**1. Introduction**

Nowadays, light-emitting diodes (LEDs) have replaced traditional incandescent light bulbs in virtually all everyday applications, becoming the most frequently used light source [1–3]. Taking into account that their operation involves physical phenomena of di fferent natures, such as electrical, optical or thermal ones, the modeling of these devices calls for a truly multi-domain approach [4–6]. Beyond any doubt, among the main factors influencing the performance of LEDs and a ffecting their parameters is temperature. Therefore, the accurate prediction of LED junction temperature is crucial for the stability of their lighting parameters and the long life of these light sources [7–11]. Thus, the design and the thermal managemen<sup>t</sup> of luminaires containing LED light sources requires accurate thermal models [12–16]. Moreover, LED light sources are often manufactured also as modules including drivers consisting of power transistors on the same substrate, hence thermal models of these devices should accurately reflect both self- and mutual heating e ffects [17–24]. Unfortunately, in most cases, the detailed models of LED modules are not readily available or they have unacceptably long simulation times. Thus, these models are usually realized in a reduced SPICE-like compact form, which could be then easily included in some standard electrical or multi-domain simulators [7,25].

In this paper, the authors present a methodology to generate such compact thermal models based on the practical example of a module containing six power LEDs, which are soldered to an metal core printed circuit board (MCPCB) in the shape of a regular hexagon. This module was developed for specific customer needs and it will serve for the lighting of a worker's operating field at an assembly line, where the intensity of light will be automatically controlled depending on the available daylight [26]. In such applications, the use of multi-LED modules is beneficial because it allows a more accurate

distribution of light intensity for lower currents flowing through multiple LEDs. Moreover, taking into account that, because of the limited space, this module in its end-use application is to be cooled only by the means of natural convection without any heat sink, two versions of the module, di ffering in the size of the thermal pads under the LED packages, were considered.

The following section of this paper introduces the prototype modules, measurement equipment and the adopted research methodology. Then, the temperature measurement results are presented in detail. The acquired experimental data allowed the computation of the thermal structure functions and time constant spectra, hence rendering possible the generation of compact thermal models, which were obtained in the form of Cauer RC ladders. These models were used for the simulations of device heating curves taking into account thermal couplings between the devices. The simulation results were validated against measurements. Finally, the Cauer ladders were converted into their Foster counterparts and their element values were analyzed, demonstrating the important influence of an increased thermal pad area on device temperature.
