# Theoretical efficacy limit for LED

Discussion in 'Lighting' started by Frank Knappe, Jun 20, 2010.

1. ### Frank KnappeGuest

Hello!

In several presentations I have seen graphs from the DOE where they
publiched the evolution of the efficacy of LED vs. time. In this graphs
were also two line which should represent the theoretical efficacy limit
for warm (~160lm/W) and cool white LED (~230lm/W). Can anybody give me a
reference where I can find the calculations of these limits?

Are these wall-plug efficacies (including all electrical losses) or just
the limits caused by the conversion of optical Watt to Lumen?

2. ### Frank KnappeGuest

Thanks. If it is for the LED alone with the electrical W as input or the
optical W? The latter one should IMHO only based on the spectral
distribution (find the right phosphors) whereas the electrical version
should also take into account the power converted into heat. I'm just
trying to get a clear picture into my head.

3. ### Paul KeinanenGuest

The human photopic vision is most sensitive at 555 nm and by
definition that corresponds to 683 lm at 1 W of radiation.

For other wavelengths, look for instance at
http://hyperphysics.phy-astr.gsu.edu/hbase/vision/efficacy.html
The photopic vision efficacy remains above 100 lm/W between
approximately 383 .. 645 nm, so clearly for multicolor "white" light,
the average sensitivity must be far less.

Then there is of course the problem what "white" light actually is.
One accepted definition is 6000 K black body radiation (the Sun).
"Warm white" is usually a black body radiator at 2700 K, with lots of
radiations below 555 nm. With the eye sensitivity dropping fast in the
red end, the efficacy numbers are worse than for higher color
temperatures.

Unfortunately, the CFL and white LED spectral distribution differs
significantly from a black body radiator, so it is questionable, if
those quoted values 160/230 lm/W make any sense in the real world.

Those sensitivity figures quoted in the link would correspond to the
ideal 100 % electric/light conversion efficiency.

I am very sceptic about LED manufacturers claiming over 100 lm/W,
which typically are obtained with spectral distribution very different
from what most people would consider "white".

4. ### Don KlipsteinGuest

So far, I agree!
So far, I agree!
I would like to beg to differ a bit - I sense that includes some
factor for conversion efficiency / "wallplug efficiency" for electrical
energy to light energy.

In large part, I see how even "cool white" LEDs and other
"artificial white light sources" achieve over 250 lumens per radiated
watt, and "warm white" ones achieve over 300:

For one thing: http://members.misty.com/don/lfunfac2.html#ole

Heck, I cited a 5450 K laboratory prototype at 331 lumens per
radiated watt! This was an actual working model!

=================

How about a few more figures that I have from actual takes from a
"reasonably properly calibrated" spectrometer and my post-analysys:

(Disclaimer - +/- whatever including small sample sizes)

A Nichia NSPWR70CSS-K1 LED, an especially efficient one with
below-average color rendering index (I estimate low to mid 60's) and
CCT around 5000 K: 334 lumens per watt radiated in the 380-780 nm range

"Old Tech Cool White" fluorescent: (around 4100 K with CRI probably
around 62) - 352 lumens per watt that is radiated into the 380-780 nm
range.

A high-color-rendering-index nominally-5000 K LED with CRI 90-plus
(Ra8) achieved 272 lumens per watt radiated into the 380-780 nm range.

A nominally 2700 K CFL achieved 360 lumens per watt radiated into
the 380-780 nm range. That one supposedly achieves "Ra8" CRI of 82.
If the overall color of the emitted light appears to be "white" and the
color rendering properties are no worse than or improve upon those of
"old tech cool white" fluorescent lamps, then I think the lamp-in-question
produces what most people would consider to be white light.

5. ### boxmanGuest

There is no straight forward way to calculate this number as it is
highly dependent on several parameters. The following article does a
reasonably thorough job of calculating some numbers for LEDs and
outlines their assumptions clearly. The calculation for LEDs is at the
end of the article.

http://www.photonics.com/Article.aspx?AID=28677

6. ### Paul KeinanenGuest

During evolution, the human visual system spectral sensitivity has
been matched with the only natural light source at 6000 K black body
radiation (the Sun), both having a spectral peak around 500 nm.

One purpose of artificial lighting is to expand the human activity to
the dark hours of the day.

In order to measure how effective the artificial lighting is, one
should compare the human ability to perform various tasks (such as
reading texts in different colors with different backgrounds) compared
to strongly attenuated solar spectrum (e.g. a small window).

I am not so sure that the color temperature, CRI and Ra figures would
produce a repeatable way to describe how humans would handle these

7. ### Andrew GabrielGuest

Well, we also spent lots of time living during dawn and twilight,
not to mention moonlight...

8. ### Don KlipsteinGuest

I correct myself here:

100 or more lumens per radiated watt means "photopic function" of
wavelength being at least 100/683, or at least .1464.

I have the version that CIE adopted in 1988 in:

http://members.misty.com/don/photopic.html

383 nm has photopic function of .000299, and when multiplied by 683 this

The shortest wavelength achieving 100 lumens per radiated watt is 481
nm.

The longest wavelength achieving 100 lumens per radiated watt is 644 nm.
(That one was hardly "off" at all.)

Meanwhile, wavelengths somewhat shorter than 481 nm are important for
stimulating "blue receptors" in human vision in order to efficaceously
form "white light". In fact, use of wavelengths around 445-450 nm
minimizes "waste into lower luminous efficacy wavelengths" to make the
best use of a smaller amount of "blue light". The
greatest-overall-luminous-efficacy white LEDs have their "blue peak" at
such shorter blue wavelengths - for example, Nichia NSPWR70CSS-K1.

9. ### Don KlipsteinGuest

I have a minor petty quibble with 6000K as "average daylight". Direct
sunlight has a color temp. of 5785 K before it hits Earth's atmosphere.

It appears to me that the atmosphere often reflects disproportionately
shorter wavelengths back out to space, resulting in "average daylight"
having an even lower color temperature.

Daylight color slide film is nominally tuned for 5500 K. Peak
wavelength of that is 527 nm. Spectral power distribution is at 90% of
peak around 431 and 654 nm and higher in-between - most of the visible
spectrum. The 80% points of a 5500 K blackbody are around 396 and 726 nm.

(According to MWPL.EXE, which I publish in
http://members.misty.com/don/software.html - free software with source

10. ### Paul KeinanenGuest

Sorry for the typo, it should read 483 .. 645 nm.

11. ### Paul KeinanenGuest

The Rayleigh scattering is strongly frequency dependent and after
several scatterings, some blue light will be radiated back to space.
However, at least half will reach the ground through the blue sky.

The color temperature depends of the angle of view of the
spectrometer. An angle of view of just 0.5 degrees aimed towards the
sun will fill the angle of view, resulting in the lowest color
temperature.

Using a wider angle of view will allow more and more scattered blue
light into the instrument, increasing the effective color temperature
closer to original solar color temperature.