How do you exactly calculate the theoretical maximum efficiency of an LED?

[HomeExperiement]

Hi!

I found interesting post here:
https://electronics.stackexchange.com/questions/325762/how-efficient-are-leds
However, it only gives the final results and not the steps he made. I tried to learn the formulas on wikipedia on my own but I couldn't figure out what variables need to have what values.

For example in that linked post the author stated:

Maximum for CRI=95 at 2800 K: 370 lm/W

If I have CRI=a and temperature = b, what would be maximum lm/w? PS sorry if it is in wrong forum, was a bit confused where to exactly post it.

 

[Anand Sivaram]

You mean the formula here?
https://en.wikipedia.org/wiki/Luminous_efficacy#Mathematical_definition

I am not sure how you got 370 lm/W, the same Wikipedia link shows 299 or 343 lm/W for >2% or >5% of range

 

[HomeExperiement]

It's not I who got 370 lm/W. I simply copied it from the post that I linked. I was asking how to calculate these. This formula got me confused because it has many variables for which I don't know value. I was asking that if I have CRI=a and CCT=b then how would this formula look like? For example how do I calculatelm/W if CRI = 95 and CCT=1800k?

 

[Anand Sivaram]

Interesting question. I am looking forward for how it is calculated practically.

 

[Andy Resnick]

I found interesting post here:
https://electronics.stackexchange.com/questions/325762/how-efficient-are-ledsIf I have CRI=a and temperature = b, what would be maximum lm/w? PS sorry if it is in wrong forum, was a bit confused where to exactly post it.

I'm not entirely sure what you are asking (efficiency of electrical power in converted to visible light out?), but this Wiki page has some info:

https://en.wikipedia.org/wiki/Luminous_efficacy#Photopic_vision
First off, your eye is not uniformly sensitive to all wavelengths of light: the unit 'lumen' is what you get when you start with the radiometric unit 'Watt' and spectrally weight it by the human eye response, which is normalized to the response at 555nm. So, for example, 'cold' blackbodies primarily radiate in the IR and so emit no lumens (0 lm/W) and as the blackbody temperature inceases, the luminous efficacy also increases until the peak emission wavelength again passes out of the visible range (towards the UV).

So, in order to start to answer your question, you need the radiometric efficiency (Watts of electricity to Watts of light) and the spectral output of the source, to convert Watts to Lumens.

But wait, there's more: since the LED is an extended source, you also need to know how the emitted radiation is distributed in angle- a point source radiates equally in all 4π steradians, a Lambertian source radiates differently, etc. etc. How much of the radiated light is transmitted forward into the optical system? What is the relative orientation between the axis 'normal' to the LED and the axis of the detector?

Now, as for the CRI/CCT specifications: The CRI (color rendering index, for those of you playing at home) is a crude way of specifying the spectral profile of the source (which can be continuous or discrete). The CCT (correlated color temperature) is a sort of 'black-body equivalent' metric for the source.

https://en.wikipedia.org/wiki/Color_rendering_indexhttps://en.wikipedia.org/wiki/Color_temperature#Correlated_color_temperature
I'm not sure if a CRI spec can easily be made to generate a luminous efficiency value; CCT may be a better metric to use.