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Many people wonder why their Arduino boards get hot when they use Vin = 12V, and in fact, this issue comes up about once or twice a week on the Arduino Forum.
The short answer is that most Arduino boards use small surface-mount (smt) voltage regulators, which get hot even at moderate load currents, and especially when larger Vin values are used. Many Arduino boards are advertised as having "1A" voltage regulators, but in the real world, you cannot run load currents anywheres close to this level, because of overheating. See Table 2 below.
The real problem is that power dissipation and heating is related to both the voltage-drop across a device and the current through it, so the result is a "multiplicative" effect of the two factors, and not related to just the Vin or load current value alone. Ie,
Pd = Vdrop * Iload --> heat generated
Once this relationship is grasped, the overheating issue is easily understood.
Table 1 - Thermal Ratings
Power dissipation for voltage regulators is based upon package size (TO-220 vs smt DPAK, SOT-223 or SOT-23), plus amount of heatsinking. The amount of "temperature rise", above ambient, versus power dissipation for these devices is as follows:
The first two regulators are the style used in OT-Hobbies boards, and the latter in many Arduino boards. The smaller ones are clearly 3X-4X worse than the larger, in regards heat buildup.
For the TO-220 device, a 20mm x 18mm pcb copper heatsink area under the regulator will reduce the temperature rise by approx 40%, relative to the value shown above (cf, Table 1 in LM1117 datasheet), and use of a metal heatsink under the device will further reduce heat buildup.
For the DPAK and SOT-223 devices, the values shown assume minimum pad size (ie, pcb copper heatsinking area) of 5mm x 5mm, 2-oz copper (cf, fig 21,22 in NCP1117 datasheet). And if the copper area is increased by 400% (to 10mm x 10mm), then the temperatue rises are approx 20% and 40% smaller, respectively.
Note also - that "typical" pcbs use 1-oz rather than 2-oz copper, so copper area heatsinking will be about 33% less effective than the values given above (cf, fig 6 in LM2940 datasheet).
Thermal Shutdown. Voltage regulators are generally rated for thermal shutdown at 150-175 °C, however, for reasons such as not overheating the pcbs and not burning one's fingers, maximum operating temperatures of 80-100 °C are much more practical. After all, 100 °C is already the temperature of boiling water!
Table 2 - Temperature Rises
The following table shows the power dissipation (Pd) and estimated temperature rise, above ambient, for different 5V regulators at various load currents, with Vin = 12V and 7V. The first temperature rise column indicates the result of using a metal heatsink with 50% effectivity under the TO-220 device.