sizing thermal ground planes

[stephenjvb]

I need to figure out how big a board I need to dissipate heat in a power supply design. I can find no actual calculations on this. I can find calculations for the thermal vias themselves but nothing on the ground plane area. I have seen references saying ground plane heat sink areas over 1 sq.in. are ineffective along with thermal images but can't seem to find this again. Does anyone know where I can find information or images?

- Thanks

 

[marce]

What device are you using, and how many layers is your design gonna be.

 

[stephenjvb]

I have seen the simplification that over 1 sq.in. is ineffective many places but it seems almost anecdotal - I have never seen any references or actual numbers other than what's below and I have no idea where I got it, other than from the internet. The tabs and formatting are gone but it should still be readable. I hope this helps ...

Heat Sink Temperature Calculator
For automotive applications, use 80°C for the ambient temperature. For maximum junction temperature, 150°C is a common value, but check the part's data sheet to be sure. The junction to case thermal resistance varies by package, see the table below for common values. For the thermal resistance 1 field this could be the case to ambient temperature thermal resistance if there is no heat sink, or if a heat sink is used, it's the thermal resistance of the heat sink. The second thermal resistance field is not typically used.
When choosing heat sinks, you want the smallest thermal resistance possible, which means that the heat will be more easily dissipated.
For surface mount (SMT) parts, where the PCB copper is used as a heat sink, for 1 ounce copper the heat dissipation asymptotically approaches 1 square inch, in other words, having a PCB heat sink greater than 1 inch doesn't do you any good. There are some tricks that can help, such as placing vias, into the pad, so that heat is transferred to the bottom layer as well. It's also possible to use surface mount heat sinks.
Typical values of Thermal Resistance for Various Electronics Packages
Package Junction to Case (°C/Watt) Junction to Air (°C/Watt)
TO-3 5 60
TO-39 12 140
TO-220 3 62.5
TO-220FB 3 50
TO-223 30.6 53
TO-252 5 92
TO-263 23.5 50
D2PAK 4 35
Thermal Resistance for PCB Copper
Heat Sink Thermal resistance (°C/Watt)
1 sq inch of 1 ounce PCB copper 43
.5 sq inch of 1 ounce PCB copper 50
.3 sq inch of 1 ounce PCB copper 56
Aavid Thermalloy, SMT heat sink: PN:573400D00010 14

The convection thermal resistance of still air is about 166 C/W sq in, or in words, 1 Watt going through a square inch will cause an increase of 166 deg C in temperature. (that number may be a little conservatively high). So, say you wanted to keep your temperature rise at 80 deg. C (would put our device a little over boiling), @ 2W, you would need ~4 square inches. But you also have to take into account the resistance the heat encounters while spreading out.
An interesting note from Kollman is that heat travels 30 times more easily through 1oz (1oz / sq. foot, 1.4mils thick) copper than .06” FR4, 60 times when 2oz copper is used. So the best way to spread heat out is to employ large copper planes.
What about planes on both sides of the boards? Despite the high resistance of the FR4 material, the large surface area moves heat somewhat easily between top and bottom planes, more than 20 times easier than the heat transfers to the air via convection (p. 4-14). So planes on both sides will help immensely. A handful of vias can help distribute heat, too. Twelve 17mil sample vias equate to the same resistance as 1 sq. inch of bottom-to-top plane resistance (8 deg C/ W in the paper).
One other factoid about heat spreading through planes is that gaps significantly block transfer, so continuous planes are most helpful.
Kollman simulates a small 5mm circular 2W heat source on a board with copper on the top and bottom (2oz). Most of the heat was dissipated within the first inch around the device. The final simulated resistance was around 15 deg C/W, but Kollman says practical experience places this value closer to 20 or 30 deg C/W.
In our testing of the Roboduino, which has copper fills on both sides of the board, many vias connecting the planes at the regulator, but also lots of traces cutting up the planes, we got measured about 38 deg C/W with the following conditions:
Tamb = 24 deg C Tdevice ~= 100 deg C Q (heat) = 2W Total resistance = (100 – 24 ) / 2 W = 38 deg C/W.
One final note is that some heat will also leave via radiation. Kollman estimates radiation to be about half as effective as convection (in a black body room), but he says that most engineers use this as a margin of safety rather than incorporating those calculations.
Trace Width Calculations: How Wide for a Given Current?
https://circuitcalculator.com/wordpress/2006/01/31/pcb-trace-width-calculator/ is a useful calculator for calculating necessary trace widths . You will, however, need to decide what an acceptable temperature rise is before using the calculator.
Judging from comments posted around the internet, it seems that most people use a 10 deg acceptable temperature rise when they want to question of whether the device will work or not. Some others from industry claimed to have used 30 deg C for products.
If you are fairly sure your device will not operate in an ambient temperature greater than 50 deg C, (122 deg F), 30 deg. seems excessively conservative.
FR4 has a Tg (glass transition temperature) typically between 115 and 125 deg. C (this depends on the exact materials used by the manufacturer). The glass transition temperature is roughly when the material changes from a hardened state to something less hard, maybe rubbery. The article points out two consequences of reaching that temperature:
The bond strength between the resin, laminate and copper foil becomes weaker, so pads and traces are more likely to lift. Also, the coefficient of thermal expansion (how much larger things get for each degree increase in temperature) goes up dramatically, which can cause plated through holes and via barrels to *****. Finally, prolonged exposure to higher temperatures can oxidize the hidden side of traces, which further weakens their connection. There is also the RTI (relative thermal index), which is published by the UL. This number is supposed to be the point where the device will operate for 100,000 hours and still retain 50% of its original properties. It's unclear how to go from either of these numbers (Tg or RTI) to an acceptable temperature rise.

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I also found an app note I had saved with some nice information and thermal images which show why large copper areas are ineffective: Cirrus Logic AN315.