Table 4 Calculating the required thermal properties of a heatsink

Using the following thermal model (eq. 1, [85], Fig. 2F) and calculating or estimating all the individual parameters (eq. 2–4), the required thermal properties of a heatsink can be calculated.

Where:

Typically, the maximal junction temperature can be found in the datasheet for the LED. For a Royal-Blue Luxeon Rebel LED on a SinkPAD-II that is used in this paper, the listed temperature is 150 °C. Ideally, the operating temperature should be well below that limit, as even reaching this temperature for a fraction of time could influence the properties of the LED [92,93,94,95]. Therefore, we decided to set the maximum junction temperature to 100 °C. Next, the power dissipation of the same LED can be calculated by multiplying the forward voltage rating of the LED with the drive current in Amperes (eq. 4). Since we use a fixed 700-mA LED driver and know the maximal voltage drop of the LED (3.5 V), P_d is easily calculated (eq. 4). Finally, the maximal thermal resistance should be calculated by taking in the maximum working ambient temperature into account, which was determined to be 25 °C (20 °C room temperature + 5 °C margin, eq. 3). Importantly, note that our set-up is located in a climate-controlled room. If this is not the case, a wider margin for temperature fluctuations and higher maximum temperature based on local environmental conditions should be considered. Rewriting eq. 1 and calculating Rθ gives (eq. 5):

This means that the total thermal resistance of the system can be maximally 30.6 °C/W (eq. 2) when one aims for junction temperatures that are maximally 100 °C. In order to see what that means for the required heatsink, all the known thermal resistances (Fig. 2F) can be collected from the datasheets of the LED (junction to thermal pad: 6.0 °C/W and thermal pad to solder pad: 0.7 °C/W) and used adhesives (4.5 °C/W). Rewriting eq. (2) gives (eq. 6):

Theoretically, a heatsink in this set-up can have a maximal thermal resistance of 19.4 °C/W and any heatsink with lower resistance than that can be used. We used a finned heatsink with thermal resistance of 5.2 °C/W to keep the set-up compact and still achieve sufficient cooling. Next, we continued with an empirical approach to verify whether appropriate heat dissipation could be obtained with this set-up. Therefore, we measured the actual junction temperature and the voltage drop of the LED mounted to the OptoArm (Fig. 2D). With a Fluke TM80 module and associated test probe, we measured the temperature at the specified test location (Fig. 2F) of the LED for about 1 min until the temperature stabilized. At the same temperature, we also determined the actual voltage drop of the LED. We measured a temperature of 55.68 ± 0.76 °C (n = 10) and a forward drop of 2.972 ± 0.004 V (n = 5). By using eq. (7), the actual junction temperature can be derived:

With an estimated junction temperature of 69.2 °C, the system fulfills our criteria for a system with appropriate thermal cooling. This is further evidence by the temperature measured after 10 min of constant illumination at the maximal capacity: 55.81 ± 1.09 °C (=junction temperature of 69.3 °C, n = 10).