# Experimental Study on Chromaticity Control in Visible Light Communication Systems
## 3 Research on RGB LEDs Dimming  
### Dimming Method and Calculation Method  
Dimming technology has become an important aspect of LED driver technology, and there are three commonly used LED dimming methods: DC dimming, PWM dimming, and thyristor dimming [21]. When the current is too small, the thyristor will turn off, making the dimming effect unstable and unsuitable for use in visible light communication systems [21]. Meanwhile, DC dimming is achieved by changing the driving peak current of the LED to change the luminous flux. This dimming method can affect the chromaticity shift and color temperature change in the LED [22]. The PWM dimming method is achieved by changing the duty cycle of the LED light source, thereby changing the average luminous flux. The dimming performance is flexible and can accurately control the luminous flux, thereby accurately controlling the brightness change in the LED and reducing the impact of current changes during amplitude modulation on the stability of the light source [23]. In engineering practice, the color difference caused by PWM dimming is often not considered [24]. In the PWM dimming method, the peak value of the driving current remains unchanged, and the LED is dimmed by adjusting the duty cycle of the PWM. The expression is as follows:  
\[I_{avg}=I_{peak}\cdot D, \tag{8}\]  
where \(I_{avg}\) represents the effective value of the driving current, \(I_{peak}\) represents the magnitude of the driving peak current, and \(D\) represents the duty cycle of PWM. For the convenience of calculation, it is usually assumed that the PWM duty cycle of the input driver module is directly proportional to the luminous flux output by the light source [25], which satisfies the following:  
\[\Phi=D\Phi_{\text{Max}}, \tag{9}\]  
where \(D\) is the duty cycle of the input PWM signal, \(D<1\); \(\Phi_{\text{Max}}\) is the maximum output luminous flux; and \(\Phi\) is the luminous flux of the output signal. According to [PERSON]'s law of color mixing, there is a formula for the luminous flux output of a three-color mixture [26]:  
\[\Phi=D_{r}\Phi_{r}+D_{g}\Phi_{g}+D_{b}\Phi_{b}, \tag{10}\]  
where \(D_{r}\), \(D_{g}\), and \(D_{b}\) are the input duty cycle of PWM; \(\Phi_{r}\), \(\Phi_{g}\), and \(\Phi_{b}\) are the maximum output luminous flux of each light source; and \(\Phi\) is the output luminous flux of the mixed light. In the CIE-1931 standard colorimetric system, it is specified that the stimulus value of \(Y\) is equal to the luminous flux, so in the following text, it can be changed to \(Y\). According to the principle of color mixing and the CIE 1931 color coordinate calculation method, the color coordinates after mixing with three light sources should meet the following [27]:  
\[x=\frac{R_{r}D_{r}x_{r}+R_{g}D_{g}x_{g}+R_{b}D_{b}x_{b}}{R_{r}D_{r}+R_{g}D_{g} +R_{b}D_{b}}, \tag{11}\]  
\[y=\frac{R_{r}D_{r}y_{r}+R_{g}D_{g}y_{g}+R_{b}D_{b}y_{b}}{R_{r}D_{r}+R_{g}D_{g} +R_{b}D_{b}}, \tag{12}\]  
where \(x\) and \(y\) represent the color coordinates of a mixed light source consisting of three types of light sources; \((x_{r},y_{r})\), \((x_{g},y_{g})\), and \((x_{b},y_{b})\) represent the color coordinates of red, green, and blue LEDs, respectively; \(R_{r}=\frac{Y_{r}}{y_{r}}\), \(R_{g}=\frac{Y_{g}}{y_{g}}\), and \(R_{b}=\frac{Y_{b}}{y_{b}}\) represents the sum of the three stimulus values of the light source under full current operation; \(D_{r}\), \(D_{g}\), and \(D_{b}\), respectively, represent the PWM input duty cycle of red, green, and blue LEDs.