Color mixing models for smart lighting systems based on RGBW and WW LEDs
Color mixing models to obtain white light with a predetermined values of correlated color temperature and brightness are presented. One model describes mathematical algorithm for combination of spectra for WW LEDs lighting systems, and other one for systems based on RGBW LEDs. Results of testing of...
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Інститут фізики напівпровідників імені В.Є. Лашкарьова НАН України
2015
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| Цитувати: | Color mixing models for smart lighting systems based on RGBW and WW LEDs / V.I. Kornaga, V.M. Sorokin, A.V. Rybalochka, O.S. Oliinyk, N.P. Kornaga // Semiconductor Physics Quantum Electronics & Optoelectronics. — 2015. — Т. 18, № 3. — С. 302-308. — Бібліогр.: 10 назв. — англ. |
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nasplib_isofts_kiev_ua-123456789-1212022025-02-10T00:27:43Z Color mixing models for smart lighting systems based on RGBW and WW LEDs Kornaga, V.I. Sorokin, V.M. Rybalochka, A.V. Oliinyk, O.S. Kornaga, N.P. Color mixing models to obtain white light with a predetermined values of correlated color temperature and brightness are presented. One model describes mathematical algorithm for combination of spectra for WW LEDs lighting systems, and other one for systems based on RGBW LEDs. Results of testing of created sample of LED light source for indoor lighting (“Amstrong” type) with implemention of presented color mixing models are shown. 2015 Article Color mixing models for smart lighting systems based on RGBW and WW LEDs / V.I. Kornaga, V.M. Sorokin, A.V. Rybalochka, O.S. Oliinyk, N.P. Kornaga // Semiconductor Physics Quantum Electronics & Optoelectronics. — 2015. — Т. 18, № 3. — С. 302-308. — Бібліогр.: 10 назв. — англ. 1560-8034 DOI: 10.15407/spqeo18.03.302 PACS 85.60.Jb https://nasplib.isofts.kiev.ua/handle/123456789/121202 en Semiconductor Physics Quantum Electronics & Optoelectronics application/pdf Інститут фізики напівпровідників імені В.Є. Лашкарьова НАН України |
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Color mixing models to obtain white light with a predetermined values of correlated color temperature and brightness are presented. One model describes mathematical algorithm for combination of spectra for WW LEDs lighting systems, and other one for systems based on RGBW LEDs. Results of testing of created sample of LED light source for indoor lighting (“Amstrong” type) with implemention of presented color mixing models are shown. |
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Article |
| author |
Kornaga, V.I. Sorokin, V.M. Rybalochka, A.V. Oliinyk, O.S. Kornaga, N.P. |
| spellingShingle |
Kornaga, V.I. Sorokin, V.M. Rybalochka, A.V. Oliinyk, O.S. Kornaga, N.P. Color mixing models for smart lighting systems based on RGBW and WW LEDs Semiconductor Physics Quantum Electronics & Optoelectronics |
| author_facet |
Kornaga, V.I. Sorokin, V.M. Rybalochka, A.V. Oliinyk, O.S. Kornaga, N.P. |
| author_sort |
Kornaga, V.I. |
| title |
Color mixing models for smart lighting systems based on RGBW and WW LEDs |
| title_short |
Color mixing models for smart lighting systems based on RGBW and WW LEDs |
| title_full |
Color mixing models for smart lighting systems based on RGBW and WW LEDs |
| title_fullStr |
Color mixing models for smart lighting systems based on RGBW and WW LEDs |
| title_full_unstemmed |
Color mixing models for smart lighting systems based on RGBW and WW LEDs |
| title_sort |
color mixing models for smart lighting systems based on rgbw and ww leds |
| publisher |
Інститут фізики напівпровідників імені В.Є. Лашкарьова НАН України |
| publishDate |
2015 |
| url |
https://nasplib.isofts.kiev.ua/handle/123456789/121202 |
| citation_txt |
Color mixing models for smart lighting systems based on RGBW and WW LEDs / V.I. Kornaga, V.M. Sorokin, A.V. Rybalochka, O.S. Oliinyk, N.P. Kornaga // Semiconductor Physics Quantum Electronics & Optoelectronics. — 2015. — Т. 18, № 3. — С. 302-308. — Бібліогр.: 10 назв. — англ. |
| series |
Semiconductor Physics Quantum Electronics & Optoelectronics |
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2025-12-02T04:17:22Z |
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| fulltext |
Semiconductor Physics, Quantum Electronics & Optoelectronics, 2015. V. 18, N 3. P. 302-308.
doi: 10.15407/spqeo18.03.302
© 2015, V. Lashkaryov Institute of Semiconductor Physics, National Academy of Sciences of Ukraine
302
PACS 85.60.Jb
Color mixing models for smart lighting systems based on RGBW and
WW LEDs
V.I. Kornaga1, V.M. Sorokin1, A.V. Rybalochka1, O.S. Oliinyk1, N.P. Kornaga2
1V. Lashkaryov Institute of Semiconductor Physics, National Academy of Science of Ukraine,
41, prospect Nauky, 03028 Kyiv, Ukraine
2National Technical University of Ukraine “KPI”, Kyiv, Ukraine
E-mail: kornaga@isp.kiev.ua
Abstract. Color mixing models to obtain white light with a predetermined values of
correlated color temperature and brightness are presented. One model describes
mathematical algorithm for combination of spectra for WW LEDs lighting systems, and
other one for systems based on RGBW LEDs. Results of testing of created sample of
LED light source for indoor lighting (“Amstrong” type) with implemention of presented
color mixing models are shown.
Keywords: smart lighting system, color mixing, RGBW and WW LEDs, correlated color
temperature, brightness, Planckian locus.
Manuscript received 12.03.15; revised version received 18.06.15; accepted for
publication 03.09.15; published online 30.09.15.
1. Introduction
To date, the most promising in terms of providing
energy efficiency and lighting quality are the so-called
smart lighting systems (SLS). These systems are not just
lighting devices, but programmable complex, the main
point of which is the automated control of the lighting
parameters and, if necessary, cooperation with other
similar systems that are included, for example, into the
complex “smart house”. SLS typically have
opportunities to operate in automatic mode, manual
adjustments and settings modes, to change the brightness
and color parameters according to a given algorithm.
Also, using them one can implement algorithms to
change the lighting characteristics according to the
natural cycle, which are based on the data of recent
studies on the impact of dynamical changes in the
spectral parameters of natural lighting on the
concentration of the hormone melatonin in the human
blood, which is a regulator of the states of cheerfulness
and human sleep [1, 2].
Among the large number of existing today light
sources for creating SLS, there are most suitable LEDs
that are both solid and based on organic light-emitting
diodes (OLED) [3]. OLED prevail through the absence
of spot light and possibility of creating light surfaces
with almost arbitrary shape and size, but their efficiency
is still low, and the cost is high. Solid-state LEDs, unlike
the structures OLED, have high luminous efficiency and
moderate price, and that is why they are the best solution
to date for applying in SLS, even if the use of the
auxiliary optics and structural elements needed to create
the desired lighting effects leads to some reduction in the
energy efficiency of the system as a whole.
To implement the changes in the spectrum and
intensity of radiation by using SLS in accordance with the
natural dynamics of the change in spectral composition of
daylight, in the most simple case it is sufficient to use two
types of white luminophore LEDs with two different
values of correlated color temperature (WW system) [4].
The use for this purpose RGB LEDs [5] provides to obtain
except controlled white light also a large range of colors,
which enables in these systems to implement additional
features such as decorative lighting and signaling. A
significant drawback of the systems built on RGB LEDs
is a low value of the color rendering index Ra (CRI) when
Semiconductor Physics, Quantum Electronics & Optoelectronics, 2015. V. 18, N 3. P. 302-308.
doi: 10.15407/spqeo18.03.302
© 2015, V. Lashkaryov Institute of Semiconductor Physics, National Academy of Sciences of Ukraine
303
obtaining white light. A variant, in which one can get
high-quality white light in SLS with the possibility to
reproduce a large range of other colors, is their
construction on RGBW and RGBA LEDs [6].
This paper shows the ways of obtaining white light
with predetermined values of correlated color
temperature and chromaticity coordinates that are
maximal close to the Planckian locus based on modeling
spectral characteristics when using RGB LEDs in
combination with different types of white (WW) LEDs.
An example of practical implementation of mathematical
models created by mixing colors on the test samples
WW RGBW and smart lighting systems.
2. Mathematical model for combination of spectra
for two white luminophore LEDs
When mixing emission of two light sources (e.g., LED1,
xLED1, yLED1 and LED2 xLED2, yLED2), one can obtain light
with a range of possible colors, which, in the diagrams
of color space CIE 1931 and CIE 1960, falls into direct
segment LED1-LED2 between the chromaticity
coordinates of these two light sources (Fig. 1) [7]. That
is why when mixing light of two WW LEDs, one can get
no more than two variants of all possible ones of white
colors, the chromaticity coordinates of which correspond
directly to the Planckian locus values. For all other
colors, one can speak only about determining the certain
value of correlated color temperature for them.
To obtain light of a correlated color temperature, it
is necessary to find a point on the segment LED1-LED2,
in which this point corresponds to the desired color
temperature in the Planckian locus. For this purpose, we
must go to the chromaticity diagram CIE 1960 and to
find the coordinates of the desired color temperature by
the following formulas:
3122
4
++−
=
óõ
xu ,
3122
6
++−
=
óõ
óv . (1)
The cross-section of perpendicular to the Planckian
locus in the point with a certain color temperature and
the segment LED1-LED2 determines a point with the
corresponding correlated color temperature. Knowing
the chromaticity coordinates of LEDs, the equation of
this straight line can be found as follows:
12
1
12
1
LEDLED
LED
LEDLED
LED
vv
vv
uu
uu
−
−
=
−
− , (2)
where u and v are the coordinates of chromaticity
diagram CIE 1960, xLED1, yLED1 and xLED2, yLED2 are the
chromaticity coordinates of the first and second LED,
respectively.
Fig. 1. The segment with the possible colors when mixing light
of two white LEDs in the color diagram CIE 1931.
The equation of perpendicular to the Planckian
locus at the point with the coordinates (u0, v0) takes the
following form:
( ) ( )0
0
0
1 uu
uf
vv −
′
−=− , (3)
where ( )0uf ′ is the derivative of the function that
approximates the Planckian locus.
Since the implementation of this function in
hardware requires some computing resources, and for
practical implementation in SLS, it is important to
minimize them, then simplification of the calculation of
perpendicular to the Planckian locus at the point (u0, v0)
is possible through determining it as perpendicular to the
straight line that goes through two adjacent points
located in the Planckian locus from both sides to this
point with known chromaticity coordinates (u1, v1) and
(u2, v2) (Fig. 2):
0
12
12
0
12
12
)(
)(
)(
)( v
vv
uuu
vv
uuuv +
−
−
+
−
−
−= . (4)
With the equations for perpendicular passing through the
point (u0, v0) and the straight line passing through the
coordinates of two luminophore LEDs (uLED1, vLED1),
(uLED2, vLED2), one can find the coordinates of their
intersection point with the corresponding value of
correlated color temperature to the value at the point
(u0, v0):
)()()()(
)()()()()()()(
12121212
1212101212121210
LEDLEDLEDLED
LEDLEDLEDLEDLEDLEDLEDLED
c vvvvuuuu
uuuuvvvvvvuuvvuvv
−⋅−+−⋅−
−⋅−⋅+⋅−⋅−+−⋅−⋅−
=
)()()()(
)()()()()()()(
12121212
1212112121001212
LEDLEDLEDLED
LEDLEDLEDLEDLEDLEDLEDLED
c uuuuvvvv
vvvvuuuvvvvuuuuuu
−⋅−+−⋅−
−⋅−⋅+−⋅−⋅−+⋅−⋅−
= (5)
Semiconductor Physics, Quantum Electronics & Optoelectronics, 2015. V. 18, N 3. P. 302-308.
doi: 10.15407/spqeo18.03.302
© 2015, V. Lashkaryov Institute of Semiconductor Physics, National Academy of Sciences of Ukraine
304
Fig. 2. Method for obtaining the coordinates of points with the
given correlated color temperature in the interval LED1-LED2.
These coordinates are now required to recalculate
into the coordinates of the chromaticity diagram CIE
1931:
482
3
+−
=
cc
c
c vu
ux ,
482
2
+−
=
cc
c
c vu
vy . (6)
It is possible to find the corresponding coordinates
Xс, Yc, Zc, taking that the coordinate Yc (brightness) is
equal to unity, that is:
1=cY ,
c
c
cc ó
YõX ⋅= , ( )
c
c
ccc y
YyxZ −−= 1 . (7)
In the same way, one can find the coordinates of
two luminophore LEDs XLED1, YLED1, ZLED1, XLED2, YLED2,
ZLED2. Adding them with the coefficients k1 and k2, one
can get the resulting light with the chromaticity
coordinates Xс, Yc, Zc:
2211 LEDLEDc XkXkX ⋅+⋅= , 2211 LEDLEDc YkYkY ⋅+⋅= ,
2211 LEDLEDc ZkZkZ ⋅+⋅= . (8)
Since the Y coordinate is brightness, when finding
the coefficients k1 and k2, we can calculate the ratio of
the LED brightnesses. One of three possible variants of
determining these coefficients from the system of
equations (8) have the form:
1
22
1
LED
LEDc
Z
ZkZk ⋅−
= ,
1212
11
2
LEDLEDLEDLED
LEDcLEDc
XZZX
XZZXk
⋅−⋅
⋅−⋅
= . (9)
Thus, one can get the ratio of brightnesses for two
white LEDs with various correlated color temperatures,
when the correlated color temperature of their mixed
white light will match a given color temperature in the
Planckian locus.
Program implementation of the demonstrated
model for mixing of colors of two white luminophore
LEDs in SLS will provide the ability to change the
correlated color temperature of white light in according
to an arbitrarily given algorithm of change, including the
natural cycle. But the question how to obtain different
color light remains open. Solution of this question will
allow to expand the functional possibilities of the
lighting system and to increase the field of its
application. This problem is solved through the use in
SLS of RGBW LEDs, the mathematical model of color
mixing for which will be discussed below.
3. Mathematical model of color mixing
of RGBW LEDs
Now consider finding the ratio of the RGB LED
brightnesses to obtain a given color temperature in SLS.
To do this, it is necessary to measure their emission
spectra at maximum brightness. It will provide a
transition matrix with XYZ in the RGB space. Using this
matrix, one can calculate the ratio of brightnesses
between red, green and blue LEDs for resulting light
with some brightness and correlated color temperature
[8]. The transition matrix consists of the values XR, YR,
ZR for red LED, XG, YG, ZG for green LED and XB, YB, ZB
for blue LED at their maximum brightness. If one knows
the coordinates хr, уr, хg, уg and хb, уb for each color of
RGB LEDs, from the formula (7) he can calculate their
coordinates X, Y, Z and plot a transition matrix from the
RGB space into the XYZ space. This matrix has the
following form:
⎥
⎥
⎥
⎦
⎤
⎢
⎢
⎢
⎣
⎡
=
BGR
BGR
BGR
ZZZ
YYY
XXX
M . (10)
To find the value of correlated color temperature and
light brightness, one can calculate the ratio of the
brightnesses between emitting elements of RGB LED as
follows:
⎥
⎥
⎥
⎦
⎤
⎢
⎢
⎢
⎣
⎡
⋅
⎥
⎥
⎥
⎦
⎤
⎢
⎢
⎢
⎣
⎡
=
⎥
⎥
⎥
⎦
⎤
⎢
⎢
⎢
⎣
⎡
−
Z
Y
X
ZZZ
YYY
XXX
B
G
R
BGR
BGR
BGR
1
, (11)
where R, G, B are the brightness of red, green and blue
LEDs.
This system enables to obtain a large range of
colors, the coordinates of which are limited by the
Maxwell triangle (Fig. 3), but the resulting white light
will have a color rendering index that is much lower (no
more than 50) than that in WW LED system, for which
this parameter is usually more than 75. The increase in
the color rendering index can be achieved by adding a
range of white or orange LED.
Semiconductor Physics, Quantum Electronics & Optoelectronics, 2015. V. 18, N 3. P. 302-308.
doi: 10.15407/spqeo18.03.302
© 2015, V. Lashkaryov Institute of Semiconductor Physics, National Academy of Sciences of Ukraine
305
Let’s consider the model of color mixing in SLS
based on RGBW LEDs. Fig. 3 shows the Maxwell
triangle, vertices of which are chromaticity coordinates
of LEDs, from which RGB LED consists, and the point
Ww that are the coordinates of white LED. All the
variants of colors with the values of chromaticity
coordinates locating in the middle of the triangle are to
be found using RGB or RGBW LEDs. It should be noted
that usually, when mixing of emission of three
components of LEDs in RGB or four components of
LEDs in RGBW, at maximum brightness of each of
them, one will get the points in the chromaticity diagram
WRGB and WRGBW that are not located in the Planckian
locus. The coordinates of the point WRGBW can be found
as follows:
,
,
,
WBGR
WBGR
WBGR
ZZZZZ
YYYYY
XXXXX
+++=
+++=
+++=
(12)
where XW, YW, ZW – chromaticity coordinates of white
luminophore LEDs.
Because chromaticity coordinates of obtained light
do not localized in the Planckian locus, it is necessary to
enter the coefficients r, g, b, w, to adjust the brightness
of each LED so that the resulting chromaticity
coordinates fulfilled it:
⎪
⎩
⎪
⎨
⎧
+++=
+++=
+++=
WBGR
WBGR
WBGR
wZbZgZrZZ
wYbYgYrYY
wXbXgXrXX
,
,
or
⎥
⎥
⎥
⎥
⎦
⎤
⎢
⎢
⎢
⎢
⎣
⎡
⋅
⎥
⎥
⎥
⎦
⎤
⎢
⎢
⎢
⎣
⎡
=
⎥
⎥
⎥
⎦
⎤
⎢
⎢
⎢
⎣
⎡
w
b
g
r
ZZZZ
YYYY
XXXX
Z
Y
X
WBGR
WBGR
WBGR
. (13)
Fig. 3. The Maxwell triangle for RGB LEDs.
Eq. (13) is convenient for calculating chromaticity
coordinates of resulting radiation as it is done in other
systems [9, 10], but to find four unknown r, g, b, w
coefficients in this system it requires a fourth equation.
To do this, one should use the equation to get a certain
point of the Maxwell triangle space with the known
values XYZ. This point can be Ww that has chromaticity
coordinates of white LED added into SLS. The situation,
in which the color and brightness of white LED match
those of light obtained by using red, green and blue
LEDs, is described by the formula:
0=−++ WBWGWRW YYbYgYr , (14)
where rW, gW, bW – coefficient values of brightness of
red, green and blue LEDs, which are calculated from
Eq. (11) for obtaining light with color temperature and
brightness, they match white LED Ww.
From the equation system (13), taking into account
the expression (14) the coefficients r, g, b, w are
determined as follows:
⎥
⎥
⎥
⎥
⎦
⎤
⎢
⎢
⎢
⎢
⎣
⎡
⋅
⎥
⎥
⎥
⎥
⎦
⎤
⎢
⎢
⎢
⎢
⎣
⎡
−
=
⎥
⎥
⎥
⎥
⎦
⎤
⎢
⎢
⎢
⎢
⎣
⎡
⋅=
⎥
⎥
⎥
⎥
⎦
⎤
⎢
⎢
⎢
⎢
⎣
⎡
−
−
00
1
1
Z
Y
X
YYbYgYr
ZZZZ
YYYY
XXXX
Z
Y
X
K
w
b
g
r
WBWGWRW
WBGR
WBGR
WBGR
RGBW
(15)
Setting the brightness of RGBW LEDs in
proportion to the values of the corresponding
coefficients, we obtain the resulting light with given
chromaticity coordinates.
Software implementation of the demonstrated
above model of color mixing of RGBW LED in SLS
will provide an opportunity to obtain white light with
different color temperatures with a high color rendering
index. The luminous efficiency of lighting systems based
on RGBW LED is less than that for the systems, in
which two white LEDs are used. Such systems allow to
obtain, first, white light with the coordinates in the
Planckian locus, and, second, – light with various shades
and colors.
4. Experimental studies of the mathematical model
of color mixing of WW and RGBW LEDs
To test the mathematical models of mixing colors of two
white luminophore LEDs with various correlated color
temperatures and RGBW LEDs, the model of SLS was
used. It is a lamp of “Armstrong” type with the size
60×60 cm (Fig. 4), in which as an optical system used
was a combination of two plastics – a transparent one
with covered (on its reverse side) system of microlenses,
acting as a lightguide, and opaque one, acting as a
scatterer. Two models of SLS were produced. In the first
model, along the perimeter there were the lines with
WW LEDs that alternated between them, in the second
model – lines with RGB and WW LEDs that are also
alternating between them.
Semiconductor Physics, Quantum Electronics & Optoelectronics, 2015. V. 18, N 3. P. 302-308.
doi: 10.15407/spqeo18.03.302
© 2015, V. Lashkaryov Institute of Semiconductor Physics, National Academy of Sciences of Ukraine
306
Fig. 4. Model of smart lighting system.
Fig. 5. Complex for measuring the light and electrical
parameters of lighting systems.
To measure performance lighting engineering
characteristics of SLS models, used was the measuring
setup (Fig. 5), consisting of integrating sphere with the
2-m diameter, a spectrophotometer, power supplies and
PC with the appropriate software. Using it, we measured
spectra and XYZ coordinates of LEDs that were applied
to create models of WW (Fig. 6) and RGBW (Fig. 7)
smart lighting systems.
For WW LEDs, it was obtained XLED1 = 1150,
YLED1 = 1025, ZLED1 = 319 and XLED2 = 1007, YLED2 =
1100, ZLED2 = 968 with corresponding coordinates
xLED1 = 0.4610, yLED1 = 0.4110 and xLED2 = 0.3275,
yLED2 = 0.3577.
The measured XYZ coordinates for RGB and WW
LEDs allow to calculate and write the transition matrix
based on Eq. (15):
⎥
⎥
⎥
⎥
⎦
⎤
⎢
⎢
⎢
⎢
⎣
⎡
−
=
10014.250.6636.31
43.6906.48354.1302.0
10021.179713.62
53.10214.9166.2353.148
RGBWK . (16)
With these results, we have performed calculations
for brightness of some emitting elements of SLS models
to obtain white light with the given color temperature
and have held its direct determination by using a setup
for measuring lighting and electric parameters of
lighting systems.
Listed in Table for two variants of SLS models are
the given values of correlated color temperature (Tg) and
chromaticity coordinates (xg, yg), experimentally
obtained values of correlated color temperature (To) and
chromaticity coordinates (xo, yo), as well as absolute
values of the difference between them (ΔT = To – Tg,
Δx = xo – xg and Δy = yo – yg).
a
b
Fig. 6. The emission spectra of two white luminophore LEDs
with correlated color temperature: a) 2700 K, b) 5700 K.
Semiconductor Physics, Quantum Electronics & Optoelectronics, 2015. V. 18, N 3. P. 302-308.
doi: 10.15407/spqeo18.03.302
© 2015, V. Lashkaryov Institute of Semiconductor Physics, National Academy of Sciences of Ukraine
307
a
b
c
d
Fig. 7. The emission spectra: a) red (R), b) green (G), c) blue
(B) and d) white (W) LEDs.
The data in Table shows that the WW LED-based
model demonstrated the possibility to obtain white light
with the difference between the obtained and given
values of chromaticity coordinates in the range 0.0014
and the values of color temperature – in 14 K. This
difference in chromaticity coordinates is well in the
limits of experimental errors in these parameters
measurements, which equals to ±0.0015 for the used
complex. For such a value of measurement error in the
chromaticity coordinates, the ranges of allowable values
of correlated color temperature for their limit values are
as follows: (3159…3240) K for 3200 K and
(7083…7278) K for 7200 K.
For the RGBW LED-based model of SLS, it was
determined the maximum differences between the
obtained and given values in the chromaticity
coordinates and in the correlated color temperature:
0.0035 and 30 K, respectively. The revealed large
difference in these parameters regarding the model of
system on WW LEDs can be explained by the
increasing number of LEDs of different types, which
leads to increase in the number of given parameters,
and to increase in influence of factors such as the
accuracy of location of LEDs, the temperature of
individual crystals in them, its dependence on operating
mode, etc. Despite the fact that the difference between
given and obtained chromaticity coordinates exceeds
the measurement error for some values of color
temperature, the difference in color does not exceed the
value of two-step MacAdam ellipse. This is
significantly less than the 7-step MacAdam ellipses,
using which the range of color difference is set when
determining one of eight nominal values of color
temperature according to the standard of chromaticity
C78.377A (Fig. 8).
The resulting color difference in two MacAdam
ellipses can be considered quite acceptable, also because
it corresponds to the maximum level of discreteness in
color according to the standard NEMA SSL-3 Binning
Standard in binning LEDs by their luminous flux value,
forward voltage value and chromaticity.
Table. Results of studying the mathematical models of color mixing in WW and RGBW LEDs in smart lighting systems.
Given values Obtained values Number of
measuring Tg, K xg yg To, K xo yo
ΔТ, K Δx Δy
For WW LEDs
1 3200 0.4228 0.3958 3201 0.4217 0.3953 1 –0.0011 –0.0005
2 3700 0.3946 0.3845 3700 0.3944 0.3844 0 –0.0002 –0.0001
3 4200 0.3724 0.3756 4197 0.3732 0.3759 –3 0.0008 0.0003
4 4700 0.3546 0.3685 4687 0.3560 0.3692 –13 0.0014 0.0007
5 5200 0.3401 0.3627 5186 0.3410 0.3631 –14 0.0009 0.0004
For RGBW LEDs
6 3400 0.4110 0.3935 3411 0.4119 0.3970 11 0.0009 0.0035
7 4400 0.3644 0.3661 4370 0.3646 0.3626 –30 0.0002 –0.0035
8 5400 0.3348 0.3431 5410 0.3345 0.3416 10 –0.0003 –0.0015
9 6100 0.3202 0.3300 6109 0.3200 0.3308 9 –0.0002 0.0008
10 7200 0.3038 0.3139 7217 0.3035 0.3143 17 –0.0003 0.0004
Semiconductor Physics, Quantum Electronics & Optoelectronics, 2015. V. 18, N 3. P. 302-308.
doi: 10.15407/spqeo18.03.302
© 2015, V. Lashkaryov Institute of Semiconductor Physics, National Academy of Sciences of Ukraine
308
Fig. 8. The difference between the chromaticity coordinates of
obtained and given light in SLS based on RGBW LEDs, which
involves at least two steps of MacAdam ellipses.
Note that more opportunities of RGBW systems in
terms of getting the white colors directly in the
Planckian locus and colors of other shades from the
Maxwell triangle lead to higher specifications in terms
of practical implementation of SLS (LED locations and
ensuring uniformity of color mixing) as well as to
control and ensure stability of LED parameters
depending on the power mode. Controlling the
brightness of lighting for both types of systems is carried
out by proportional change in the effective value of
current through individual crystals of all LEDs that
consist them.
5. Conclusion
Considered in this work are the mathematical models of
mixing colors in SLS based on WW and RGBW LEDs.
They were software implemented and tested on
experimental samples of the lamps of type “Armstrong”
with the size 60×60 cm.
Software implementation of the model of mixing
colors of two white luminophore LEDs showed the
ability to dynamically change the correlated color
temperature of light with the difference between the
given and obtained values no more than 14 K, which is
in the limits of measurement errors.
Software implementation of the model of mixing
colors of RGBW LEDs demonstrated the possibility of
obtaining white light with various color temperature,
chromaticity coordinates of which are directly in the
Planck locus. Unlike the WW system, it allows to
expand the range of permissible values of color
temperatures of white light, which is limited only by the
area of the Maxwell triangle for RGB LEDs, as well as
the ability to get the color of any shade from this
triangle. The difference between the given and obtained
values of color temperature of white light is in the two-
step MaсAdam ellipse, which corresponds to the
maximum requirement of the standard NEMA SSL-3
Binning Standard in the accuracy of selection in the
color when binning white LEDs by manufacturers.
The performed studies show promising application
of the considered models of mixing colors in SLS for
reproduction of shades of white light by any given
algorithm of changes, including the possibility of
implementing changes in lighting in according with
natural circadian rhythm or other algorithms of change
in the color temperature and brightness.
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