Thar she blows! (Thermal issues with printed circuit boards.)
In my previous column, we looked at the all-important power budgeting process. Now that we have developed a fairly confident model of how much power -- on average and on peak -- will be required for our design, we want to know if the associated structures in the PCB will be overly stressed or not. As long as we can provide the current and decoupling needed for the devices in use without hiccups, the other thing to consider is the board itself.
A PCB fuse trick?
Before we dive deeper into this topic, let me first share a little story. When I was a wet-behind-the-ears college student, I had a part-time job doing PCB design and assembly at a "ma and pa" electronics company in my hometown. They were really cool people and I learned a great deal from the proprietor about PCB design and hand prototyping, design for assembly, and testing. I was impressionable in those days, and one thing he impressed me with at the time was how he used to design fuses into his PCBs with thin trace segments, along with a component land pattern for a real fuse should the PCB trace need "replacing." The fuse was apparently rated at 2A, and was a 10mil width in standard 1 oz. copper. I wondered if he had some magic formula or if he had empirically chosen the width. He wouldn't tell me.
There are several factors at work in the PCB which can undermine longevity or performance, not the least of which is temperature change. We normally do consider temperature rise, because what we really want to know is how to prevent failure or damage due to overheating. More generically, however, large temperature swings can also limit the useful life of the product due to other thermo-mechanical stresses.
Every experienced board designer knows the headache of design trade-offs. When the allowed layer count, component placement (i.e., 3D mechanical requirements), and difficult routing all conspire to bring unavoidable neck-downs in power distribution polygons, like the one shown in Figure 1.
Figure 1: The 1V8 power supply to the camera module on the STM3240G-EVAL board
(Click here to see a larger image.)
Intuitively, this looks like a bottleneck we want to avoid, but the question is: "Will it be a problem in the actual use of our device?" Figure 1 shows a 1V8 power supply net polygon which takes the 1.8V supply rail from the linear regulator's output to a small camera module (the kind of camera your kids are taking 'selfies' on). Additionally there's an extension camera header connector for the board to allow more substantial external cameras to be connected to the board. The main camera module only draws 50mA or less, so it's unlikely to cause an issue, but plugging something external into the extension header could cause a problem.
To work out the basics of the problem, remember that the etching process leaves the copper traces (in this case the polygon's narrow point) wider at the base, with a trapezoidal cross-section like the one shown in Figure 2.
Figure 2: Trapezoidal shape of the PCB copper conductor at the neck-down or trace.
Heating and fusing of the copper begins as a typical Joule Heating problem. As a quick high school physics review, the amount of energy transferred due to work done (i.e., power dissipation by time) is directly proportional to a change in temperature in the material in question. In our case, the power dissipated from a tiny bit of PCB copper like that shown in Figure 2 is easily calculated by using the resistivity of copper.
Where "Q" is the energy transferred in Joules, "m" the mass of the copper, "c" is the specific heat of copper (about 0.387 KJ/KgK), and "ΔT" is the change in temperature. "Q" relates the change in temperature to the power dissipation for a given time, and since P = I2R, Q = I2Rt. The resistance of the copper is based on the area, length, and resistivity:
Where "ρ" for copper is 1.68x10-8 ohm-meters at 23°C, "L" is length and "A" is cross-sectional area. So in a basic sense we can figure out trace temperature rise in the trace based on the DC current and its cross-sectional area:
However, this is neglecting the conduction of heat away from the trace into the board and convection of surrounding air, and it is also neglecting the fact that copper resistivity is a function of temperature -- the resistance of the trace or neck down rises as it gets hotter. Combine this with the arbitrary nature of board design (differing materials and layer stacks), and you come to realize the only completely accurate way of calculating the temperature rise in the conductor of interest is to use a coupled electrical and thermal conduction model in a finite-element analysis tool (sigh).
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