eldo_user

Monte Carlo Analysis
Model-Based Approximations Example
Lower Pr. Value Upper CV(%) #Runs Speedup
Tail / Complementary
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8.86e-05 9.60e-05/1.00e+00 1.03e-04 7.69 3530 1.9e+03
Additionally, the quantile estimator returns a value of 1.74980×10 9 , which is very close to the
value specified in the MCPROB extract statement. The speedup of the ISMC method over the
standard Monte Carlo method is modest, but still very interesting. The standard Monte Carlo
method would require 6.7 million runs to reach the same precision.
Model-Based Approximations Example
Netlist file: monte_carlo_ssd.cir
This example centers around an 8-bit CMOS ripple carry adder, which is able to add to 7-bit
binary numbers in parallel. The adder is constructed from a chain of 7 cascaded one-bit adder
stages, with each stage connected to the next via a carry-link.
The maximum operating frequency of such an adder is limited by the time it takes for the carry
signal to propagate (ripple) through the chain, from the far-right stage to the sum6 and sum7
outputs on the left. Given the circuit topology, this propagation delay depends on:
• The design parameters (geometries of transistors in the carry path).
• The statistical variations in transistor parameters due to manufacturing tolerances.
• Environmental temperature.
You, the designer, can choose the values of the design parameters. Temperature and some
manufacturing process parameters may be controllable, but more often are not “designable.”
The objectives for the 8-bit adder in this example are:
• To simulate the fluctuation of the maximum operation speed due to manufacturing
variations and as a function of temperature.
• To predict the likely manufacturing yield with respect to a user-specified lower limit on
the operating speed.
• To compare the standard Monte Carlo method and the supersaturated design (SSD)
approach.
Approximation of the Parametric Yield
Here, we calculate an approximation of the probability that a given circuit fails to satisfy a set
performance specification. In the example, this value is obtained using the LBOUND and
UBOUND arguments on the .EXTRACT command:
.EXTRACT TRAN LABEL=OPFREQ (1/MAX(EXTRACT(DELAY6), EXTRACT(DELAY7)))
+ LBOUND=280Meg
532
Eldo® User's Manual, 15.3