# Monte-Carlo simulation

1. ## Monte-Carlo simulation

Hi!
I try to run a monte-carlo simulation analysis in cadence.
I run gauss mode with sampling method - Latin Hypercube.
And what is the general difference between two analisys - uniform and gauss?
As I know, the gauss mode of simulation is more realistic than the uniform mode. The gauss mode uses a bell curve approach as it randomly pick values in the range of error specified but with the majority of the values near the resistor value. And, the uniforn mode of deviation randomly selects values within the range specified oblivious of what the actual value of the resistor is.

Thanks in advance. •

2. ## Re: Monte-Carlo simulation

You already described the difference between the two distribution types correctly, I think. Considering its application depends on what you need: if you want to MC-simulate the variance of a device parameter, the Gauss distribution is the adequate choice, because devices are made to meet a required value which spreads around its mean value with a Gauss type distribution.

Uniform distribution could be chosen if you are looking for the right value of a device parameter between two limits - but this wouldn't necessarily need a MC simulation - a sweep could achieve the same purpose. •

3. ## Re: Monte-Carlo simulation

In General, Statistical Probability Distribution a Process Variable in a PDK is given by Gaussian/Natural Distribution that is logical. •

4. ## Re: Monte-Carlo simulation

The proper distribution to use, depends on the real
distribution.

For example a process feature (say, sheet resistance)
which has +/- 3 sigma limits based on large lot sample
history is probably a good bet for a gauss() (normal)
distribution model.

That same process, if acceptance limits are closer-in
(say, process scatter runs to +/-30% but you insist
to screen to +/-10% for production) may well look
more like "uniform" because you're throwing away the
"tails".

And many attributes tend to follow other distributions
(log-normal is especially common).

For a real, relevant Monte Carlo you also need the
correlation coefficient matrix (for example, TOXP and
TOXN would be highly correlated and not allowed to
wander apart; beta and Early voltage, highly anti-
correlated and no point simulating an op amp with
both gm and Rout impossibly high at once). Param
interactions can make screwy results if you let all
of the model params that matter, be random and
entirely independent.

1 members found this post helpful. 5. ## Re: Monte-Carlo simulation

And what is the general difference between two analisys - uniform and gauss?
The short answer is: it depends. The long answer is going to be long.

You need to look at the system and their behaviour. Basically all Monte Carlo methods are useful in integration. You are basically evaluating a function at random points and comparing the expected vs the real value.

If your variables are distributed approximately randomly in a Gaussian manner, then go ahead and use the gauss mode. But this information must come from the user (and that is the reason there is another option for uniform distribution.

You simulate 1000 random number and plot; you will get an uniform distribution.

You use the same 1000 random numbers and use a running average of two consecutive numbers (i and i+1) and plot the graph: you will get a gaussian distribution.

Sometimes a Gaussian distribution with a large variance may be easier to simulate as a uniform distribution.

1 members found this post helpful. --[[ ]]--