Now you can rest easy! A thorough explanation of RGB LED color mixing calculations

"I can't get the color I want when I mix R/G/B," "White turns yellow/pale," "Lot variations occur even with the same product"
Common issues in development can be resolved by managing the chromaticity (x,y) and brightness of the LEDs and performing appropriate color mixing calculations.
In this column, we will explain a color matching workflow that you can start using today using practical examples, from the principles of RGB LED color mixing to the difference between PWM and current control, and specific methods for color mixing calculations.

RGB LED

An RGB LED is a device that contains three color chips, R (Red), G (Green), and B (Blue), in a single package.
RGB are the three primary colors of light, and by combining these three colors of light, a variety of colors can be expressed.
For example, mixing red and green produces yellow, and mixing blue and green produces cyan.
The range of possible color mixing is determined by the chromaticity and brightness of the chip, so you should understand the range of possible color mixing based on the chromaticity points listed on the datasheet.

Figure 1: RGB LED image

Comparison of color mixing control methods

There are two control methods: PWM control and DC current control.
The characteristics of each are as follows:

Table 1: Comparison of control methods

method	merit	Disadvantages
PWM control	- Color can be easily controlled using a general LED DRIVER IC or MCU PWM output. - Smooth color changes are possible if sufficient resolution and frequency are ensured. -Software control allows for a high degree of freedom in color, brightness, and animation. - Color adjustment is possible without adding any components, and the circuit is simple.	- Low brightness gradation becomes rough due to insufficient number of PWM bits. ・The duty cycle and pulse width must be managed to prevent the IF peak from exceeding the rated value.
DC Current Control	- Current can be set using only a resistor, making the circuit simple. ・Flicker caused by PWM does not occur in principle. - No control IC required, suitable for constant lighting applications.	- Color matching is difficult because brightness and color do not change linearly with current. ・When using resistors, physical replacement is required, which increases the effort and inventory costs. - Unsuitable for gradation/animation because continuous duty ratio control is not possible.

Color mixing calculation procedure

This section explains how to calculate the duty ratio for PWM control, which allows for easy color control.

Determine the target color and brightness

Define the target color and brightness numerically.
Colors are expressed as x,y coordinates in the CIE1931 color space.
Example: (x,y) = (0.33,0.33), Iv = 1.2 cd

Measurement of each chip

Each chip is measured to obtain its individual chromaticity and brightness.
We also have an article explaining optical measuring equipment and the equipment we own, so if you have time, please take a look at this article as well.

LED/Laser Technology Column: Essential for LED product development! The importance of optical measurement and our measurement services

Color mixture calculation

An essential part of understanding color mixing calculations is the XYZ color system, a method of expressing colors.
The XYZ color system is an international standard based on the mechanism of human vision, allowing any color to be expressed numerically. X, Y, and Z are not actual colors, but rather theoretically defined virtual primary colors. By combining these, the colors we see can be accurately quantified. These X, Y, and Z values are called tristimulus values and form the basis of color mixing calculations. However, since it is difficult to intuitively grasp the appearance of colors using the XYZ values alone, the CIE 1931 chromaticity diagram represents colors on a two-dimensional plane using the normalized x and y values. This makes it easier to visually understand the relationships between colors and the results of color mixing.
The XYZ values after color mixing can be calculated by multiplying the tristimulus values of each RGB LED chip by the PWM duty ratio and adding them together.
Here, if we set each variable as follows, the tristimulus values after color mixing can be expressed by equation ①.

Tristimulus values of red chip: _XR, _YR, _ZR; tristimulus values of green chip: _XG, _YG, _ZG; tristimulus values of blue chip: _XB, _YB, _ZB
Tristimulus values of target color: _XT, _YT, _ZT
Duty ratio of red chip: D _R, Duty of green chip: D _G, Duty of blue chip: D _B

Transforming this equation to find the duty ratio gives us equation ②.

Here, the tristimulus values can be expressed as equation ③ using the coordinate system (x, y) in the CIE1931 color space and brightness I.

Therefore, the tristimulus values can be calculated from the measured brightness and chromaticity coordinates of each chip.
By substituting equation ③ into equation ② and rearranging it based on the chromaticity difference between the chromaticity coordinates of each chip and the target color, we can transform it into equation ④.

Case Study

Now let's actually measure and calculate color mixing using an RGB LED.
In this case, the target values are (x, y)=(0.2, 0.3) and the brightness is 1.5cd.
Next, we measure the chromaticity and brightness of each RGB LED chip.
The measurement results for each chip are as follows:

Table 2: Measurement results for each chip

Tips	Chromaticity coordinates (x,y)	Luminous intensity [cd]
Red	(0.6982, 0.3017)	0.5806
Green	(0.2119, 0.7322)	1.4698
Blue	(0.1341, 0.0561)	0.3266

Substitute the measured values into equation ④ and solve the determinant for D _R, D _G, and D _B.

The duty ratios for each were found to be red: approximately 18%, green: approximately 83%, and blue: approximately 51%.
Figure 3 shows the RGB LED lit at the duty ratio determined using a source meter.
The results of checking the chromaticity and brightness at this time are shown in Table 3.
Both the chromaticity and brightness were almost exactly as we had hoped.

Table 3: Measurement results after color mixing

Chromaticity coordinates (x,y)	Luminous intensity [cd]
(0.2045, 0.3046)	1.4999

Summary

This time, I explained how to mix RGB LED colors. What did you think?
The more LEDs there are, the more work it takes to match colors due to individual differences.
For this reason, it is not uncommon to use a control method that uses a representative value within the rank of the LED being purchased. However, this inevitably results in large variations between individual LEDs.
The ams O STATIC RAMS LEDs we handle include RGB LEDs that have brightness and chromaticity data built into each chip at the time of shipment, as well as RGB LEDs that have a 2D code engraved on them to Access the brightness and chromaticity information.

If you have any questions about color mixing or are interested in the RGB LEDs mentioned above, please feel free Inquiry.