eldo_user

Monte Carlo Analysis
Importance Sampling Monte Carlo Examples
VCO Circuit
Netlist file: monte_carlo_vco_lc_tank.cir
The sample circuit is configured for .SST analysis and transient simulation (much slower than
.SST). The circuit is a simple LC-tank VCO oscillating at 1.8GHz (adapted from Craninckx &
Steyaert, IEEE JSSC, May 1997). The oscillation frequency is obtained using the .SST analysis
of Eldo RF (requires an Eldo RF licence).
The phase noise at 1meg offset from the carrier is also extracted using the steady-state noise
analysis of Eldo RF. Both the oscillation frequency and the phase noise are strongly non-
Gaussian. The distributions are heavily skewed (left and right respectively). This means that
Gaussian extrapolations using the estimated standard deviation with a few hundred runs are
completely wrong.
With this analog IP block, the ISMC method can easily capture extreme events. In contrast, the
standard Monte Carlo method is useless as soon as the probabilities are in the range of 10 −3
because the number of runs needed to obtain a decent confidence interval becomes prohibitively
large.
This example sets up four simultaneous measurements: two probabilities and two quantiles.
With importance sampling, the total number of runs grows roughly linearly with the number of
measurements, so simulations are shorter if only one probability or quantile is measured at a
time. For this reason, when preparing and checking simulations, it is better to proceed one
.EXTRACT command at a time.
Even with moderately small probabilities and quantiles, the speedup of the ISMC method over
the standard Monte Carlo method ranges from 200 to 26,000. This can be observed in the .mcm
output file. Refer to “Probability and Quantiles using Importance Sampling Monte Carlo” on
page 483 for more information.
The results of the transient simulation are obtained using Monte Carlo extracts. First, the
following statement sets up a Monte Carlo simulation using the ISMC method:
.MC 500 DATAFLOW=1 SAMPLING=ISMC
The 10 −4 -quantile for the oscillation frequency is close to 1.75Ghz (see below). The following
statement extracts this quantile:
.EXTRACT MC LABEL=quantile_fosc_left_1em4 MCBOUND(fosc_tran, 1e-4)
The following statement extracts the probability that the oscillation frequency is lower than
1.75GHz:
.EXTRACT MC LABEL=proba_fosc_left_1_75 MCPROB(fosc_tran, LE, 1.75G)
The following results are obtained for the probability estimator:
Eldo® User's Manual, 15.3 531