# Hierarchical statistical characterization of mixed-signal circuits using behavioral modeling

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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### Cites methods from "Hierarchical statistical characteri..."

...1 stochastic testing [15] Method 1 [32] Monte Carlo Monte Carlo Method 2 Alg....

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...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....

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...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]....

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...In Method 1, both low-level and high-level simulations use Monte Carlo, as suggested by [32]....

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...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....

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99 citations

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##### References

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### "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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### "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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3,222 citations