Reading the LEDEngin book on Thermal Management Practical Application for the High Power LED emitters.
It says that the fundamental equation is this:
RΘJunction-Ambient = (ΔT junction – Ambient) / Pd
Where
ΔT = T junction – T Ambient
Pd = Forward current (If) * Forward voltage (Vf)
That seems wrong to me. I think it should be
RΘJunction-Ambient = ΔT junction / Pd
RΘJunction-Ambient = RΘJunction-Slug (J-S) + RΘSlug-Board(S-B) + RΘthermal interface + RΘHsk-
Ambient(B-A) (2)
Where
RΘJunction-Slug (J-S can be found in the specific data sheet
RΘSlug-Board(S-B) includes the thermal resistance from the slug in the die
package to the board material
RΘthermal interface is the thermal resistance of the material interface between the
MCPCB and the heat sink
RΘHSK-Ambient(HSK-A) is the thermal resistance from the heat sink to ambient air
So to calculate all of this, we need to know the thermal resistance of:
RTheta(Junction-Slug):=
RTheta(Slug-Board):=
RTheta(Thermal-Interface):=
RTheta(HeatSink-Ambient):=
I’d like to set up an array of LEDs on an metal core circuit board, so we’ll need the array formula as well.
For an array of n LED emitters, the total RΘjunction-board-interface would follow
the equation below
1 / RΘjunction-board-interface = Σ(1/ RΘ(junction-board-interface)) i where i = 1…..n
For the 5-Watt LEDEngine:
Deep Red LZ1-00R205 RΘJ-C 5.5 °C/W (Voltage @ 1A, 2.8V) (Voltage @ 1.5A, 3.1V)
Far Red LZ1-00R305 RΘJ-C 5.5 °C/W (Voltage @ 1A, 2.4V) (Voltage @ 1.5A, 2.6V)
Dental Blue LZ1-00DB05 RΘJ-C 5.5 °C/W (Voltage @ 1A, 3.6V) (Voltage @ 1.5A, 3.8V)
Since its the same for all of these, we can just calculate the total resistance:
2 = 1/(2/5.5) = 2.75
4 = 1/(4/5.5) = 1.38
6 = 1/(6/5.5) = 0.92
8 = 1/(8/5.5) = 0.69
10 = 1/(10/5.5) = 0.55
12 = 1/(12/5.5) = 0.46
14 = 1/(14/5.5) = 0.40
16 = 1/(16/5.5) = 0.34
Interestingly, if you multiply the power (5W) each times the number of LEDs, you get 27.5 C. That means that at best we will get a 27.5 degree difference just between the junction and the case, before any other calcs.
20-25C is ambient temperature.
The maximum current (and therefore the maximum power output) decreases linearly until the temperature gets to 125C. The nominal ratings are at 25C.
The maximum junction temperature is 125C.
Typical MCPCB values < 3 C/W
If we use thermal grease between the board and the heat sink, such as Chomerics T660, it has a very low resistance 0.02 (C-in2/W), so it is practically no effect.
So the total thermal resistance is dominated by the junction to slug and should be around 8 plus whatever the heat sink provides. At 5 watts, that means a difference of 40 C, giving us 125-25 = 100 C margin. So we need a heat sink capable of better than 5 C/W.
It seems pretty easy to get large heat DC convertor heatsinks for about $3, that are on the order of 3-4″ finned aluminum blocks. These have a heat resistance of 2-4 C/W, which should be fine.