Empirical model-building and response surface
Empirical model-building and response surface
Signals & systems (2nd ed.)
The Wiener--Askey Polynomial Chaos for Stochastic Differential Equations
SIAM Journal on Scientific Computing
Asymptotic probability extraction for non-normal distributions of circuit performance
Proceedings of the 2004 IEEE/ACM International conference on Computer-aided design
Proceedings of the 45th annual Design Automation Conference
Hermite Polynomial Based Interconnect Analysis in the Presence of Process Variations
IEEE Transactions on Computer-Aided Design of Integrated Circuits and Systems
Quadratic Statistical Approximation for Parametric Yield Estimation of Analog/RF Integrated Circuits
IEEE Transactions on Computer-Aided Design of Integrated Circuits and Systems
A Fast Non-Monte-Carlo Yield Analysis and Optimization by Stochastic Orthogonal Polynomials
ACM Transactions on Design Automation of Electronic Systems (TODAES)
Efficient parametric yield estimation of analog/mixed-signal circuits via Bayesian model fusion
Proceedings of the International Conference on Computer-Aided Design
IEEE Transactions on Very Large Scale Integration (VLSI) Systems
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Stochastic device parameter variations have dramatically increased beyond the scale of 65nm and can significantly lead to large mismatch for analog circuits. To estimate unknown analog circuit behavior in performance space under the given stochastic variations in parameter space, many state-of-art approaches have been developed recently. However, either Gaussian distribution or response surface model (RSM) with analytical formulae has to be assumed when connecting performance space and parameter space. A novel point-estimation based approach has been proposed in this paper to capture arbitrary stochastic distributions for analog circuit behaviors in performance space. First, to evaluate high-order moments of circuit behavior in an accurate fashion, the point-estimation method has been applied with only a few number of simulations. Then, probability density function (PDF) of circuit behavior can be efficiently extracted by the obtained high-order moments. This method is further extended for multiple parameters under linear complexity. Extensive numerical experiments on a number of different circuits have demonstrated that the proposed point-estimation method can provide up to 181X runtime speedup with the same accuracy, when compared with Monte Carlo method. Moreover, it can further achieve up to 15X speedup over the RSM-based method such as APEX with the similar accuracy.