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18 The PCB Design Magazine • February 2017 Onderdonk's equation applies to a single copper wire in space and assumes there is no cooling of the wire. Therefore, it only applies for a very short period of time, perhaps up to five or 10 seconds, depending on conditions. We used TRM to simulate the conditions On- derdonk assumed for a bare wire in space and also for conditions on a normal PCB. The re- sults are shown in Figure 9. The simulation shows that at very high cur- rents, both the bare wire and the trace fuse very quickly. But at lower currents, it takes much longer for a trace on a board to melt than it does for a bare wire. The separation of the curves in Figure 8 is a direct result of the cooling mecha- nisms on the board. TRM allowed Johannes and me to explore paths that had never been available to us be- fore. And it turned out, several of these new paths led to additional paths, and they to yet more paths. I am now convinced that designers who really need to know the thermal properties around their traces, or who really need to op- timize the thermal properties of their designs, will need to use a tool like TRM. Graphs and equations are no longer ade- quate. And we have been here before. A great many designers needed to start worrying about impedance-controlled traces in the early 1990s. At that time, impedance equations were avail- able to us in a variety of publications. But today we all know that the equations are no longer accurate enough and we need "field effect" (i.e., computer model) solutions. And today that is starting to happen on the area of PCB trace thermal design. Technical note: In this article, I have shown how the TRM (Thermal Risk Management) soft- ware tool can be used to analyze thermal issues of and around individual traces, and I've found that the tool is very well suited to doing this. But this may leave the reader with the mistaken believe that this is the limit of what TRM can do. In fact, TRM is much more powerful than this! Dr. Adam originally conceived and designed TRM to analyze temperatures across an entire circuit board, taking into consideration the complete trace layout with optional Joule heat- ing as well as various components and their own contributions to heat generation. Although the program could be adapted to the measurement of an individual trace, as we have done here, it was not originally conceived with that use in mind. TRM has the ability to look at an entire board whose data can be entered into the soft- ware using, for example, the entire set of Gerber and drill files. This article includes images of thermal dia- grams the software produces relative to a single trace under analysis. But Figure 10 illustrates EXCITING NEW TECHNOLOGY: THERMAL RISK MANAGEMENT Figure 9: Fusing equations for a 1.0 oz. 200 mil wide trace. Figure 10: With TRM, a thermal profile can be generated of an entire board, including compo- nents, under load.