# Conductor heating of embedded resistors: resistor heating has the potential for problems, but knowing the power dissipation and temp limits allow designers to thermally manage the outcome.

MY COAUTHOR RICHARD Snogren and I have been discussing embedded resistors and the heating associated with them for the past two years. We have had conversations with quite a few others regarding this topic and recently have been garnering a lot of attention.

I started creating thermal models of embedded resistors in circuit boards so that I could gain an appreciation for the problem. I ran parametric studies to get a handle on temperature rise vs. power dissipation and power density. Some of the variables studied were: dielectric material, board thickness, influence of copper planes, dielectric spacing from planes, mounting configurations and air vs. vacuum. I looked at all the same things that were being studied with traces, vias and thermals.

Some of the cases were the size of a resistor, the power dissipated in the resistor and the temperature rise associated with it. I then expanded the models, adding multiple resistors in patterns (all dissipating the same power) (see FIGURE 1), and calculating temperatures. At that point I started to change the position in the board of the resistor patterns, to look at edge effects. All these cases were for a configuration that resembled the test configuration used for testing traces.

[FIGURE 1 OMITTED]

Using the models, it became apparent that resistor heating has the potential for problems if hot thermally managed. The next thing to do was to consider the internal copper planes and mounting configurations. The copper planes have a thermal conductivity that is three orders of magnitude better than the dielectric material. That means that it can more the heat away from those resistors 1,000 times better than hot having the copper there. (Yes, copper is awesome!) After getting several configurations of copper planes assembled, I began putting bolted fasteners into the models and wedge locks on the sides.

The results are impressive. Depending on the application, one can manage the heating, depending on the amount of power being dissipated in an application, how much power is being dissipated by the other components and the temperature limits required in the design. Utilizing what you have in a given design will maximize the results. There are limitations, of course, and that is what we want to help define, in order to provide guidelines that make the process easier.

As Richard noted in May, the plan is to start testing, with the objective to characterize embedded resistor heating. In order to accomplish this, we will enlist the help of resistor material suppliers to create test patterns. We will draw on the experiences of others who have performed testing as an influence on the work that gets performed. We will use thermal models to make predictions and evaluate test results. Right now, we are in the process of contacting a laboratory to perform this testing and will soon find out the potential of this opportunity.

One of the best parts of this is that I just teamed with Harvard Thermal Inc., a company that develops thermal analysis tools and offers consulting. A couple years ago, Harvard developed a software tool that can read in ECAD data, every trace, via, plane, and component and run a thermal analysis. Result: we can make thermal models of the exact geometry that we are testing, apply current to traces and resistors and calculate the temperature rise that results. This is the only analysis tool in the world that can give us this kind of detail. Timing just doesn't get any better than that!

Readers, the first issue we face in the test vehicle development is devising a reliable technique to measure resistor temperature. We have some ideas on this including very fine thermocouples as well as using very-fine adjacent copper traces (above or below the resistor). We would appreciate your suggestions.

Next month's column will explore material, process and design variables that affect resistor heating.

MIKE JOUPPI is a mechanical engineer and specialist in electronics heat transfer. He is founder of ThermalMan Inc. (thermalman.com). He can be reached at mikej@thermalman.com.
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