Power Dissipation and Thermal Resistance

In a previous post I was designing a 9V Class A amplifier that took the 1VPP output from the Teensy's Audio Adaptor board and amplified it to 9VPP.

So I figured, “Hey, why power the amp and the Teensy separately when I can just power them both from a single 9V DC supply?” To prevent the Teensy from going up in smoke I would need to split the power supply output between the two circuits and regulate the voltage down to 3.3V, specifically for the Teensy.

While a switching regulator would be more efficient, I was concerned about introducing noise into the audio circuit. In order to keep the design simpler I opted for a linear power supply. I chose the well-known LM317 adjustable linear regulator. It’s cheap, made by numerous manufacturers and easy to purchase from several vendors. The downside with a linear regulator is that it will simply dissipate the unused power as heat, i.e. discard it into the surrounding environment...potentially getting very hot...and in a worst case scenario shutting down entirely. Therefore, in order to design this without needing a fire extinguisher we need to consider:

how much power will the regulator dissipate in our circuit?
how can we adjust our design efficiency to prevent catastrophic failure?

A. Power Dissipation

So I decide to use the LM317 regulator. What is the main characteristic about linear voltage regulators? They are inefficient. Any unused voltage is simply discarded as heat, through the package of the regulator itself. This known as Power Dissipation, shown in Watts. You will need to know the current draw of the circuit beforehand. Helpfully, I had obtained a rough estimate of the total current that the amp would draw from a previous post (Making a common-emitter, small-signal voltage amplifier - Part 1). Let’s add up the current needed by each junction of the transistor:

Iload = Ie + Ic + Ib

Iload = 0.00725 + 0.0036 + 0.000036

= 0.010886A

= 11mA

The amp circuit is stereo so we multiply that by 2.

Now we can calculate the Power Dissipation (PD) as:

PD = ( Vin - Vout ) * Iload

PD = (9 - 3.3) * 0.022

= 0.125 W

Well that’s hardly anything. But hold on. This is not taking in account the load of the Teensy itself when it is connected to the amplifier circuit. Looking at the datasheet for the Teensy’s processor (Freescale K20P64M50SF0) the current operating requirement is 155mA. Now bear in mind this is the “absolute maximum” rating and we shouldn’t be going anywhere near this figure (at this point the whole thing would disappear in a puff of smoke).

Halfway is about 80mA. Add our 22mA. Roughly speaking it should be about 100mA .

Adjusting our calculations we now get:

PD = ( 9 - 3.3 ) * 0.1

= 0.57 W

This is the power dissipated by our regulator for our class A amplifier circuit and if we want to manage this correctly i.e. prevent the regulator from bursting into flames (or simply shutting down) we need to take this into consideration when designing our power supply.

B. Thermal Resistance

Now that we have a good indication of the power that will be dissipated by the LM317 in our circuit we need to use this in this our design to make sure it doesn’t go into meltdown. Yes that is a technical term…

The absolute maximum operating temperature of the LM317 is 125˚C. Again we don’t want to go anywhere near this...more like a comfortable halfway of 60˚C. But this still doesn’t tell us if the regulator will cope with the specific load and power dissipation we require.

To ascertain this we need to calculate the Thermal Resistance.

Junction-to-Ambient Thermal Resistance (TJA) is the ratio of temperature and watts, and specifies how many ˚C the junction temperature will rise for each watt of power dissipated.

Therefore, a lower TJA value in a component indicates a higher efficiency at dispersing power as heat.

We want to know how our power dissipation requirements of our circuit will affect the TJA of the LM317. We will call this value: TJA. We calculate this with the following formula:

TJA = TJ - TA / PD

As mentioned we don’t want to push the LM317 beyond 60˚C and assuming an ambient room temperature of 20˚C, the calculation is:

TJA = 60˚C - 20˚C / 0.57 Watts

= 70 C˚/W

So we need a regulator package that has a rated TJA of 70 or less.

Helpfully, the vendor-provided datasheets specify the TJA of their components according to package. Here is the table from TI’s LM317:

Clearly the through hole TO-220 package is the winner and it’s not surprising considering it can be mounted vertically. However, we want to use surface mount. At 41.0 the TO-263 (DPAK) is the better option. But as it appears that our requirements are satisfied by the SOT-223 and because I would prefer to use the smaller package of the two, we will use the SOT-223.

At this point it’s probably worth taking special note of the disclaimers in the datasheet. Without putting myself in an actionable position, let’s just say I would like to swing the TJA in my favor as much as possible.

You can do this by using exposed copper on the PCB as a built-in heatsink. The junction pad on the back of the SOT-223 package will be soldered directly to this PCB “heatsink”.

There is an excellent study by ON Semiconductor on PCB Heatsinking - “AN1028: Maximum Power Enhancement Techniques for SOT-223 Power MOSFETs” - which runs a series of tests on the optimum area size of PCB heat-sinking for this exact package.

Perhaps the results are not surprising: Use as much space for heat-sinking as your design will allow. However, it also concludes that you will get the best results first by adding exposed copper to the top side (the mounted side) and then second by adding another exposed copper area to the bottom side. However, doing so (and adding more area than the overall package size) will only improve TJA in diminishing returns. The biggest reduction in TJA is seen in the first 0.2in2 (5.08mm2)

Therefore, I will need a minimum requirement of 5mm2 exposed copper pad. But let’s not be conservative. I might as well add a corresponding heatsink to the bottom side and join the two with “via stitching” if the design allows.

C - References

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Power Dissipation and Thermal Resistance

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