In this article, I will try to teach you the basics about how to do
it right, and keep your circuits cool.
Another commonly done mistake is assuming that the power rating of a small, non-heatsinked part applies just for the part alone. In truth, a rectifier diode rated at 3A will actually survive that current only if it is heatsinked through its terminals, which are made from thick copper wire for exactly that purpose! If you connect that diode to thin wires instead of a large heatsinking metal part, it will not live very long. Speaking of rectifiers, many people wrongly calculate the power loss in a diode based on a voltage drop of 0.7V for silicon junction diodes and 0.4V for Schottkies. In truth, at their full current rating, the voltage drop of silicon diodes is more like 1.2V, and that of Schottkies is 0.6 to 1V!
So, it pays to read the detailed specifications of a part, understand
them, and extract the really important information for your project.
Conduction is the simplest to understand. Just like electricity flows through an electric conductor, the electrical resistance of the conductor causing a voltage drop proportional to resistance and current, heat can flow through a thermal conductor, with its thermal resistance causing a temperature drop proportional to thermal resistance and heat flow. Thermal resistance is specified in Kelvin per Watt, meaning that a thermal conductor of, say, 2.5 K/W will cause a temperature drop of 5 K (which is the same as a drop of 5°C) when a thermal power of 2 W is flowing through it.
When heat is conducted into a fluid, such as water or air, then convection (motion of the fluid) helps the heat move. Very simply stated, when the fluid moves away from the hot area, it carries along the heat just absorbed. So, thermal conduction through the fluid is aided very significantly by physical motion of it.
This convection can be forced, by a fan for example, or it can be natural, based on the fact that most fluids expand when heating up, lowering their specific weight and thus rise up, causing a vertical flow through or around the hot device.
Radiation does not require a medium, and is thus the only way of heat transfer that works even in a vacuum. Every object radiates heat, and captures radiated heat. The radiation depends on the body's absolute temperature, and on its color! The higher the reflectivity, the lower is the radiation. So, a completely black body produces a thermal radiation that can be easily calculated from its temperature alone, while more shiny objects radiate less and need to be evaluated according to their surface. A perfect mirror cannot radiate heat, even when it is very hot. But in practice there is no way to make a mirror that is perfect over the entire electromagnetic spectrum, from DC to cosmic rays, so in practice every object will radiate some heat. Still, between flat black paint and polished aluminum there is a huge difference in thermal radiation!
The surface color also influences how much radiated heat a body can
absorb. So, a black body will also be a better receiver of heat, which
is why many people living in hot climates prefer shiny white cars over
Just like electrical resistance, thermal resistance can be placed in
series, in parallel, or in combinations, and the same equations apply as
for electrical resistance.
You will first need to know how much power needs to be dissipated as heat. To keep things simple, let's consider just the pass transistors for now. The dissipated power is calculated by the output current multiplied by the voltage drop over the pass transistors. This latter value changes with conditions, so you must assume the worst-case conditions to be safe. If your power supply is designed for a filtered secondary voltage of 20V average under full load, which would be typical, you can have up to 22V when the line voltage is about 10% above nominal. So, you must assume 22V. The voltage applied to the transistors is this, minus the output voltage of 13.8V, so you have a voltage drop of 8.2V, which multiplied by 20A is 164 Watt.
There's also a small power dissipated by the base drive, but this is usually small enough to be ignored. Depending on the circuit layout, actually the base drive could be adding to the output current, but with a lower voltage drop, thus reducing the total dissipation a little bit from the calculated value. But again, this effect is small enough to be ignored. The design tolerances eat it up.
Now you need to know how much temperature drop can be allowed. This is the difference between the highest permissible temperature of the silicon junction, and the ambient temperature. Silicon usually can tolerate up to 150°C, so if the manufacturer doesn't state a different value, use this one. The other end of the span is not so easy to decide on: In an air-conditioned room, with the heat sink standing in free air, you might get away assuming 25°C, but in many cases you will find warmer environments. So you must decide which will be the allowable operating limit of your project. If you design for 60°C, you should be pretty safe even in very hot places, unless you are designing a system that will have the heat sink inside the box, where the air might be even hotter.
For normal home use, I usually design for a maximum ambient temperature of 40°C. When it's hotter than that, I probably won't be using any electronic equipment, but rather would be trying to survive the heat wave in the swimming pool or the shower!
So, between the 150°C the silicon can survive, and the 40°C of the ambient, we have a span of 110°C, or 110K, which is the same. Since we need to dissipate 164W, we need a total thermal resistance of no higher than 0.67K/W. Now let's see how we can achieve that.
I like the 2N3055 transistor. It's dirt cheap, made by many factories, available everywhere in the world, and quite capable. It is rated for 115W at 25°C, which means that its internal resistance is about 1.1K/W (115W cause the silicon chip to be at 150°C when the case is at 25°C). The transistor comes in a TO-3 case, which is quite large and thus has reasonably low thermal resistance to the heat sink.
When using heat conducting grease between the surfaces, a TO-3 case to heat sink connection has a thermal resistance of about 0.4K/W. But when using a mica insulator between the two, there are two grease interfaces plus the mica, so the total thermal resistance of the connection goes up to about 1K/W! Bad news...
In short, the thermal resistance from the silicon chip of a 2N3055 transistor, to the heat sink, including insulation, will be about 2.1K/W.
Now we need to balance the number of transistors to use, against the size of the heat sink. Putting transistors in parallel lowers the total thermal resistance. The absolute minimum number of transistors would be 4, since even with three we have still more thermal resistance in the transistors and heat sink mounting than the total allowable. But with 4 transistors, the total chip-to-heatsink thermal resistance will be 0.525K/W. Since we can tolerate a total of 0.67K/W, this leaves 0.145K/W for the heat sink. Now, the problem is that a heat sink of this low thermal resistance would be huge, heavy, and very expensive!
If you liked this, you may want to use an even smaller heat sink. Let's
suppose that you have a heat sink rated at 0.5K/W. This would leave 0.17K/W
for the transistors. At 2.1K/W each, you would need about a 12 of them.
Probably this is no longer cost effective, and the best tradeoff may be
using about 8 transistors, with a 0.4K/W heat sink.
A 250W transistor would have a thermal resistance of 0.5K/W. But the
thermal resistance of its mounting to the heat sink would be exactly the
same as that for the 2N3055, given that they use the same TO-3 case! So,
the total thermal resistance for each transistor plus mount would be 1.5K/W
for the 250 Watt transistor, versus 2.1K/W for the 2N3055. You get only
40% advantage, not the expected 117%! As a result, instead of 8 2N3055
you could use 6 2N5886, which will be hugely more expensive! If you use
just 4 of them, with the 0.4K/W heat sink, they will burn out.
By skipping the insulation we save about 0.6K/W in the total silicon-to-heatsink path. So, the directly mounted 2N3055 ends up with about 1.5K/W - just as good as the much more expensive 2N5886 when mounted with insulation! So, 6 directly mounted 2N3055 on a 0.4K/W heat sink would work.
You may wonder why I used only 4 transistors in the project just mentioned? Well, it uses a very low drop regulator design and a large filter capacitor, which allow to reduce the average filtered secondary voltage to about 18V nominal or 20V worst case. That gives about 120W dissipation for the pass transistors, which can be handled by just 4 of them. But then you must add the heat produced by the driver and the rectifier bridge, which brings up the total to about 200W. So, a pretty large heat sink is still needed, if you want continuous duty at 20A!
You may even wonder why reputed companies make 13.8V, 20A power supplies
that have just two pass transistors on a rather small heat sink. That's
very simple to explain: These power supplies are not designed for
continuous duty at 20A! They are typically used for SSB transceivers, and
so they are rated for 20A peak current, while the average
current shall not be higher than 5 or 6A! That can easily be managed with
two 2N5886s, or three 2N3055s.
Thermal conductivity is measured in W/(m*K). That is how much heat power, measured in Watt, will flow through a cubical block of 1 meter on each side, when the temperature difference between two opposing surfaces is 1K. Here are some values:
Pure silver: 418.7
Pure copper: 372.1
Pure aluminum: 209.3
Duraluminum (the kind commonly used for extrusions and tubing): 129.1
Brass: Roughly 100, depending on exact alloy
Steel: Roughly 50, depending on alloy
Insulating material such as mineral wool: Typically 0.03
Still air: 0.022 (but convection makes this irrelevant in most cases)
This table shows the huge range of thermal conductivity you can find. While silver is the winner, its conductivity isn't good enough to justify its use for heat sinks, given that copper is almost as good and very much cheaper. But between copper and aluminum one has a choice: Copper is much better, but also much heavier and more expensive. The general choice is to use aluminum for the large parts of a heat sink, and a small copper "spreader" between the heat sink and physically small components that produce very much heat, such as RF power transistors. The cases of transistors usually are made of copper too.
It's clear that duraluminum is a bad choice, given that pure, soft aluminum is cheaper and has much better heat conductivity! Unfortunately, many commercially available heat sinks are made from duraluminum. Sometimes we have to live with them. But all other metals should be avoided.
Mica is a really lousy heat conductor! The problem is that few electrical insulators are good thermal conductors. Among them, some oxides, such as alumina and beryllia, are decent. But they are brittle, rather expensive to make into usable insulators, and in the case of beryllia, highly toxic. Synthetic rubber is used nowadays in place of mica, but it is even worse. Its advantage is that it doesn't need thermal grease for mounting, so the end effect is similar to a mica insulator mounted with grease, but cleaner.
Speaking about grease, the number given here is for pure grease. The
one used for thermal bonding is loaded with oxide powder, which makes it
somewhat better for heat transfer, but it is still very far from the thermal
conductivity of metal! Even so, it's a huge lot better than air. This defines
the proper way of using it: You must apply enough to fill out all the spaces
left by the imperfections of the metal surfaces, which would otherwise
trap air, but not a tad more! Using too much thermal grease can be worse
than using none at all! And the grease must be fluid enough to be easily
squeezed out when moderately tightening the mounting bolts, and the oxide
powder must be very finely ground.
On the other hand, if you bolt your transistors to the back panel of a box, by all means paint that panel flat black! A flat panel dissipates more heat by radiation than by conduction, and here a flat black surface helps a lot! But it helps only if it looks at other objects that are dark, and cooler than the panel, or if it looks at free space. If you place such a black heat sink in the sun, it will absorb heat rather than radiating it, and get very hot! Likewise, placing a black heat sink inside a shiny aluminum box is useless, because its radiated heat will reflect back onto itself. For that reason, paint the inside of aluminum boxes flat black too, so that the electronic parts inside the box can cool themselves by radiation into the aluminum box!
Do you want another table? Well... here is one about the radiation constant of different materials. This is expressed in (10-8)W/(m2 K2) , at 20°C.
Perfect black body: 5.67
Matted steel: 5.4
Matted zinc: 5.3 (that's why zinc roofs get so hot in the sun!)
Oxidized copper: 3.6
Polished copper: 0.28
Matted aluminum: 0.4 (that's why aluminum roofs are much fresher in summer than zinc ones!)
Polished aluminum: 0.23
Polished silver: 0.17
There is a simple pattern: Shiny, light surfaces emit and capture very
little radiation, while reasonably dark surfaces, specially if matted,
are almost perfect radiators and capturers.
I can give you an empirical equation that is about right for an optimally shaped heatsink in completely free air, running at 50°C above the surrounding air:
Heatsink volume (liters) = 0.8 / thermal resistance1.47
As an example, if you need a thermal resistance of 1°C/W, this would equate to a heatsink volume of 0.8 liters, while a heatsink of half as much thermal resistance would require a volume of 2.2 liters, much more than twice the volume of the other! Which leads to the conclusion that several small heat sinks can be more convenient than a single large one. This of course holds true only if they are placed far enough from each other, so that cool air can freely circulate through each of them.
Remember that this empirical equation is reasonably accurate only if the heat sink has enough fins efficiently using its volume, if air can circulate freely, if the thermal conductivity of the material is so good that there is negligible temperature drop along the heat sink, and also it is valid only at 50 degrees difference between the heat sink and the air. So, the 0.8 liter heat sink would heat up to 50 degrees above the ambient when you apply 50 Watt to it, but if you apply 25 Watt, it will heat up more than 25 degrees above ambient, and if you apply 100 Watt, it will not reach 100°C above the ambient! Stated in words, the thermal resistance decreases as the temperature difference increases, because the larger temperature difference speeds up convection. And this change is pretty large: The power to temperature rise ratio is almost square law, that is, with twice the temperature difference a given heat sink can dissipate four times as much power! This effect is easy to explain: If the temperature difference is twice as high, each quantity of air absorbs twice the heat, but also the air will flow twice as fast, so that it will take away four times as much heat.
We can merge the square law relationship with the equation relating volume to thermal resistance at 50 degrees rise. The following results:
TempRise [°C] = 10 * ( 0.8 / Vol[liters])0.68 * Power[Watt]0.5
So, a heat sink having a volume of half a liter and carrying a transistor that produces 50 Watt of heat would rise its temperature roughly 97°C above the surrounding air. Most likely this would be too high a temperature, so that we need to use a bigger heat sink or add a fan.
But don't take this as an exact science. At high airspeeds, the friction
loss again bends the equation, and any radiative effects also distort it.
So, my equations can give you a basis from which you can start, but in
many cases you will need to adjust the results through experiment.
How much does a fan lower the thermal resistance, you may ask? To find out, I built a test heatsink from pure copper, of two liters volume, and with almost a square meter of fin surface. This gave me a thermal resistance of roughly 0.5°C/W at 50°C difference. Then I added a small 12V, 1W fan to it. The thermal resistance plummeted to 0.13°C/W! It was now more limited by conduction along the baseplate, than by the dissipation capabilities of the fins. Which means that a heat sink with thick fins, designed to be used with a fan, will benefit more than one with thin fins, designed for natural convection. Note that to obtain the same 0.13°C/W thermal resistance with a fanless heat sink, it would need a calculated volume of around 16 liters, thus being 8 times as large as the one with fan!
With a fan, air flow is basically constant, so the heat sink/fan combination
has a pretty constant thermal resistance, regardless of temperature difference.
A chimney is simply a thermally insulating tube placed above the heat sink or hot part. The warm air rises, fills the chimney, and the tall column of warm air produces a strong convective force, so that much more air flows through the heat sink, than if there was no chimney! Without one, only the air inside and very close the heat sink causes a convective force. With a chimney, you can have a warm air column much taller than the heat sink's size, and thus get much improved cooling without any noise, energy waste, nor risk of failures!
The only disadvantage of chimneys is that they need to be taller to become more effective. To really reach an effectiveness close to that of a fan, a chimney may need to be almost as tall as the room is high! That may look outlandish, but I know people so fed up with the noise of their computer's fans, that they have thrown out the fans and installed tall chimneys on their computers! If you have the room and don't mind the funny look, a chimney can be a lot more attractive than a fan, at least for equipment not moved around too often.
A heater element placed low in the chimney, just above the part to be
cooled, will aid the chimney's efficacy, with no penalty in noise, but
with a large energy waste. In some cases, this method can be warranted!
The heater should be installed in such a way that it doesn't radiate heat
into the part to be cooled.
Water cooling is attractive too for high power electronics. Our sample
power supply could be built with the transistors mounted to a small hollow
copper block fed by a flow of only about a half liter of water per minute,
for the same 5 K rise! A very small pump, made with a rocker motor or a
solenoid pushing against a silicone hose, could supply that flow. The heat
exchanger may be built like a car "radiator", and since it can be made
large without the problem of thermal resistance hampering heat flow along
it, a very silent and effective cooling system can be built. High power
transmitters very often use water cooling.
An effective even if ugly method for improving cooling is to paint shiny parts flat black, and do the same to the box' inside and outside! The radiative cooling obtained in this way is very noticeable!
A grave mistake shared by hobbyists with many "professional" designers, is placing small electrolytic capacitors close to hot spots. It's true that semiconductors don't like heat, but electrolytic capacitors like it even less! At 100°C, a silicon junction can live forever. At the same temperature, an electrolytic capacitor can die in a matter of hours! A typical electrolytic capacitor can live for 30 years at room temperature, one year at 60°C, one month at 85°C, and one hour at 110°C. They are often rated for a given temperature, typically 85°C, which is the temperature at which they will live for 1000 hours. Of course, 1000 hours is not an acceptable life span for an electronic component, and so the designer must make sure that the capacitor will stay at a temperature very much lower than this! That precludes placing it close to power resistors, rectifier diodes, and the like.
Unfortunately many electronic designers in the industry don't know this, don't care for it, or perhaps even intentionally misdesign equipment so that it fails soon and forces the consumer to buy a new one, keeping the money rolling. I have been repairing electronic equipment for two decades, and in my experience the single most recurring failure is small electrolytic capacitors dried out from excess heat, in TVs, monitors, and switching power supplies for all kinds of gadgets. In some cases this is compounded by the designers allowing too much ripple current to flow in a small capacitor, which heats it from the inside and makes it fail even sooner. The bootstrap capacitor in switching power supplies using the ubiquitous UC3842 IC is one very typical victim, and the poor beasts pressed into TV and monitor deflection service come second in the list of electrolytic capacitors assassinated by poor equipment design.
It seems that I'm veering off the proper course, complaining about bad
engineering instead of teaching you heatsinking tricks. So it may be better
if I stop here!
Back to homo ludens electronicus.