eldo_user

Monte Carlo Analysis
Primary Statistics of Uncertainty Analysis
Tail Bndry/ Lower Pr. Value Upper CV(%) #Runs Speedup Name
Dist. Sigma Tail / Comp of Meas
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Left 1.75e+09 7.69e-05 8.45e-05/1.0e+00 9.22e-05 9.05 3530 1.6e+03 FOSC
-4.631 NQ=(-3.785 -3.761 -3.739)
Right -1.10e+02 3.53e-06 3.88e-06/1.0e+00 4.23e-06 9.05 5560 2.2e+04
21.303 NQ=( 4.492 4.472 4.453)
PHASE_N
These values may be compared with the results obtained using the standard Monte Carlo
method (refer to “Probability Estimator using Standard Monte Carlo” on page 480).
Using the standard Monte Carlo method, the upped bound for the phase noise response was
5.99×10 −4 . The ISMC method returns 3.88×10 −6 as an estimation of the probability, with 9%
precision. The confidence interval (3.53×10 −6 , 4.23×10 −6 ) for this estimator is given on the
same line. Notice the major gap (almost two orders of magnitude) between the upper bound
based on the binomial law and the value obtained using ISMC. This implies that the probability
of the phase noise exceeding -110dBC/Hz is much less than the conservative estimation
computed using the standard Monte Carlo method.
An estimation of the speedup over the standard Monte Carlo method is given in the .mcm file. In
the case of the phase noise response, approximately 5560 × 2.2 × 10 4 ≈ 120 million standard
Monte Carlo runs would need to be carried out to obtain equivalent results (in terms of value
and precision).
The .mcm file contains the normal quantiles (NQ) corresponding to the probability estimator
and its confidence interval. The normalized distance of the user specification to the mean of the
distribution (q σ ) is also given. In the above example, the first response is slightly non Gaussian
(compare NQ = -3.761 with q σ = -4.631), while the phase noise has a very right-skewed
distribution which is clearly non-Gaussian (compare NQ = 4.472 with q σ = 21.303). In this
second case, making the assumption that the output distribution is Gaussian can lead to severe
underestimation of the true risk.
The ISMC method produces an .mcm file containing the following data about quantile
estimators:
Tail Probability Lower Quantile Upper Prec(%) #Runs Speedup Name
(Goal Value) Value of Meas
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Left 1.00e-04 1.750e+09 1.751e+09 1.752e+09 0.06% 3010 2.0e+02 FOSC
Right 1.00e+00 -1.124e+02 -1.121e+02 -1.119e+02 0.27% 2510 1.1e+02 PHASE_N
Two columns are added to the standard Monte Carlo results: the number of runs associated with
the estimator and the speedup over the standard Monte Carlo method. The precision is obtained
by inverting the confidence interval on the underlying probability estimator.
484
Eldo® User's Manual, 15.3