IEEE TRANSACTIONS ON POWER ELECTRONICS, VOL. 24, NO. 8, AUGUST 2009 1967 A General Photo-Electro-Thermal Theory for Light Emitting Diode (LED) Systems S. Y. (Ron) Hui, Fellow, IEEE, and Y. X. Qin Abstract—The photometric, electrical, and thermal features of LED systems are highly dependent on one another. By considering all these factors together, it is possible to optimize the design of LED systems. This paper presents a general theory that links the photometric, electrical, and thermal behaviors of an LED system together. The theory shows that the thermal design is an indispens- able part of the electrical circuit design and will strongly influence the peak luminous output of LED systems. It can be used to explain why the optimal operating power, at which maximum luminous flux is generated, may not occur at the rated power of the LEDs. This theory can be used to determine the optimal operating point for an LED system so that the maximum luminous flux can be achieved for a given thermal design. The general theory has been verified favorably by experiments using high-brightness LEDs. Index Terms—Electronic control, lighting-emitting diodes, ther- mal design for LEDs. I. INTRODUCTION L IGHT emitting diodes (LEDs) have emerged as promis- ing lighting devices for the future. However, LEDs are still primarily restricted to decorative, display, signage, and sig- naling applications so far and have not reached the stage of massively entering the general and public illumination markets. In photometry, one important factor commonly used for com- paring different lighting devices is the luminous efficacy (lumen per Watt) [1]. One major hindrance to the widespread of LED applications in general and public illumination is that the lumi- nous flux of LEDs will decrease with the junction temperature of the LEDs [2]–[4]. This phenomenon leads to observations by some researchers and users that the maximum luminous out- put of LEDs in some designs occurs at an operating power less than the rated power of the LEDs [5]. It is rightly pointed out that the quantum efficiency and junction thermal resistance of LED are the two limiting factors in LED technology [6]. The luminous efficacy of various LEDs typically decreases by ap- proximately 0.2–1% per degree Celsius rise in temperature [5]. Due to the aging effect, the actual degradation of luminous ef- ficacy could be higher than this quoted figures. Recent research reports [2]–[4], [7], [8] have highlighted the relationship of ef- ficacy degradation and the junction temperature of the LEDs. Accelerated age tests carried out in [9] show that the light output can drop by further 45%. For aged LEDs, the efficacy degra- dation rate could be up to 1% per degree Celcius. In some Manuscript received August 3, 2008; revised November 28, 2008 and February 10, 2009. Current version published August 12, 2009. This paper was supported by the Strategic Research Grant of CityU SRG Project 7001993. Recommended for publication by Associate Editor M. Alonso. The authors are with the Department of Electronic Engineering, Centre for Power Electronics, City University of Hong Kong, Kowloon, Hong Kong, China. Color versions of one or more of the figures in this paper are available online at http://ieeexplore.ieee.org. Digital Object Identifier 10.1109/TPEL.2009.2018100 applications such as automobile headlights and compact lamps, the ambient temperature could be very high and the size of the heatsink is limited. This serious thermal problem has been ad- dressed in [10] and [11]. The drop in luminous efficacy due to thermal problem would be serious, resulting in reduction of luminous output [12]. Photometric parameters such as luminous flux and luminous efficacy, electrical parameters such as electric power, current, and voltage of an LED, and thermal parameters such as junc- tion and heatsink temperature and thermal resistance are closely linked together. In [7] and [8], the relationship between the lumi- nous output (photometric variables) and thermal behavior has been reported. Reference [13] highlights the highly nonlinear thermal behavior of the junction-to-case thermal resistance of LED with electric power consumption of LED. The junction- to-case thermal resistance is affected by many factors such as the mounting and cooling methods [14], [15], the size of the heatsink and even the orientation of the heatsink [13]. Thus, analysis on the junction thermal resistance [13], [16], [17] and thermal management [18], [19] have been major LED research topics. To deal with various factors that affect the luminous out- put, control methods have been proposed to control the luminous output of LED systems [20], [21]. An LED device model has been proposed to model the thermal junction resistance and the light output [22]. But this model is for the LED device and not for the LED system including the thermal design of the heatsink and the electric power control. In this paper, a general theory that links the photometric, electrical, and thermal aspects of an LED system is presented. This theory is based on a simple thermal model of the LED and heatsink and can be used to predict the optimal operating point (i.e., maximizing the luminous output) and provide design parameters for optimal thermal design. Tests have been carried out to verify the general theory. Examination of the theory also provides clear explanation on why the optimal operating points of some LED systems occur in an operating power less than the rated power of the LED. Practical results obtained in the experi- ments also highlight the major limitations of the existing LEDs. Both the theory and practical results provide useful insights for LED system designers and allow users to determine the advan- tages and disadvantages of using LED in different applications. II. GENERAL PHOTO-ELECTRO-THERMAL THEORY A. General Analysis Let φ v be the total luminous flux of an LED system consisting of N LED devices. φ v = N × E × P d (1) 0885-8993/$26.00 © 2009 IEEE