# Spectra Prediction for WLEDs with High TLCI
## 2 Materials and Methods
### Experimental Methods  
To study the spectral prediction model of dual-phosphor WLEDs, the authors of this study performed the steps illustrated in the flowchart in Figure 1.  
Currently, the Gaussian function is widely used to simulate the spectral power distribution (SPD) of monochrome LEDs [25; 26; 27]. However, in order to more accurately obtain the spectra of chips and phosphors, the following methods were used in this paper. Firstly, single-phosphor LED samples (packaged with green or red phosphor) were fabricated on a ceramic substrate (Figure 2). Silicone resin-containing phosphor was encapsulated on a chip, and the LEDs were sealed for the phosphor packages. The LED samples were fixed on an aluminum fin heat sink to dissipate heat, and silicone grease was applied between the module and the heat sink. The thermal conductivity of silicone grease is 8.5 \(W\)/(m\(\cdot\)K). The aluminum fin heat sink was cooled with a fan; see Figure 2. The dimensions of the aluminum fin heat sink are 50 \(\times\) 50 \(\times\) 10 mm. The air flow of the fan is 49 CFM, the air pressure is 1.43 mmHg2O, and the rated speed is 2500 rpm \(\pm\) 10%. The integrating sphere was employed to measure the output of the LEDs. The LEDs were driven using a DC power supply with driving currents of 1A, 2A, 3A, and 4A, respectively. The ambient temperature was 20 \({}^{\circ}\)C. A thermistor was used to measure the temperature of the LED modules. The spectrum is shown in Figure 3. Without changing the phosphor concentration, increasing the thickness of the phosphor can allow it to absorb more blue light. However, this will cause a serious increase in the junction temperature of the LED modules, which is not realistic. We adopted the method of subtracting the blue light spectrum from the mixed spectrum to obtain the phosphor emission spectrum. Therefore, we packaged LEDs with a single phosphor and made the peak intensity of the phosphor powder roughly equal to the peak intensity of blue light. The output spectrum, formed by blue light exciting the phosphor, can be expressed as:  
\[S_{mix}(\lambda)=S_{B}(\lambda)\cdot(1-W)+S_{P}(\lambda)\cdot Q\cdot W, \tag{1}\]  
where \(S_{mix}(\lambda)\) is the mixed spectrum, \(Q\) is the conversion efficiency of phosphor, and \(W\) is the proportion of blue light absorbed by the phosphor, which is related to the concentration and thickness of the phosphor. \(W=0\) means that the LED is not packaged with phosphor. \(Q\) and \(W\) jointly determine the color temperature of the WLED. \(S_{B}(\lambda)\) and \(S_{P}(\lambda)\) are the emission spectra of the chip and phosphor, respectively. Clearly, different chips and phosphors have different emission spectra. The light emission spectrum is determined by the energy band gap of the material [23]. At the same junction temperature, the normalized blue light spectrum is not affected by the presence or absence of phosphor. That is, the shape of the spectrum remains the same. As shown in Figure 3, it is evident that the emission spectrum of phosphor can be obtained by subtracting the blue light spectrum from the mixed spectrum. The ratio of the blue light peak intensity of mixed spectra to the peak intensity of the chip is the proportion of blue light absorbed by the phosphor. The integration of spectral power distribution is energy. Figure 1: The flowchart for establishing the model. The conversion efficiency of the phosphor can be determined by calculating the energy of the emission spectrum of the phosphor and the energy absorbed by it:  
\[Q=\frac{P_{E}}{P_{A}}, \tag{2}\]  
where \(P_{E}\) is the energy emitted by the phosphor, and \(P_{A}\) is the energy absorbed by the phosphor. In this study, for simplicity, the phosphor conversion efficiency is assumed to be constant, and the phosphor light intensity is linearly converted from the blue LED light intensity [24]. Thus, we can obtain the emission spectra of chips and phosphors as well as the conversion rate of phosphors.