Thar she blows! (Thermal issues with printed circuit boards.)
Fusing time and current
Fortunately, there has been good research performed over the last decade to produce a empirical models that can predict temperature rise accurately enough for standard PCB applications. One of our main concerns is: "Can the trace or neck-down region cope with the current required in the design without fusing?"
The PCB design community has followed the lead of folks like Douglas Brooks on this one. Brooks cites Onderdonk's equation (a curve-fitted model of circular conductor fusing current) as follows:
And a simplified version as follows:
These were formulated a long time ago using copper wire with circular cross-sectional area "A" in square mils, time "t" in seconds to fusing, and the melting point of copper "Tm" in °C ("Ta" is the ambient temperature). The simplified version has been used by PCB designers and in various calculators and toolkits for a long, long time. It's nice and convenient because it relates fusing time directly to current and area -- in other words current density. However, it results in grossly pessimistic fusing current estimates for PCB traces, predominantly because of the heat-sinking effect of the surrounding board materials and copper planes. Some designers still like to use the simple equation because this pessimism results in boards with a large margin of safety. It's pretty easy to create a tool to apply these as shown in the spreadsheet illustrated in Figure 3:
Figure 3: Calculating fusing current, current density, and power dissipation of a small PCB track segment
(Click here to see a larger image.)
But this can backfire! Looking back at those "PCB fuses" I realize that this was how my old boss had calculated the "About two amps" with a 10-mil wide track. I also realize how dangerous this idea is and why you should never use PCB traces as fuses intentionally, because the fusing current is invariably much higher than that predicted by Onderdonk's (and also Brook's) equations. This means a fault can occur well above the current at which you expect the fuse to protect the system; indeed, it may not blow at all.
Moreover, the melting point of copper is 1083°C, but the glass-transition ("Tg") temperature of FR-4 epoxy is usually about 140°C. At this temperature, the epoxy starts to go soft and gooey again. I am much more interested in making sure that the PCB doesn't fail because of this. If the board has hot regions that approach "Tg" (bear in mind the "Tamb" of the product), all sorts of reliability problems will arise: delamination, blistering, dielectric breakdown, lost impedance control, and more. Not to mention wasted energy in a world ever more concerned about reduction, recycling, and reusing.
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