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News:

Spectrum Software has released Micro-Cap 11, the eleventh generation of our SPICE circuit simulator.

For users of previous Micro-Cap versions, check out the new features available in the latest version. For those of you who are new to Micro-Cap, take our features tour to see what Micro-Cap has to offer.

 

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Monte Carlo Tolerances and Distributions

 

Several recent requests about the nature of the Monte Carlo LOT and DEV tolerances have prompted us to include an article on the subject.

In Micro-Cap both absolute (LOT) and relative (DEV) tolerances can be applied. A LOT tolerance is first applied to each device which uses the same model statement. A DEV tolerance is then added to the first through last device relative to the LOT toleranced value originally chosen for the first device. In other words, the first device in the list receives a LOT tolerance, if one was specified. All devices, including the first, then receive the first device's value plus or minus the DEV tolerance. DEV tolerances provide a means for having some devices track in their critical parameter values.

Note that both LOT and DEV tolerances are calculated based on the original value. Let's look at an example. In the circuit below there is a single resistor R1 whose nominal value is 1000. It uses the RMOD model statement which looks like this:

.MODEL RMOD RES (R=1 LOT=10% DEV=1%)

The resistor value is 1000*R, where R is the toleranced Resistance Multiplier model parameter.

If the Worst Case distribution is used, all resistor values must be one of these four:

1000*(1+.1+.01) = 1000+100+10 = 1110
1000*(1+.1-.01) = 1000+100-10 = 1090
1000*(1-.1+.01) = 1000-100+10 = 910
1000*(1-.1-.01) = 1000-100-10 = 890

So whether you do 10 runs or 1000 runs all of the values will be chosen from this set of four.

Schematic to be Monte Carlo analyzed

To illustrate how this works, run AC analysis. Its Analysis Limits dialog box looks like this.



MC circuit analysis limits



Here we're plotting just the resistance of R1. We're using just two data points per run to speed things up. As the resistance doesn't vary with frequency, what we'll see is a set of horizontal lines whose Y value equals the resistance computed for that run. Here is what the 40 runs look like.

Analysis run

As expected, we see four horizontal lines representing the resistance values of the 40 runs. The reason there are only four is that using a Worst Case distribution with a LOT and DEV tolerance only four values are possible. To see this in a Monte Carlo sense, look at the next figure which shows the histogram and a list of the resistance values.

Histogram for the Worst Case distribution


This figure shows the histogram for the 40 runs using a Worst Case distribution. Since there are only four possible values, we get only four bars. In the list to the right are shown the 40 values used in the Monte Carlo run. As you can see there are are 40 instances, but only four distinct values. The key point of this simplified example is to demonstrate how the values are computed and show that they really are computed that way. In most Monte Carlo situations, one uses a Gaussian distribution. This is how the resistance distribution might look for a typical run using a Gaussian distribution.


Histogram for the Gaussian distribution

 
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