Now, we calculate the target intensity per pixel using the desired target luminance (TL) and pixel pitch (PP) in millimeters using the formula:
Target Intensity (cd) = TL × (PP/1000)2 = 8000 ×(12.5/1000)2 = 1.25 cd.
Having determined the total required intensity per pixel, we can calculate the respective luminous intensity required for the red, green, and blue emitters using the formula:
(R, G or B Mixing value/Sum of RGB mixing value) × Target intensity :
Red = (4.1/15.7) × 1.25 = 0.3264cd
Green = (10.6/15.7) × 1.25 = 0.84395 cd
Blue = (1.0/15.7) × 1.25 = 0.0796 cd
Next, we must return to the LED data sheet. You can estimate the drive current required to produce the desired luminous intensity using the drive current vs. light output graph in the LED datasheet (Fig. 4). Using the example graph, the drive currents required to produce the desired luminous intensities for the three emitters are approximately 8.8 mA for red, 10.5 mA for green, and 4.2 mA for blue. These current requirements can be used to determine the hardware component values used to bias the driver ICs and the variable values used to set the output range of the LED driver software.
Delivering optimal color
This exercise illustrates the challenges involved with achieving an accurate target white output from LED displays as a result of the spectral properties of the red, green, and blue LEDs. The LEDs used for electronic signs have spectral properties that are not identical to those of the corresponding phosphors used in traditional CRT displays.
Using the traditional 3:6:1 ratio will result in inaccurate reproduction of a target white illuminant. A new ratio should be calculated for each application. These calculations are also to be made using the target white point and luminance level that customers want to use for their particular design. In these LED-based applications, the mixing ratio must be calculated based on the specific spectral characteristics of the light produced by the red, green, and blue emitters before determining each device’s drive current requirements.
The straightforward procedure detailed here is an important tool for designing full color signs. It enables the engineer to select the LEDs and drive values that insure the display meets the customer’s performance requirements. This method also allows a designer to quickly re-estimate the RGB mixing ratio and drive current requirements for an application if a change occurs to the LEDs used and therefore the chromaticity coordinates, to the target white point, to the pixel pitch, or to the target luminance.
SIDEBAR: Calculate RGB color mixing values using the center of gravity method
In everyday practice, designers of signs or other color-lighting products can usually obtain the mixing ratio for a target color from widely available software packages. For a person unfamiliar with color mixing theory, however, deriving the ratios manually using the technique demonstrated here will help develop a better understanding of the process.
There are three commonly used methods for deriving additive color mixing ratios in displays and lighting systems: tristimulus values method, center of gravity, and vector diagram.
For the purposes of this tutorial, we will use the center-of-gravity technique to illustrate how the 3:6:1 color mixing ratio used by most CRT-based displays was derived from the properties of the standard red, green, and blue phosphors and the D65 target white illuminant, which were defined by the early television industry and are still used today.
The spectral characteristics of the red, green, and blue LED emitters are provided in manufacturers’ data sheets as coordinates. A similar set of coordinates define the D65 target white illuminant, which is typically chosen to match the requirements of the target application and is most likely determined by the customer requirements for the end product in question. Once all the coordinates are plotted onto the CIE 1931 diagram (see Fig. 3 from the main article) they may be used to derive the RGB mixing values required to produce the target white illuminant. You take the set of (x,y) coordinates plotted in Fig. 3 and work through a relatively simple progression of algebraic equations to determine the ratio mix. For convenience, those coordinates are:
Red: 0.67, 0.33
Green: 0.21, 0.71
Blue: 0.14, 0.08
D65 White Point: 0.3128, 0.3292
Step 1: Using the initial values, first solve the linear equation
that describes a line formed between the red and blue color coordinates that passes through the Purple Point (P). You first determine the line’s slope (mRB):
mRB = (yR – yB) / (xR – xB) = (0.33-0.08)/ (0.67-0.14) = 0.4717
Now you can calculate the constant C using the blue coordinates:
CRB = yB –mRB × xB = 0.08 – 0.4717 × 0.14 = 0.01396
Solving for the linear equation for y yields an equation that represents the line between the blue and red points:
y = 0.4717x +0.01396
Step 2: Now derive a second linear equation (y = mx+c) that describes the line that is formed between the green point and the purple point and that passes through the target white point D. The D coordinates provide the second set of coordinates required for the derivation along with the green coordinates.
mGD = (yG – yD) / (xG – xD) = (0.71-0.3292)/ (0.21-0.3128) = -3.7043
CGD = yG –mGDB × xD = 0.71 – (- 3.7043) × 0.21 = 1.4879
y = -3.7043x +1.4879
Step 3: Now we have two linear equations with two unknowns. Thus, we calculate the coordinates of the purple point that is located at the intercept point of the two linear equations.
y= 0.4717x +0.01396
y= -3.7043x +1.4879
We can solve for x because linear equations are both equal to y:
0.4717x +0.01396 = -3.7043x +1.4879
4.176x = 1.47394
x = 0.35296
Now we can solve for y:
y = 0.4717(0.35296)+0.01396 = 0.18045
The resulting x and y coordinates for the purple point P are (0.35296, 0.18045).
Step 4: Now we can calculate the RGB color-mix ratio required to produce the D65 illuminant by applying a ratio of mixtures formula R = - (y2/y1) × (y1-y3) / (y2-y3). The geometric basis for the solution is illustrated in Fig. S1.
