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14 The PCB Design Magazine • February 2017 But TRM also allows us to view things in many other dimensions. For example, Figure 2 shows the thermal profile of a cross-sectional view of the board underneath the trace. The thermal profile underneath the trace through the board without the plane extends all the way to the far side, but the thermal profile of the board with the plane changes dramatically at the plane. I know of no other way to look at this profile other than with a computer simulation. But the result that really got us excited, and led to an entire series of studies that culminated in the book, came about when we used TRM to look at the temperature of a via. There is no other practical way to explore the temperature within the barrel of a via. What we found was, for a normal trace, the via is cooler than the trace! (Figure 3). It turns out that it is not the current through the via that determines the temperature of the via; it is the temperature of the adjacent trace [3] . Therefore, if the trace is sized correctly, only a single via is required (in most practical situations) and its size can be much smaller than previously assumed. The software allowed us to look at the tem- perature profile around a right-angle corner. There is some suggestion that the inside of the corner is hotter than the outside of the corner. Our simulations in Figure 4a showed this to be true. But the reason is a little surprising. The reason is not because the current density is con- centrated at the inside corner. When we look at Figure 4b, we see that the thermal profile ex- tending out from the trace into the dielectric around the inside of the corner is different than EXCITING NEW TECHNOLOGY: THERMAL RISK MANAGEMENT Figure 2: Thermal profiles underneath the traces and through the boards in Figure 1. Figure 3: Thermal profiles around a typical via.

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