**4. Conclusions**

The research results presented in this paper demonstrated the existence of important thermal couplings in the modules containing multiple LEDs and cooled by natural convection without a heat sink. In particular, it was experimentally shown that when cooling is poor the diode self-heating can contribute only a small portion to the total device junction temperature rise over the ambient. Thus, the heating by neighboring devices might become more important than the temperature rise due to the heat generated in a particular device. Therefore, the CTMs used for the simulations of such modules should take into account the mutual thermal interactions between the devices when applied cooling is poor. Obviously, this problem will not be so severe, when a proper heat sink is attached, but sometimes this might not be possible because of various design constraints. Another important contribution of this research was to demonstrate that the thermal pad area noticeably influences the junction-to-board thermal resistance.

From the theoretical point of view, this paper illustrated the methodology to derive compact thermal models when power is dissipated in multiple devices. This methodology turned out to be

effective and the thermal simulations carried out with the resulting dynamic compact models were accurate. However, it should be underlined that in the considered case, the geometry of the circuit layout was symmetrical and the circuit contained devices of the same type. Thus, in the general case, the reciprocity of mutual thermal influences would not hold. The main limitation of the proposed methodology was that the compact model element values depend on the device operating conditions and that they also vary among individual devices. Therefore, the compact models have to be derived separately for each LED. These differences result not only from different LED temperature sensitivities, but also from different LED soldering thermal resistances and other factors. Another interesting observation from the system designer point of view is that increasing the area of LED thermal pads can effectively reduce the device temperature rise already after a second. In the steady state, it was possible to lower the temperature even by 10% when only one device was active. This effect could be increased when more devices are dissipating power. In further investigations, a more in-depth study of the thermal pad area should be carried out.

**Author Contributions:** The measurements presented in this manuscript and their evaluation was carried out by P.P. and T.T. The research on the generation of compact models and thermal simulations was done by M.J. Finally, M.J. and K.G. supervised the research and prepared the manuscript. All authors have read and agreed to the published version of the manuscript.

**Funding:** This research was supported financially from the Ministry of Science and Higher Education program "Regional Excellence Initiative" 2019-2022 project No. 006/RID/2018/19, the sum of financing 11,870,000 PLN.

**Conflicts of Interest:** The authors declare no conflict of interest.
