eldo_user

Monte Carlo Analysis
Local and Global Variations
Statistical Model
It is clear that X is a vector of independent variables, because there is no functional dependences
between these circuit parameters. From the designer’s view, the true physical model is actually
characterized by the correlations between the global and local variations. This can be made
explicit by rewriting the relations between the random variables. A new vector of random
variables is defined by:
such that:
The pair of variables
represents the effective length variations specified
in the circuit by the command expressions .PARAM VARL=0.0 LOT/UNIF=0.05U DEV/
UNIF=0.1U. In this example, the distribution of the variable L R1 is the sum distribution of DL R
+ DL R1 . This distribution can be obtained explicitly as the convolution product:
From these equations, it can also be deduced that the new variables are correlated. The
correlation structure is given by the following arguments: define the matrix A such that
. The variance of a linear transformation is known to equal:
Since the random variables X are independent, Var{X} = diag(σ), and
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Eldo® User's Manual, 15.3