Simple calculation method for theoretical light effect of white LED under a certain color temperature

Because white LEDs have many advantages such as high efficiency, small size, long life and many other advantages, it is considered to replace traditional incandescent lamps and fluorescent lamps as the mainstream light source for general illumination. In addition to the general color rendering index CRI, the most important thing is the light efficiency, that is, the conversion efficiency of the input electric power to the output luminous flux. It consists of two parts: the conversion efficiency from electrical energy to light energy (also known as radiation efficiency), and the conversion efficiency from light energy to luminous flux (also known as optical performance LER). The LER is determined by the spectral power distribution of the light source, and is the only efficiency that can be improved by optimizing the spectrum, thereby improving the overall light efficiency of the white LED. The formula for calculating LER is as follows:
1 white LED
There are two basic methods for implementing white LEDs: the first is to obtain white light by phosphor conversion, called PC-LED (phosphor-co nverted LED), and the other is to package different colors of chips in the same device. Multi-chip hybrid emits white light, referred to as MC LED (multi-chip LED). The former has higher light efficiency, but the color rendering is poor in the red region, and it is difficult to synthesize white light below 4000K color temperature, while the latter can perform more flexible spectral modulation, but due to the difference in thermal characteristics of each chip, it is easy to cause spot or Color drift and other phenomena, less applied in the field of general lighting.
Recently, Cree has announced that its white LED laboratory has a luminous efficacy of 303 lm/W. This new record was measured at standard room temperature, 5150K color temperature and 350 mA drive current. In this paper, based on the known color temperature of the light source, the actual spectral power distribution of the chip is derived using the PC LED model, and the optimization law and limit of the theoretical light effect of the white LED are discussed.
1 calculation
1.1 Establishment of the spectral model
High-efficiency white LEDs are generally composed of an InGaN violet blue LED (spectral half-height width = 20 nm) with a peak wavelength of about 460 nm and a YAG yellow-green phosphor (spectral half-height width = 100 nm) with a peak wavelength of about 570 nm. We use the above four parameters as initial variables, using Yoshi Ohno's LED spectral Gaussian distribution mathematical model definition:
2 spectrum
Since the different concentrations of the phosphor will cause a change in the conversion ratio and even all the parameters of the white light spectrum, we assume that the peak wavelength power of the yellow light is K times that of the blue light. Next, you only need to obtain the K value to get all the parameters of the LED spectrum and the optical performance and color rendering index.
1.2 Calculation process
When the color temperature is constant, the specific steps for calculating the spectral power distribution of the LED are as follows:
3LED spectral power
The above calculation is essentially the process of finding the intersection of two lines in the CIE 1931 xy color space, as shown in Figure 2. The straight line l1 is the isochromatic temperature line determined by the correlated color temperature of the light source and the McCamy formula, and the straight line l2 is determined by the color coordinates of the two initial light colors, which can be calculated by the relative spectral power distribution of the model. It should be noted that the McCamy formula fits the relationship between the correlated color temperature and the color coordinate through the cubic curve equation. There are two redundant solutions, which need to be verified after the correlation color temperature of the final spectrum is verified.
1.3 Characteristic parameters of the spectrum
The spectral power distribution of white light after light mixing can be obtained from the value of K, as shown in Fig. 3.
4 white light after mixing
2 Discussion
It is inferred from the above calculation results that after superimposing the radiation efficiency (including the external quantum efficiency of blue light and the phosphor conversion efficiency of 85%), the spectrum can achieve an actual luminous efficiency of 271 lm/W. The error is mainly caused by the difference between the spectral mathematical model and the actual spectrum.
The four initial condition parameters of the model (the peak wavelength and the half-height width of the blue and yellow spectrum) are separately fine-tuned, and the iterative optimization calculation is performed to obtain the peak wavelength of the blue light of 46010 nm and the peak wavelength of the yellow light of 57010 nm. High LER = 399 (CRI = 55, Duv = 0.0337). The corresponding actual light efficiency is about 305 lm / W, which is consistent with the latest research and development results of Cree. However, the Duv value of this spectrum is too high, which has deviated from the CIE's definition of traditional "white light" (Duv < 0.0054), and the color tone is greenish, requiring a finer phosphor ratio to correct it. Its spectral power distribution is shown in Figure 4.
5 white light
We try to extend the color temperature to 4000K, 5000K, 6000K. After the half-height width is determined to be 20nm (blue light) and 100nm (yellow light), the blue light peak wavelength is 46010nm and the yellow light peak wavelength is 57010nm. The LER and CRI results are shown in Table 1, where "-" means no solution, and the bold result means that the Duv value of the spectrum is <0.0054, that is, the color rendering index is meaningful.
6 white light led
From the above results, the general rule of spectral optimization is also found: for the most commonly used blue and yellow phosphor PC LEDs, the lower target color temperature can increase the highest LER value, but the value is also limited, at 4000K color temperature. It is 355 lm/W; after fixing the target color temperature, the change of the peak wavelength of the blue light has little effect on the parameters of the whole spectrum, and the closer the peak wavelength of the yellow light is to the peak of 555 nm, the higher the theoretical light effect can be achieved. At this time, the K value is also large because a small amount of blue light component is used only for correcting the color temperature, and has little effect on light efficiency and color rendering. Moreover, such a spectrum may exist only in theory, may not be able to find a suitable peak wavelength and conversion efficiency of the phosphor, and its color coordinates have mostly deviated from the black body radiation curve.
The importance of high-efficiency lighting for energy efficiency is self-evident, making it possible to make smaller, lower-cost lighting solutions possible. Through theoretical calculations, it can be seen that in order to achieve the goal of improving light efficiency, the requirements for spectral optimization design direction, we should also note that high light efficiency is inevitably accompanied by a decrease in color rendering index, and may not only pay attention to color development effects such as road lighting. The occasion applies. In addition, before the application of high-efficiency white LEDs to practical applications, cost-effective, mass-produced products are of practical significance.

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