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Hierarchical statistical characterization of mixed-signal circuits using behavioral modeling

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TLDR
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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Journal ArticleDOI

Rapid Yield Estimation and Optimization of Microwave Structures Exploiting Feature-Based Statistical Analysis

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.
Journal ArticleDOI

Enabling High-Dimensional Hierarchical Uncertainty Quantification by ANOVA and Tensor-Train Decomposition

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.
Proceedings ArticleDOI

Asymptotic probability extraction for non-normal distributions of circuit performance

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.
Journal ArticleDOI

Asymptotic Probability Extraction for Nonnormal Performance Distributions

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.
Journal ArticleDOI

Random-Space Dimensionality Reduction for Expedient Yield Estimation of Passive Microwave Structures

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.
References
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Book

Response Surface Methodology: Process and Product Optimization Using Designed Experiments

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.
Book

A User's Guide to Principal Components

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.
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Linear Models

Book

Monte Carlo methods

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.