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Monte Carlo Analysis
Model-Based Approximations Example
For 10,000 runs, 9765 circuits are obtained that pass the specification. The approximate yield is
therefore 97.65%.
Comparison of Standard Monte Carlo and SSD Methods
The Monte Carlo simulations of reference involves 1000 runs, and the SSD sampling is defined
with a simulation budget of 100 runs. The results provide in Table 11-2 are extracted from the
.mcm file. A comparison is generated only for the extract OPFREQ (in Hz).
Table 11-2. Comparison of Standard Monte Carlo and SSD Methods
This simple example shows the SSD algorithm correctly captured the central location and the
range of the distribution. The relative error on the range is about 5% with respect to the golden
Monte Carlo simulation. The worst error is given by the approximation of the third moment.
The skewness of the distribution is clearly underestimated. This fact comes from the linear
model used to approximate the output response. This model cannot identify asymmetric
distributions.
The choice of simulation budget here is based on preliminary experiments. NRUN=100 was
used here, but sometimes it is necessary to increase this budget. A use model, could be to first
run a golden Monte Carlo simulation on typical circuits that represent a large class of other
circuits and then find a sufficient number of runs for the SSD algorithm.
Related Topics
Data MC Reference
(command .MC 1000
SAMPLING=RAND)
Fitted Distribution
(command .MC 100
SAMPLING=SSD) with
relative error Err%
Mean Value 3.18873×10 8 3.20965×10 8 (Err% = 0.6 %)
Standard Deviation 2.66935×10 7 3.16319×10 7 (Err% = 18%)
Skewness 2.23588×10 −1 1.26011×10 −2 (Err% = 94%)
Kurtosis 3.02094 2.84756 (Err% = 5.7%)
Shortest Coverage Interval
(L,U) with α = 0.95
(2.70380×10 8 , 3.72227×10 8 ) (2.55207×10 8 , 3.78589×10 8 )
(Err% = (5.6%,1.7%))
Model-Based Monte Carlo Simulation
Further Examples
Example 17—Monte Carlo Sensitivity of a Two-Stage Operational Amplifier
Eldo® User's Manual, 15.3 533