citations
Cites methods from "Hierarchical statistical characteri..."
...One approach [ 6 ] is to use a combination of analytical techniques and RS methodology to predict the statistical behavior of performance measures from the distributions of lower level process parameters....
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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