# Why’s It So Hot in here?

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## Thermal Basics

### Thermal management of electronic components is often a misunderstood area of design. Often thermal solutions are “I hope this works” guesses. In this article, I cover the basics of thermal management so you can design circuits that don’t overheat.

• What are the basics of thermal management when designing embedded systems?
• How do I know if I need a heatsink?
• What is thermal resistance?
• LF33 3.3V regulator

Have you ever built a circuit that dissipates power, such as a voltage regulator or audio power amplifier, and wondered how to keep it cool? Ever wonder how Intel chooses the heatsink and fan for the CPU in a desktop PC or server? Why do people go to the expense of water cooling a PC or other system?

Keeping electronics from overheating is an important part of circuit design. It’s both a scientific process and a little bit of magical mystery. (I say “magical” because sometimes you don’t know everything you need to know to make it pure science.)

The goal of thermal management in most electronics is to keep the semiconductors from overheating. Other parts can overheat as well—see my Circuit Cellar article about resistors (“Getting Started with Resistors: Workhorses Devices,” Circuit Cellar 382, May 2022) for more detail about that [1].

##### POWER

Any electronic component—whether integrated circuit, transistor, resistor, motor, or any other part—dissipates power when current flows through it. The power dissipated in the device gets turned into heat. Even a wire dissipates power, although if the wire is sufficiently large, it doesn’t dissipate much. A wire may carry 100A to an industrial welder without dissipating much power in the wire if the resistance is low enough. Power is calculated as VI—voltage times current. So, the power dissipated by a wire or a resistor is the voltage across the wire times the current through the wire.

An ideal digital integrated circuit, like an ideal wire, would dissipate no power at all. Every component inside the part would either be using zero current or have zero voltage across it, so VI would always be zero. But unfortunately, you can only find zero-power integrated circuits in the physics department of your local university, on the same shelf as the massless ropes and the frictionless surfaces.

Since real integrated circuits dissipate power, they generate real heat. In some cases that heat must be transferred elsewhere to avoid overheating the device. And that’s where thermal management has to happen. I’ll focus only on semiconductors in this article, but the same principles apply to things like power resistors.

##### THERMAL PARAMETERS

For an integrated circuit, it’s important to keep the junction, the semiconductor element, from overheating. The word “junction” might imply that there’s only one junction in the device; this is a carryover from the days of transistors. “Junction” means the semiconductor inside the IC package, regardless of how many transistors it contains.

The important thermal number is the junction-to-ambient thermal resistance, RΘ. RΘ can be just the RΘ of the part, or the RΘ of the part plus additional components such as a heatsink. This is a measure of how efficiently the package transfers the dissipated power to the ambient temperature. Thermal resistance is expressed in °C per watt. A TO-220 package might have an RΘ of 50°C/W, which means that if the part is dissipating 1W, the junction temperature will be 50°C above ambient.

Ambient temperature is important in thermal management because the temperature of the IC case can never be lower than the ambient temperature. Say an IC has a maximum junction temperature of 125°C and has 100°C/W RΘ. If the device is dissipating 0.5W, then the junction will be 50°C hotter than the ambient (0.5W x 100°C/W = 50°C). So, if it is dissipating 0.5W, then to avoid overheating the device, the maximum ambient temperature is 125°C – 50°C, or 75°C. (I’ll be rounding temperatures to the nearest degree.)

For a power IC there will normally be at least two thermal resistances specified: the RΘ of the junction-to-ambient (usually RΘja), and the RΘ of the junction-to-package (RΘjp) which applies if you have something attached to the power tab. Connecting a heatsink to the power tab provides a better transfer to the ambient temperature.

Thermal resistance of a device is supplied by the manufacturer. The calculation for thermal resistance requires that you know the surface area of the material, the thermal conductivity, and the thickness of the portion of the material between the junction and ambient air. It’s impractical for someone designing with a part to know all of that, especially about an IC, so the manufacturers provide it in the datasheets.

Since there’s no way to get heat out of the device other than through the device package (which includes the power tab, if there is one), the entire goal of thermal management is to efficiently transfer heat into the ambient surroundings. “Ambient surroundings” isn’t necessarily the temperature of the room. It might be the temperature inside the enclosure, or the temperature of the chassis if the chassis is used as a heatsink. A passive heatsink can’t cool a device below ambient; the best you can do is get it closer to ambient. Figure 1 is a photo of a heatsink for a TO-220 package. This would typically mount on a PCB. The fins are intended to maximize the surface area for efficient transfer of heat.

RΘ is treated mathematically as ordinary electrical resistance. Figure 2 illustrates this: an IC such as a voltage regulator is connected to a metal plate that functions as a heatsink, which is attached to the PCB. Say the IC package has an RΘ of 10°C/W and the metal plate has an RΘ of 20°C/W. So, the total RΘ between the IC junction and the PCB is 10 + 20 = 30°C/W. The PCB itself will have some thermal resistance to the ambient air, or to the chassis that it mounts to. Thermal resistance is essential in determining whether you need a heatsink in your circuit, and what kind.

##### DO YOU NEED A HEATSINK?

You might not be sure if you need a heatsink on a given part. You can determine this by the following equation:

where Tj is the junction temperature, Ta is the maximum expected ambient operating temperature, P is power in watts, and RΘ is the thermal-to-ambient temperature in °C/W. If Tj exceeds the maximum junction temperature, then you need a heatsink. And, of course, you need to know the maximum ambient temperature and the maximum power that will be dissipated.

##### EXAMPLE CIRCUIT

Figure 3 shows the schematic of a simple circuit that I built to illustrate some of these concepts. Figure 4 is a photo of the circuit, an LF33 3.3V regulator in a DPAK surface-mount package. The DPAK (which is the same as the TO-252 package) has two leads—input and output—and a tab for ground. The tab is normally soldered to a copper land on a PCB. In this case, I soldered it to a piece of 0.25” x 2” adhesive-backed copper tape and attached a small ring-terminal thermistor to the copper tape so I could measure the temperature of the LF33. The thermistor is probably not exactly at the temperature of the IC case, but it’s close enough to demonstrate the principles involved.

The circuit is powered by a 5V input and the load resistor R1 draws 330mA, dissipating 1W (I²R). The LF33 also draws 330mA, and has 1.7V across it (the 5V input minus the 3.3V output), so it dissipates 560mW (1.7V x 330mA). The thermistor is used to calculate the temperature using the resistance (measured with a DVM) and a handheld calculator (see my aforementioned resistors article for a description of thermistors [1]).

According to the LF33 datasheet [2], the DPAK case has a junction-to-ambient RΘ of 100°C/W. The LF33 junction-to-case resistance is 8°C/W from the power tab. The copper tape and the solder and even the ring terminal on the thermistor provide some amount of thermal heatsinking. For the calculations here I’ll use the junction-to-case resistance since the thermistor will be very close to the temperature of the mounting tab. The ambient temperature when I did this was 23°C. Without the copper tape heatsink the junction would be at 23°C + (560mW x 100°C/W), or 79°C. I applied power to the circuit and the temperature stabilized at 53°C, or 30°C above ambient. So, the junction temperature was the case temperature + (power x RΘ), or 53°C + (560 mW x 8°C/W) = 57°C.

For the second experiment, I soldered a 0.032” thick x ½” x 2” long piece of brass to the heatsink. This was soldered to the top of the LF33 ground tab, so it had good thermal contact with the LF33. In this configuration, the temperature was 48°C. Doing the same math, the junction temperature was 52°C, or 5°C cooler.

I then added a 2” fan to blow air over the fin; the temperature came down to 28°C—just 5°C above ambient—making the junction temperature 32°C. So even in this simple experiment, you can see that improving the ability to transfer heat into the ambient surroundings is key to controlling device temperature. The small brass fin isn’t much of a heatsink, but it provides a lower RΘ than the copper tape. Cooling with just the brass fin depends on convection. Adding the fan reduces the RΘ further because even the brass fin can transfer heat better into moving air.

##### SELECTING A HEATSINK

Now I want to extend the example and select a real heatsink for a real device. The LF33, like a lot of linear 3-terminal regulators, will shut down if it gets too hot. But, although that protects the device, having our piece of equipment randomly shut down for no apparent reason will not make it very useful and will annoy the user. So, we want to keep the device cool enough to prevent that.

The LF33 comes in both DPAK and TO-220 packages. The TO-220 has a power tab with a mounting hole for a heatsink. The TO-220 package has the same maximum junction temperature of 125°C, but the junction-to ambient RΘ is 50°C/W, half that of the DPAK package, and the junction-to-case RΘ is 5°C/W. Let’s say we’re going to supply the LF33 with an 8V input and it must supply 300mA to the circuit it’s driving. The dissipation of the LF33 will be (5 – 3.3) x 300mA, or 1.41W. Without a heatsink, the junction temperature will be 1.41 x 50, or 70°C above ambient.

With these parameters, the maximum ambient temperature is 125 – 70, or 55°C. And really, it’s lower, because you don’t want to run the part right at the thermal limit. Let’s suppose the design specification says it has to operate in an enclosure where the temperature can reach 60°C. How do you find an adequate heatsink for that?

The heatsink must have an RΘ to ambient that will prevent the LF33 from exceeding the maximum junction temperature at an ambient temperature up to 60°C. Since we’ll be using the TO-220 power tab for mounting, we’ll use the junction-to-case RΘ. The LF33 will be mounted with a thermal pad or with silicon grease to improve the thermal connection. The total RΘ to ambient is the package RΘ + the thermal pad/grease RΘ + the heatsink RΘ. For this calculation, I’ll say the RΘ of the thermal pad is 1°C/W.

So, we need a heatsink large enough that the temperature of the LF33 junction remains below 125°C with an ambient of 60°C while dissipating 1.41W. The heatsink (with the thermal pad) makes the thermal “connection” between the case and the ambient air.

The total RΘ of the package, thermal pad, and the heatsink together is:

RΘjc is the device’s junction-to-case thermal resistance (5°C/W), RΘtp is the thermal pad resistance (1°C/W), and RΘhs is the heatsink thermal resistance. The temperature rise (125°C – 60°C) when using a heatsink is then:

Power is 1.41W in this example, as discussed. Doing some algebra to find the total thermal resistance, we get:

So, the heatsink thermal resistance must be 40°C/W or less. Looking through the Digikey online catalog for TO-220 heatsinks, we find that the Aavid 577002B00000G, with an RΘ of 32°C/W, works, and with a little margin. With 500 linear feet/minute (LFM) airflow, the RΘ of the part drops to 10°C/W, a 3:1 reduction.

When choosing an off-the-shelf heatsink, you’ll want something with a thermal resistance that’s a little lower than the calculations indicate. This is because the manufacturer characterizes the heatsink based on some configuration, such as a plate that covers the surface of the heatsink and distributes the heat evenly. In reality, a TO-220 power tab in this example doesn’t cover the entire surface of the heatsink, so there is going to be some difference between the theoretical thermal resistance and the actual thermal resistance of the heatsink attached to the actual part.

The material of the heatsink also has some thermal resistance. There’s a temperature gradient on the heatsink as you move away from the heat source. To put it simply, there’s a thermal resistance between two points on the heatsink itself.

To demonstrate this, I wired a 7805 linear regulator with a 5Ω (0.5A) load and attached it to a 3” x 0.9” scrap piece of 0.064” thick aluminum. Figure 5 shows the circuit and the mechanical construction. The 12V supply was unregulated, so the 7805 was dissipating about 4.5W. I used a thermocouple to measure the temperature along the length of the aluminum piece, and it varied from 95°F right at the 7805 power tab to 91°F at the opposite end (the meter had 1°F resolution). Not a lot of difference, but then this example isn’t dissipating a lot of power. But allow some margin in your design.

##### WORKING IT BACKWARD

I’m going to create a ridiculous scenario to illustrate how this works in reverse. Say you have my original DPAK LF33 experimental circuit with the brass fin and copper tape. But now you want to take the board to production, and you need to have the same thermal characteristics but with an off-the-shelf heatsink.

From the previous experiments, the temperature of the device is 48°C, or 25°C over ambient. RΘ of the combined brass fin and copper tape can be calculated this way:

So, you’ll need to find a heatsink that has an RΘ less than 45°C/W.

Suppose there’s a new requirement: the current product uses a fan to keep the regulator cool but the fan is a high-failure item (as fans often are). You need a heatsink that will cool the device without using the fan. In my experiment, the fan brought the case temperature down to 28°C. I don’t even know how much air the fan was providing, but it doesn’t matter—we know how much the fan lowers the temperature. I’m ignoring the junction-to-case temperature of the device here. We know the case temperature from the previous measurements and just have to keep that the same as the original circuit.

With the fan, the total RΘ is (28 – 23)/560mW or 9°C/W (fan + copper tape + brass fin). So, you need a heatsink with an RΘ less than 9°C/W. That’s going to be a large heatsink, and it may be difficult to transfer the heat into the heatsink efficiently from the DPAK power tab. If you were doing this in a real application, you would want to switch to the TO220 package, which will transfer heat better into the heatsink. The real calculation is a bit more complicated than that since removing the fan may raise the ambient temperature inside the enclosure, so more thermal analysis of the entire system is needed. That’s an important point: when you use any kind of heatsink to draw heat away from a device, something else gets hotter, whether it’s ambient air, the case, or something else.

##### CASE HEATSINKS:

Sometimes the case of the product is used as a heatsink. This was common some years ago with audio amplifiers and large computer power supplies. Some parts, such as the ST TDA7292 audio power amplifier, are intended for a large heatsink such as the chassis of the equipment. You will usually need to do some thermal analysis of the case to ensure that the part won’t overheat. Many years ago, I developed military electronics that had to be in a fully enclosed, waterproof housing. In that case, the aluminum enclosure was the only heatsink available.

##### PCB COPPER HEATSINKS:

Copper on a PCB can act as a heatsink. Depending on whose numbers you use, a square inch of 1oz copper has an RΘ of about 50 to 100°C/W. 0.063” FR4 PCB material has an RΘ of about 10°C/W, so the board itself will provide some cooling. A larger copper area provides a better heatsink, but because the copper layer is so thin, it doesn’t transfer heat as effectively as an equivalent piece of, say, 0.064” thick aluminum (see the section on thermal gradients). But for surface mount parts, PCB copper is often adequate. Some ICs specify that a certain amount of copper area should be connected to specific pins or to an SMT pad under the device. A ceramic PCB (instead of FR4) has a lower thermal resistance. You can also get heatsinks that solder to a PCB to increase the effectiveness of a copper-pad heatsink.

##### ACTIVE COOLING

As already mentioned, you can direct air over a heatsink to improve heat transfer, lowering the effective thermal resistance. Fans tend to be relatively high-failure parts, so if your design depends on a fan, then you should be monitoring it and take some action if the fan stops or if temperatures get too high. And, again, a fan can take the temperature closer to ambient, but not below it. No amount of air movement will make the part cooler than the air itself.

Another type of active cooling is a liquid-cooled heatsink, where liquid is pumped through the heatsink, then cooled in a heat exchanger, and reused. The liquid-cooled heatsink just provides a more efficient mechanism to transfer the heat, making the cooled part closer to ambient. The only way to get the part colder than ambient is to use chilled liquid.

You can also get Peltier coolers that cool on one side and, of course, heat on the other. You still have to get rid of the heat; the laws of thermodynamics make sure there is no such thing as a thermal-free lunch. By attaching a heatsink and/or fan to dissipate the heat, Peltier coolers can lower the temperature of the IC package, even lower than ambient. But Peltier coolers are inefficient—they need significant power input to produce significant cooling, and they need a very efficient heatsink on the hot side. From a system perspective, you will produce more additional heat in the power supply than you will pull out of the device you are cooling. But there may be situations where you want the device to be cold and don’t care how much power it takes to do that.

##### MEASUREMENT

Thermal modeling software can predict how hot things will get, especially when designing a custom heatsink. But sometimes there is no substitute for measurement. You do the best design you can and then measure the hot devices with thermocouples or an IR gun to make sure they don’t get too hot.

##### CONCLUSION

A lot of circuit designs don’t need to be concerned with cooling. But when you do need some kind of thermal management, it’s important to be able to calculate what will work. Hopefully, this article has pointed you in the right direction.

REFERENCES
[1] Ball, Stuart: Getting Started with Resistors: Workhorses Devices. Circuit Cellar, Issue 382, May 2022, p. 12-17.
[2] LF33 Datasheet: https://www.st.com/resource/en/datasheet/cd00000546.pdf

PUBLISHED IN CIRCUIT CELLAR MAGAZINE • AUGUST 2023 #397 – Get a PDF of the issue

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