# Heat sink calculation for multiple heat sources connected to a single copper plate

I have 2 switches, both are thermally connected to one copper plate. One switch has heat resistance - junction to copper plate = 1.09 C/W and dissipates 6 W of heat. The other has heat resistance - junction to copper plate = 1.2 C/W and the disipated heat is 8 W.

If I want to connect this copper plate with one heat sink, what should be the thermal resistance of heat sink? Consider the maximum junction temperature is 100 C and ambient is 50 C.

• Welcome! Is this homework? Commented Nov 10, 2023 at 15:03
• let's see a diagram showing the temperatures, heat flows, and thermal impedances as voltages, currents and resistors respectively (there is a circuit editor built into this site for just this sort of thing). Drawing it might help you to solve it on your own. Commented Nov 10, 2023 at 15:08

Here is a start or a re-arrange of words into a schematic:

simulate this circuit – Schematic created using CircuitLab

Power dissipated is a current here, thermal resistance is electrical resistance and voltage is temperature.

What is left is to calculate R of the heatsink given the two boundary conditions of max junction temperature (voltage in the diagram above), forming an equation system.

Thanks to Tim for pointing out the grounded current sources.

• Yeah, the far end of the current sources can just be tied off anywhere; ground is as good as anything. It is kind of funny, that this is one aspect the analogy breaks down on: power isn't drawn from somewhere and delivered somewhere else, it isn't conserved the same way current is in a circuit, hehe. Commented Nov 10, 2023 at 16:30
• @TimWilliams Perhaps ground the top of each and put the voltage measurement below them? I’ll edit when I get home. Commented Nov 10, 2023 at 17:01
• This is super! I'd never seen this method of doing the thermal calculations. So simple and elegant. And it's amusing to do a digital simulation of an analogue computer too. Commented Nov 11, 2023 at 9:48
• @jonathanjo Was taught the method in engineering school. Tangent story: the best class was on analogs between formulas used in EE are identical but different physical quantities in mechanics, fluids, chemistry, acoustics and so on so SPICE was used by many fields of engineering. Commented Nov 11, 2023 at 11:31