Application Note 2.
Thermal Design Calculations.

This page gives information on thermal design and heatsink selection for audio power amplifiers. No serious mathematics is required.

The power amplifier PCBs we sell are designed so they can either be fitted directly to a heatsink, or wired to power devices on a separate heatsink assembly. In either case it is up to you to choose a heatsink with adequate cooling to the air.

There are several ways to determine the power dissipated in an amplifier,but the simplest is to find the power drawn from the supply, and then subtract the portion of that which goes into the load.
The average current drawn from the supply, Iavg, was found on the Power Output Calculation page. Multiplying this current by the rail voltage gives the power drawn- but only from one rail. There are two, hence the factor of two in the equation for Psupply below.

This assumes that each stereo channel has its own heatsink. If you have both amplifiers mounted on one heatsink- which is fine so long as it has enough cooling capability- then multiply by two once more. If you are building a 5-channel amp for home theatre use, then clearly you multiply by 5 instead.
It is also very easy, given Pout and Psupply, to find the amplifier's efficiency. This should be about 75%, and while not a very useful figure in itself- after all, there is nothing you can do to change it- it makes a very good check that the arithmetic is correct.
The figure of 75% holds only for a Class-B amplifier delivering maximum output of a sine wave into a resistive load. Lower powers give less efficiency.

This is not too hard. Just divide the total power Pdiss by the number of output devices- usually this is two, but for the Load Invariant design in particular, there may be multiple output transistors in parallel. Use the total number of transistors.

From Pdiss, found in Stage 1 above, it is very simple to work out how hot the heatsink will get. The performance of heatsinks is specified as a "thermal resistance to ambient" usually shown as a theta. The ambient Tamb is just the temperature of the air in the room where your heatsink happens to be; it is usually assumed to be 25 degC.
The thermal resistance is the number of degrees above ambient that will the heatsink will reach when 1 Watt of power is dissipated. Multiplying this by Pdiss and adding Tamb gives Tsink, the heatsink temperature.

This is of course simple only if you have the thermal resistance of the heatsink to hand. It is always provided by the manufacturer or seller, but if you already have a heatsink of uncertain provenance that you want to use, (once again these items are expensive) the vital number may not be available. In this case the best you can do is to obtain as many heatsink catalogues as possible, and find one that is close to yours. Look for number of fins, depth of fins, and length of fins. You should be able to get an approximate thermal resistance for the heatsink you have. If in doubt allow a bigger factor of safety (known in the engineering business as the "factor of ignorance") and all should be well.
You will have noticed that having a constant number called "thermal resistance" implies that heat loss in Watts is proportional to the temperature rise. Given the complexity of the convection process, this seems a bit too good to be true- which of course it is. The thermal resistance varies with the temperature of the heatsink above ambient; fortunately this effect is not strong enough to cause serious problems when sizing heatsinks for domestic amplifiers.

The heatsink temperature is important in itself- you don't want an amplifier you can burn yourself on- but its main purpose is as a preliminary stage in finding the output transistor junction temperatures. This is the vital figure which will determine if your amplifier works reliably for 30 years or fails gracelessly ten minutes into the first CD.
Once more, there are certain pieces of data you need. The maximum junction temperature for power devices is spec'd by the semiconductor manufacturer; it is usually 150 degC but some big TO3 devices (eg MJ15024) offer 200 degC.
The other piece of data provided by the manufacturer is the thermal resistance between the junction and the outside of the device package, theta-juncncase.
The final piece of data is the thermal resistance between the outside of the device and the heatsink. It is essential to have some flexible material between the transistor and the heatsink, to ensure good thermal contact. This thermal washer is usually also an insulator as the transistor cases are connected to their collectors, and so must be electrically isolated from the heatsink. Modern thermal washers are made of very thin silicone rubber and require no thermal grease. They also have their own and significant thermal resistance, theta-casesink.
The heat from the transistor junction has to go through theta-juncncase and theta-casesink before reaching the heatsink; hence the case is hotter than the heatsink, and the junction is hotter than that again. These two thermal resistances can be treated just like electrical resistors: when in put in series the values add. So to get the junction temperature we just multiply Pdevice by the sum of the two thermal resistances. This gives us the junction temperature Tjuncn. This should be comfortably less than the maximum; if the limit is 150 degC then 100 degC junction temperatures should give excellent reliability.
Note the value for Tjuncn is an average over a cycle; with very slow waveforms the junction could change temperature during a cycle of the output waveform. However, in audio, where the lowest frequency is likely to be 10 Hz or so, cyclic temperature variations appear to be negligible.

As usual in electronic matters, the cooler things run the better. Even if you observe the maximum junction temperature, large variations in transistor temperature (often called thermal cycling) can shorten device life because of the stresses and strains set up inside the package by thermal expansion.
It always pays to be generous with the heatsinking.

The Signal Transfer Company accepts no liability for any loss or damage consequent to the use of the information given here.