This article is directed at heatsink consideration for PAs, but applies equally well to almost any matter where movement of heat is desired. Paul explains thermal resistance as an almost exact counterpart to Ohm's Law. He then applies it in a practical way to a Toshiba 40W 3.456 GHz amplifier.
All heatsinks have a thermal resistance (Rth) characteristic: X°C/Watt. This is the key to understanding heatsinks. It means that for every watt you make a heatsink dissipate, its temperature increases by X°C. It is an exact analog to Ohm's Law.
By the same token, no matter what this paramter value, the lowest temperature any heatsink achieves is limited by the temperature of it's surroundings, or the ambient temperature (Ta). A heatsink with Rth = 1°C/Watt, dissipating Pd = 25W in a room with ambient temperature Ta = 71.6°F (22°C), operates at a temperature (Th/s) of:
Th/s = (Pd x Rth) + Ta = (25W x 1°C/W) + 22°C = 25°C + 22°C = 47°C.
The heatsink performance thus outlined does not include additional cooling measures, such as blowing air on the heatsink. By adding a fan, the thermal resistance of the heat sink is reduced; the efficiency of the heatsink is increased. The amount of heat energy from the thermal source does not change when a fan is added; the heatsink temperature drops because the effective thermal impedance of the heat sink is lowered. Quantifying this apriori is beyond the scope of this text.
At this time, the best means to determine the increase in heatsink efficiency caused by adding a fan would be to measure the steady state temperature T1 of an operating heatsink, adding a fan, then measuring the new, lower steady state temperature T2 of the heatsink.
For the original heatsink example above, solve the formula for Rth:
Rth = (Th/s - Ta) / Pd or, in this case, Rth = (T1 - T2) / Pd
In researching heatsinking for the Toshiba Class A 3456MHz power amplifier, we found excellent information at Elliott Sound Products (ESP), including a handy spreadsheet for making heatsink calculations. ESP has granted permission for RMG to put this handy tool on our website, and it can be found here. This spreadsheet is a two page affair, the second sheet showing diagrams of heatsink configurations and how the heatsink parameters apply to the spreadsheet.
Also found were:
A nice writeup by SM0PVO including a bit o' information on building heatsinks.
A treatment of Computational Fluid Dynamics and how it applies to heatsink function presented by Wakefield Engineering, Inc..
Now let's apply this in a practical way.
The Toshiba UM2683A 40W 3.4 to 3.7 GHz Solid State Class A Linear Amplifier dissipates just over 150W with no drive. The maximum allowed operational temperature for this PA is 85°C (185°F).
Below are a couple of examples of heat sink calculations, before adding fans or blowers, using the spreadsheet identified above:
For operation at room temperature = 22°C (71.6°F), 85°C - 22°C = 63°C possible drop for a heatsink.The maximum heatsink characteristic is 63°C / 150W = 0.42 °C/W which means the heatsink characteristic must be 0.42°C/W or less.
A flat black heatsink with eight, 6" long x 3" tall fins on a base of 6" long x 5" wide or larger would be adequate.
For operation at ambient South Texas temperature = 50°C (122°F), 85°C - 50°C = 35°C possible drop for a heatsink. The maximum heatsink characteristic is 35°C / 150W = 0.233 °C/W which means the heatsink characteristic must be 0.233°C/W or less.
A flat black heatsink with 9, 9" long x 3.5" tall fins on a base of 9" long x 6" wide or larger would be adequate.
Note: Clearly, adding a fan to the above heatsink configurations increases heatsink efficiency, lowers the operating temperature and helps the situation. How much it helps can be quantified by measuring "before and after" temperatures, as above.