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Introduction to Monte Carlo Analysis
Monte Carlo Analysis
Introduction to Monte Carlo Analysis
The main goal of the Monte Carlo command is to analyze the uncertainty in circuit performance
due to simulated random variations. It focuses on how uncertainty in input data propagates
through computations.
The input data is the various design parameters, the process parameters, and the environmental
conditions. A circuit performance may be any measure that is extracted from the simulation, and
will be noted with the functional form , where we note the input parameters with the
generic symbol x.
Eldo reads a netlist describing the circuit and translates it into mathematical equations. The
Monte Carlo simulation is performed on multiple model evaluations with randomly selected
model input variables. The results of these evaluations are then used to determine the
uncertainty in model predictions, and the input variables that gave rise to this uncertainty.
To use the Monte Carlo analysis in Eldo, you must do the following:
• Provide a working netlist with one or more user-defined circuit performances (the output
measures) based on other analyses (DC, AC, TRAN, ...).
• Specify the .MC statement in the netlist. See “Specifying a Monte Carlo Analysis” on
page 421.
• Introduce some statistical variations on circuit parameters, model parameters and/or
environmental conditions (the input variables X). See “Statistical Variations” on
page 423.
The following topics are devoted to the definition of the concept of uncertainty and its relation
to the Monte Carlo simulation.
Introduction to Uncertainty Analysis
In our context, we may define the uncertainty u(H) of a circuit performance H, as a parameter
that characterizes the dispersion of the values that can be attributed to the random variations of
this performance. This parameter may be a standard deviation or the width of an interval having
a given level of coverage or yield. Conversely, one may be interested in estimating the
probability of being between user-defined specifications.
Standard Uncertainty
An estimate of the expectation of a random variable (the circuit performance of interest) for
which n independent observations Y i =H(X i ) are simulated, is the arithmetic mean:
Eldo® User's Manual, 15.3 411