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
Radiometric percentage of red, green and blue to get various shades of white
Link to Another Resource
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".
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 16000KWondering 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 2,000s Kelvin, while a blackbody has highest luminous efficacy in the 6,000s 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).
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
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.
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.
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.
This works only roughly since LEDs have wide production tolerances in their characteristics.
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.
For red LEDs with 625 nm dominant wavelength, and CIE 1931 chromaticity about x=.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.
UPDATE 5/1/2020: I just downloaded the ColorCalculator v. 7.77 software from Osram. Although this software is significantly general-purpose for reporting spectral and colorimetric properties of light sources (and accepts several various versions of spectral irradiance files), it is somewhat specific to 14 color types of LEDs that Osram sells and has spectra of in this software, including two infrared ones. LEDs included are blue (a royal blue one with dominant wavelength of 455 nm), green (with dominant wavelength of 530 nm), and red (with dominant wavelength of 624 nm).
One thing notable here: Using royal blue LEDs with dominant wavelength of 455
nanometers instead of "regular blue" LEDs with dominant wavelength of 470
nanometers results in much lower photometric requirement of blue contribution,
for 2 reasons:
1: 455 nm blue is seen less brightly by human vision than 470 nm blue is. (Royal blue LEDs with dominant wavelength around or less than 455-458 nm are usually rated for radiometric output instead of photometric output.)
2: 455 nm blue is more effective at stimulating the blue cones in typical human retinas than 470 nm blue is, per milliwatt and not merely per lumen.
Also notable, is that more lumens of light are produced from a given amount of total electrical power by making less use of blue LEDs, which have much less luminous efficiency than red and green LEDs. Furthermore, royal blue LEDs have greater radiometric efficiency than "regular blue" LEDs have, which further helps for getting more overall lumens per watt from using 455 nm instead of 470 nm blue LEDs.
Something else here notable, to a lesser extent: These calculations using Osram's software are with green LEDs with dominant wavelength of 530 nm as opposed to the 525 nm of the green LEDs used in the previous calculations. This means a little less red and a little more green is required to make a given shade of white.
PERCENTAGES OF TOTAL LUMENS OR CANDELA OR MCD (updated 5/29/2020) Color temp. K % from red % from green % from royal blue 1450 61.175% 38.925% zero 1900 50.38% 49.4% .22% 2200 45.48% 54.088% .435% 2700 39.73% 59.42% .85% 3000 37.197% 61.69% 1.113% 3500 33.978% 64.47% 1.552% 4100 31.21% 66.726% 2.06% 4500 29.79% 67.84% 2.37% 5000 28.352% 68.92% 2.728% 6500 25.506% 70.865% 3.629% 9300 22.9135% 72.343% 4.7435% 10000 22.5193% 72.54% 4.9407% 20000 20.1927% 73.4982% 6.3091% 950000 18.5052% 73.9402% 7.5546% millions 18.454% 73.974% 7.572%Notably, Osram's ColorCalculator software reports color temperatures of greater than 950000 as 950000. Also, the CIE chromaticity (1931) of a blackbody radiator at 950000 K is x=.2402 y=.2345. The 1931 CIE chromaticity of a blackbody radiator at a few million K to infinite K is x=.2399, y=.2342. (These are +/- .0001)
PERCENTAGES OF TOTAL radiant / radiometric power (updated 5/29/2020) Color temp. K % from red % from green % from royal blue 1450 81.249% 18.751% zero 1900 72.6301% 25.8232% 1.5467% 2200 67.6649% 29.1789% 3.1562% 2700 60.7299% 32.9338% 6.3363% 3000 57.2319% 34.4168% 8.3513% 3500 52.3355% 36.0066% 11.6579% 4100 47.6847% 36.9662% 15.3491% 4500 45.173% 37.3009% 17.5261% 5000 42.5412% 37.497% 19.9618% 6500 37.0298% 37.3049% 25.6653% 9300 31.702% 36.2925% 32.0055% 10000 30.8836% 36.0725% 33.0439% 20000 26.0179% 34.3383% 39.6438% 950000 22.52403% 32.63313% 44.84284% millions 22.45% 32.63% 44.92%
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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