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Featured Resource: Monte Carlo based Thermal Calcs

Here's something I've been thinking about for quite a while, and finally had a chance to try: using Monte Carlo random sampling to calculate the expected distribution of thermal performance. Garron Morris has been writing about it in a series of CoolingZone articles. It's a great way to expand spreadsheet calculations from a nominal design point to a design region that exists because of tolerance variations in manufactured parts.

The sampling isn't totally random -- it's random within distributions of whatever you specify. In my example, the response was a heat sink temperature; the input variables were  air speed and fin thickness. Not surprisingly, the air speed is the major variable.

To start, I used a heat sink analysis spreadsheet to simulate a 2x2 full factorial experiment. Then I fit a response surface to the results. This response surface essentially is a multi-variable curve fit -- easy enough to do if you know how to use Excel's built-in Solver.

Then, I adapted Garron Morris's Monte Carlo modeling spreadsheet (see articles noted above) for the response surface of the heat sink, putting in different distributions for the input parameters. The result of the modeling is the Probability of Non-Compliance (assuming you set compliance criteria).

Using the statistical approach can help you decide how to set tolerances, especially when their effect on each other is unclear. Once you've got the response surface based on an experimental design (a task for spreadsheet or bigger, slower model -- physical or computational), it's easy to play around with different specs to see which one gives a suitable non-compliance rate. Great, too, for figuring out where to set the "pass" level in a thermal test to make sure that you won't get any field failures.

Neat Spreadsheet Feature : Labels in formulas

Labels are a terrific tool to write and debug spreadsheet calculations. Labels work for both columns and rows. I tend to use them mainly in rows, so that's what I'll describe here, but they'll even do intersections if that's what you want.

To enable the feature (it's not the default), in Excel go to Tools/Options; on the calculation tab, check the "Labels in Formulas" box.

Set up your calculation by using variable names in the first column. These variable names should be descriptive to you, but shouldn't look like a cell reference to Excel. For example, "T1" is not a good choice -- it confuses the program. "Temp1" is fine, though. Labels aren't case sensitive, so you can use caps in them for clarity but omit them when writing formulas. Spaces are usually okay, but can confuse things too; if that happens, put the label in quotes when writing the formula. For the sake of an example, set up the following labels, one per row: "Area", "resistivity", "power", "R_TIM", and "TempRise".

Next, put numerical values in the column next to the labels where needed -- for the example, enter values for area, resistivity, and power. (Be careful to use consistent units!)

Now you're ready to write the formulas. You can pretty much work the way you're used to, except that you don't need to insert the cell reference; just type the label instead. In the example, in the cell next to the label R_TIM type "=resistivity/area". Then for the temperature rise, enter the formula "=R_TIM*power". This way, you can easily debug your formulas without wondering what quantity you had entered in cell B4.

Try it out!