How Many Red, Green, and Blue LEDs to make White

And How Much Current They Need

updated 1/2/2008

Statements and Assumptions of Specific LED Types
Percentage of Total LED Count for Various Shades of White When All LEDs Get 20 mA
Percentage of Total LED Count for Various Shades of White When Red LEDs Get 30 mA and Green and Blue LEDs Get 20 mA
Theory of Math for this

Photometric percentage of red, green and blue to get various shades of white

Link to Another Resource

Statements and Assumptions of Specific LED Types

Red LEDs mentioned below are top rank Avago "AlInGaP-II" with a dominant wavelength of 630 nm, specifically HLMP-ED16-UX000 in the case of 5 mm 15 degree lamps. Luminous output is assumed to be .85 lumen at 20 mA. CIE chromaticity is x=.7079, y=.292, z=.0001. Typical voltage drop 2 volts at 20 mA. CAUTION - in my experience in 2006-2007, Avago HLMP-ED* LEDs have had a very slightly more orangish shade of red, with CIE chromaticity coordinates of x close to .702, y close to .298. This should necessitate a very slight increase in red requirement and a very slight decrease in green requirement.

Green LEDs mentioned below are Nichia NSPG series of brightness rank T and color rank G (their usual shade of green with dominant wavelength of 525 nm), specifically NSPG-500S-GT in the case of 5 mm 15 degree lamps. Luminous output is assumed to be 2.6 lumens at 20 mA. CIE chromaticity is x=.17, y=.7, z=.13. Typical voltage drop 3.6 volts at 20 mA.

"Regular" blue LEDs mentioned below are Nichia NSPB series of brightness rank T and color rank W (their usual shade of blue with dominant wavelength of average units being being 471 nm), specifically NSPB-500S-WT in the case of 5 mm 15 degree lamps. Luminous output is assumed to be .55 lumen at 20 mA. CIE chromaticity is x=.13, y=.075, z=.795. Typical voltage drop 3.5 volts at 20 mA.

Alternative blue LEDs mentioned below are Nichia NSPB series of brightness rank S and color rank V (deeper than their usual shade of blue, with dominant wavelength of average units being 462 nm), specifically NSPB-500S-VS in the case of 5 mm 15 degree lamps. Luminous output is assumed to be .45 lumen at 20 mA. CIE chromaticity is x=.145, y=.055, z=.800. Typical voltage drop 3.6 volts at 20 mA.
These specific part numbers and color/brightness subtypes/ranks/bins were available or "best-available" in 2002 or so. Since then, some efficiency improvement of at least some types has occurred.
It is to be noted that the "blue impact" of Nichia's VS rank is greater than that of their more popular, more available WT rank despite lower photometric output since the V rank's spectral output is a better match to the spectral response of the blue receptors of the human eye.

Nichia blue LEDs of color rank "V" were never easily available and in recent years have not been mentioned in their literature. However, other manufacturers do offer blue LEDs in both "regular blue" (dominant wavelength around 470 nm) and deeper blue (dominant wavelength 455-460 nm), sometimes referred to as "royal blue".

Percentage of Total LED Count When All LEDs Get 20 mA


Color    % of LEDs R, G, B     Overall        % of LEDs R, G, B    Overall
Temp.      with "regular"      Efficiency    with "alternative"    Efficiency
Kelvin    Nichia WT blue      lumens/watt     Nichia VS blue      lumens/watt

2700    63.5%R, 31.6%G,  4.9%B    26.9      63.5%R, 32.2%G,  4.3%B    27.0

  12/6/1 ratio is very close to 2750K     12/6/1 ratio is close to 2850K

3000    60.4%R, 32.8%G,  6.8%B    26.7      60.4%R, 33.6%G,  6.0%B    26.8
3500    56.2%R, 33.9%G,  9.9%B    26.3      56.1%R, 35.1%G,  8.8%B    26.4
4100    52.2%R, 34.4%G, 13.4%B    25.7      52.0%R, 36.0%G, 12.0%B    25.85
5000    47.8%R, 34.4%G, 17.8%B    24.8      47.4%R, 36.5%G, 16.1%B    25.05
5500    45.9%R, 34.1%G, 20.0%B    24.4      45.5%R, 36.5%G, 18.0%B    24.65
6500    43.1%R, 33.5%G, 23.4%B    23.65     42.4%R, 36.3%G, 21.3%B    23.95
9300    38.5%R, 31.7%G, 29.8%B    22.25     37.5%R, 35.2%G, 27.3%B    22.6

      1/1/1 ratio is close to 13000K      1/1/1 ratio is close to 16000K

Wondering why so much red and so little blue are needed?

The main reason is that the red LEDs have a 2 volt voltage drop while the green and blue ones have a 3.5-3.6 volt voltage drop and will consume 75-80 percent more power than the red ones will. Also, the blue ones put out almost 50 percent more radiometric output than the green ones do.
The "regular" Nichia blue LEDs of color rank W are slightly cyanish and will reduce green requirement, as opposed to Nichia's less common V rank which is closer to pure blue. But since Nichia's G-rank greens are slightly whitish, forcing increased use of these green LEDs by use of a purer blue can reduce requirements of blue and/or red. V-rank reduces blue requirement (compared to W-rank) also by being better at stimulating the blue receptors of human vision than the W-rank blue is.

Wondering why overall luminous efficacy here is maximized at lower color temperatures in the upper 2,000's Kelvin, while a blackbody has highest luminous efficacy in the 6,000's Kelvin?

The answer here is that blackbodies radiate heavily in the infrared while LEDs do not. A 3000K blackbody has over 90 percent of its output in the infrared. With an LED combination, highest overall luminous efficacy is achieved by using the most with more luminous efficacy (green and secondarily red) and less of what has the lowest luminous efficacy (blue).

Percentage of Total LED Count for Various Shades of White When Red LEDs Get 30 mA and Green and Blue LEDs Get 20 mA

The red LED count can be reduced by about 1/3 if the red ones get 30 mA while the green and blue ones get 20 mA:


Color    % of LEDs R, G, B     Overall        % of LEDs R, G, B    Overall
Temp.      with "regular"      Efficiency    with "alternative"    Efficiency
Kelvin    Nichia WT blue      lumens/watt     Nichia VS blue      lumens/watt

2700    53.7%R, 40.1%G,  6.2%B    26.9      53.7%R, 40.8%G,  5.5%B    27.0
3000    50.4%R, 41.1%G,  8.5%B    26.7      50.4%R, 42.1%G,  7.5%B    26.8

      6/5/1 ratio is close to 3000K      6/5/1 ratio is close to 3100K

3500    46.1%R, 41.8%G, 12.1%B    26.3      46.0%R, 43.2%G, 10.8%B    26.4
4100    42.1%R, 41.7%G, 16.2%B    25.7      41.9%R, 43.6%G, 14.5%B    25.85
5000    37.9%R, 40.9%G, 21.2%B    24.8      37.5%R, 43.4%G, 19.1%B    25.05
5500    36.1%R, 40.3%G, 23.6%B    24.4      35.7%R, 43.0%G, 21.3%B    24.65
6500    33.6%R, 39.0%G, 27.4%B    23.65     32.9%R, 42.3%G, 24.8%B    23.95
9300    29.5%R, 36.3%G, 34.2%B    22.25     28.6%R, 40.3%G, 31.1%B    22.6

Theory of Math for this

Wondering how to calculate the color of the light achieved by mixing the light of a given number of LEDs of each color?

How to do this:

Determine the lumens (or other photometric unit) of light produced by all of the LEDs of each color.

Example: You have equal numbers of red, green and blue LEDs. The red ones produce 6,000 mcd, the green ones produce 10,000 mcd, and the blue ones produce 3,000 mcd and have the same beam width.

BEWARE - LEDs often vary considerably from their specifications due to wide production tolerances.

Next, get the CIE chromaticity coordinates of each color of LED.

EXAMPLE:
Red LEDs with CIE chromaticity of x=.7, y=.3 z near zero
Green LEDs with chromaticity of x=.17, y=.7, z=.13
Blue LEDs with chromaticity of x=.13 y=.075 z=.795

If z is not mentioned, it is 1 - x - y.

In this example one LED of each color is used.

Next, multiply the photometric output of each LED by the ratio of each chromaticity coordinate to the y one to get output of X, Y, and Z.

X output is the photometric output times x divided by y
Y output is the photometric output
Z output is the photometric output times z divided by y

So, in our example:

The red LEDs have Y output of 6,000, Z output of zero, and X output of 3,000 times .7 divided by .3, or 14,000.

The green LEDs have Y output of 10,000.
Their X output is 10,000 times .17 divided by .7, or 2429.
Their Z output is 10,000 times .13 divided by .7, or 1857.

The blue LEDs have Y output of 3,000.
Their X output is 3,000 times .13 divided by .075, or 5200.
Their Z output is 3,000 times .795 divided by .075, or 31,800.

Next, add up the X outputs, Y outputs and Z outputs:

You get an X sum of 21,629.
You get a Y sum of 19,000.
You get a Z sum of 33,657.

Now, to get chromaticity coordinates from this: Divide each sum by the sum of all three.

x = 21629 / 74286, or .291
y = 19000 / 74286, or .256
z = 33657 / 74286, or .453.

The final z does not need to be calculated since typically chromaticity is specified by just x and y, since z = 1 -x -y.

Plot x=.291, y=.256 on a CIE chromaticity diagram (of their usual 1931 system) and you see that this represents a blue-violetish white color. This is a rather blue-violetish white, more of a pale blue-violet than close to pure white.

EXAMPLE 2: Same LEDs, but with 3 red ones, 2 green ones, and 1 blue one.

The X, Y and Z output figures for the red are now tripled. They become:

X=42,000 Y=18,000 Z=0

The green ones have their figures doubled to:

X=4858 Y=20,000 Z=3714

The blue one remains:

X=5200 Y=3000 Z=31800

The sums become:

X=52058 Y=41000 Z=35514

Divide each of these by the sum of all three and you get:

x=.405 y=.319 z=.276

Plot x=.405, y=.319 on a CIE "1931" chromaticity diagram and you get a pinkish white that can easily appear purplish. If input to the blue LED is reduced, then the color can be changed towards a roughly incandescent or "warm white" color.

NOTE 1:

This worked exactly when photometric units were defined in terms of the pre-1988 photopic function, which the Y-bar color function was arbitrarily set equal to. The photopic function had a minor change in 1988, so the above now only works approximately. However, this should work well enough when the final color is not a deep shade of blue or a deep shade of violet.

NOTE 2:

This works only roughly since LEDs have wide production tolerances in their characteristics.

NOTE 3:

Good luck getting the colors to mix well and evenly! Even if you use LEDs that have nice smooth and nominally identical radiation patterns, you may not get uniform mixed color because red LED chips are different from blue and most green ones.

If you are mixing beams that have hot spots, dim spots, rings, irregularities, etc. then expect a messy mix where bright and dim spots have different color from each other and everything else - as well as generally a smeary/runny mishmash of different colors rather than an illumination pattern that appears to be a nice white.

Percentage of photometric content from red, green, and blue to achieve various shades of white

  For red LEDs with 625 nm dominant wavelength, and CIE 1931 chromaticity
about .700 y=.2999 z=.0001, (very slight change 1/2/2008), and
  for green LEDs with 525 nm dominant wavelength, and CIE 1931
chromaticity about x=.17 y=.7 z=.13, and
  for blue LEDs with 470 nm dominant wavelength, and CIE 1931
chromaticity coordinates about x=.13, y=.075, z=.795:

   PERCENTAGES OF TOTAL LUMENS OR CANDELA OR MCD (updated slightly 1/2/2008)

Color temp. K    % from red  % from green  % from blue

1900             50.69%      48.99%         .32%
2700             40.5%       57.5%         2.0%
3000             38.15%      59.12%        2.73%
3500             35.2%       60.9%         3.9%
4100             32.7%       62.0%         5.3%
4500             31.5%       62.35%        6.15%
5000             30.25%      62.6%         7.15%
5500             29.3%       62.65%        8.05%
6500             27.9%       62.5%         9.6%
9300             25.9%       61.4%        12.7%

x=.333 y=.333    30.2%       61.3%         8.5%

This was updated slightly 1/2/2008, with some rough correction (it is only slight) for the difference between the 1988 and the 1924 photopic functions.

Link to Another Resource

Nichia has this Application Note on color technical matters of LEDs, especially in terms of making a television or a video monitor with them.

According to this document, the photometric output of red, green and blue LEDs should be in a ratio of 3:7:1 repectively to achieve a shade of white represented by 1931 CIE chromaticity coordinates of x=.33, y=.33. This is "equal energy white", which is close to having a color temperature of 5400 Kelvin.

My figure is 30.2% red, 61.3% green, 8.5% blue. The ratio is approximately 3.5:7:1, not far from that provided by Nichia.


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