WHITE LED THERMAL ANALYSIS & Radiometric Efficiency...

Compared with other common light sources LEDs do not radiate heat. Instead they conduct heat thereby
increasing the temperature of their surroundings.
Elevated operating temperatures strongly affect LED parameters wavelength, lifetime, output brightness, and forward voltage.
Knowledgeably removing this heat is an important consideration in achieving the expected service life and performance from LEDs.

Because human vision is so sensitive to visible light intensity and color variation, both the correct thermal
characterization of LEDs and heat removal are critical since the human eye can detect wavelength shifts as
small as 2-4 nm.

There is a standard model (described below) for semiconductor thermal analysis. The model’s generality
makes it widely applicable and it provides its user a consistent and coherent method
for analyzing thethermal behavior of semiconductors. However, methods recommended throughout the LED industry for quantifying
LED thermal performance are inadequate because this model is wrongly implemented.

Two versions of the standard semiconductor thermal model are used in the LED industry when
investigating LED heat effects.

One version of the thermal model corresponds to a 0% efficient LED (an LED that emits no light!).
Surprisingly, this version is the one most prevalent in thermal management literature from LED manufacturers.

The second version corresponds to an LED that actually emits light.
Obviously this is better, but its implementation is flawed because the efficiency of input power to-light-conversion is only guessed at,
making the model unreliable.
The argument is made–correctly --that since LEDs cannot be 100% efficient some amount of input power must go into wasted heat.
But things immediately go wrong once the magnitude of heat is assigned a numerical value that is never derived and arrived at by means of some rationale
the paper’s author never explains.
This lack of rigor is the downfall of this second version of the thermal model for LEDs.
It is completely void of generality. Even though it is superior to the first, the loose manner in which LED power-to-light-conversion values are chosen makes
it as equally flawed as a reliable tool for LED thermal analysis as the first version is. Are these LEDheat/light values wives tales?
Are they rules-of-thumb? Are they universal?
How does one tell if there is merit to a value?

What is needed for a proper White LED thermal analysis is an easy-to-use method for evaluating the
percentage of electrical energy converted into photons. Because this heat must be removed in order for LEDs
to operate optimally, it is critical to bring clarity to this important area. Propagation of ambiguously
arrived at LED parameters, black magic if you will, by LED manufacturers is unquestionably an ill-suited
state of affairs for the industry. This means that to an LED user complete and accurate answers to simple
questions like ‘What size heat sink is required for my White LED?’, or ‘How efficient is my White LED?’,
are just not being presented by LED manufacturers. The LED community is not being well-served by this situation.

A way of achieving this goal is presented here that uses information always presented in LED
manufacturer’s data sheets. All LED data sheets list the following device parameters: Color Temperature
and Luminous Flux, operating current and forward voltage. With these a calculation can be made that
unambiguously finds the fraction of input power that can be assigned to the White LED; the other fraction is heat.
This number–derived in a straightforward manner --represents the heat the user needs to dissipate.

CONVENTIAL SEMICONDUCTOR THERMAL ANALYSIS
For any electronic component there is always a requirement that it not get too hot.The formula that expresses a device’s maximum allowed power dissipation, PD, is given by

(2.1) P[SUB]D[/SUB](max) ≤[T[SUB]J[/SUB](max) –T[SUB]A[/SUB]]/ Rθ[SUB]JA[/SUB]
where TJis the device die junction temperature and TA is the ambient temperature.
The term Rθ[SUB]JA[/SUB] always represents a chain of individual thermal resistances.
This power dissipation formula applies to all electronic devices (not just LEDs) cooled via heatsinking. This is the standard model for semiconductor
thermal analysis.Thermal resistance RθJAdescribes a thermal path from device die to device package/case to heat sink to ambient:

(2.2) Rθ[SUB]JA[/SUB]=Rθ[SUB]JC[/SUB]+Rθ[SUB]CH[/SUB]+Rθ[SUB]HA[/SUB]

(jnc-case) (case-hs)(hs-amb)

Device data sheets (should) always provide T[SUB]J[/SUB](max) & Rθ[SUB]CH[/SUB]& P[SUB]D[/SUB](max) values. While the power
dissipation formula is general, different expressions of Rθ[SUB]JA [/SUB]make the formula apply to a particular instance.

FLAWS IN CONVENTIAL LED THERMAL ANALYSIS

As applied to LEDs mounted on a circuit board the RθJAterm becomes

3.1) Rθ[SUB]JA[/SUB]=Rθ[SUB]JC[/SUB]+Rθ[SUB]CP[/SUB]+Rθ[SUB]PH[/SUB]+Rθ[SUB]HA[/SUB]

(jnc-case)(case-pcb)(pcb-hs)(hs-amb)


Using (3.1) and the thermal-electrical equivalents we can draw the LED version of equation (1) as shown
in Figure 2
....

Expression (3.1) and Figure 2, or some variation of them, are nearly always presented in literature on LED
heating.
The LED thermal model is correct; what is incorrect is how it is applied. At issue is the source term, P[SUB]D[/SUB][SUP]2[/SUP], shown in Figure 2 .
(By the definition of electrical power P[SUB]D[/SUB](W) = I(A)·V[SUB]f[/SUB](V), with P[SUB]D[/SUB]= LED power/heat
needing to be dissipated, I = current passing through the LED, and V[SUB]f[/SUB]= the LED forward voltage.).

LED manufacturer’s Application Notes and White Papers dealing with the topic of LED heat always make one of two choices for the PDterm:

Version One always assigns PD=V[SUB]f[/SUB]·I. Here there is no light.
In this version of the model all input energy goes to LED heat. This is an unconcealed version of the thermal
model for an ordinary semiconductor diode, not an LED! It is conspicuously incorrect.
What’s worse is that it is the most commonly used LED thermal model. It should be pointed out that an LED user following
Version One is going to unnecessarily purchase a larger capacity (and probably larger size as well as more expensive) heat sink than is actually required.
This model always over-estimates the LED heat dissipation requirement.

Version Two assigns

(3.2) P[SUB]D[/SUB]= (1-&#949·(Vf·I) + ε·light

where εrepresents the fraction of electrical energy converted into light.
At least in this model the LED emits light so equation (4) more realistically represents an actual LED.
So far so good. But a breakdown takes place almost immediately in all instances of LED manufacturer’sliterature using this approach;
in this literature there is not to be found a set procedure for reliably estimating the numerical magnitude of ε.
This is where the unreliable hand-waving comes in and values are pulled out of the air.
The numerical value of ε is never derived in any LED manufacturer’s Application Note or White Paper.
This failure compromises an otherwise good model making it a flawed tool for LED thermal analysis.

What is needed for a proper LED thermal analysis is an easy-to-use, reliable method for evaluating ε.
Since this quantity relates directly to the heat that must be removed in order for LEDs to operateoptimally, correctly deriving its magnitude is of considerable importance.

A straightforward way of calculating the numerical value ofεis presented here that uses information
always presented in LED manufacturer’s data sheets. All LED data sheets list the following device
parameters: Color Temperature and Luminous Flux. This is a general and conclusive method for
numerically calculating the fraction of electrical energy converted into light.


LED EFFICIENCY METRICS

The technical term forthe energy efficiency of a light source is its “luminous efficacy” or simply “efficacy”, η[SUB]ν [/SUB][lm/W]. It is the ratio of its emitted luminous flux (in units of lumens) to its input electrical power (in units of Watts).
Efficacy is a product of two factors: ηv= ηe·K, where ηeis the “efficiency” of the source, a dimensionless quantity defined as the ratio of emitted optical power
(in units of Watts) to its input electrical power (also in units of Watts) and K[lm/W], called the “luminous efficacy of radiation”.

(4.1) η[SUB]v[/SUB]= η[SUB]e[/SUB]·K

Luminous Flux (out) Optical Power (out) Luminous Flux (out)
-------------------------= ------------------------·=-------------------------
Electrical Power (in) Electrical Power (in) Optical Power (out)


Luminous efficacy measures the fraction of electromagnetic power which is useful for lighting.
It is a function of the spectral distribution of the source S(λ) and is given by

(4.2) K[SUB][lm/W][/SUB] = Kmax*∫V[SUB]([/SUB][SUB]λ)[/SUB]S[SUB]([/SUB][SUB]λ[/SUB][SUB])[/SUB] d[SUB]λ[/SUB]/ ∫S[SUB]([/SUB][SUB]λ[/SUB][SUB])[/SUB] d[SUB]λ [/SUB], K[SUB]max[/SUB]= 683[lm/W]


where the constant Kmax relates photometric quantities to radiometric ones.

Photometry is based on radiometry, the science of optical radiation.
Radiometry concerns itself with the measurement of the entire spectrum of optical radiation while photometry deals only with that portion of the spectrum
detectable by the human eye. The V(λ) term in (4.2)
describes the average visual sensitivity of the eye to light of different wavelengths
of light. The eye responds more strongly to some wavelengths of light than others, even within the visible spectrum.
This characterization of the eye is given by V(λ), the spectral responsivity of human vision,
an internationally recognized standard function established by the Commission Internationale de l'Éclairage (CIE) and is the response of a "typical" eye under bright conditions (photopic vision).
Since 1924 all measurements of photometry have been based upon it as the standard for human vision.

The term ηeis often called “wall-plug efficiency” and is not a constant for LEDs.
One reason is the power source. Because commercial power is AC and LEDs require low-voltage DC
power, power conversion is required. Some loss is inherent to this conversion.
Another reason is loss internal to the LED semiconductor itself. There is some loss associated with the internal quantum efficiency of LEDs, which is a measure of the fraction of photons produced for each electron injected into the device. And finally there is loss due to the light extraction efficiency directly resulting from the high
refractive index of the compound semiconductor materials used to make LEDs.
The overall wall-plug efficiency of any LED will be the product of all of these factors:

(4.3) η[SUB]e[/SUB]= η[SUB]inj[/SUB]·η[SUB]int·[/SUB]η[SUB]elec[/SUB]·η[SUB]ext[/SUB]

whereη[SUB]inj [/SUB]is the injection efficiency representing the proportion of electrons passing through the device
that are injected into the active region of the p-n junction. Not all electron-hole recombinations are radiative.

The fraction that are equals η[SUB]int[/SUB], the proportion ofa ll electron-hole recombinations in the active
region that are photon producing.

The term η[SUB]elec [/SUB]is largely the AC-DC conversion efficiency and the LED driver efficiency.

Extraction efficiency,η[SUB]ext[/SUB], is the proportion of photons generated in the active region that actually escape from the device.
Interestingly, η[SUB]e [/SUB]is a function of emission wavelength (“Efficacy Limits for Solid-State White LightSources”, E. Bretschneider, Photonics.com, March 01, 2007) with significant differences in efficiency with respect to wavelength observed for both AlInGaP and InGaN LEDs.
“In general, efficiency decreases for InGaN LEDs as emission wavelength increases. The opposite behavior is noted for AlInGaP LEDs.
Unfortunately the lowest efficiencies occur near the photopic maximum at 555 nm. “



So other than the electrical component of (4.3), wall-plug efficiency is something that, to a large degree,
the user does not have control over. Fortunately, its magnitude (shown graphically in Figure 3) is well known
so taking it into account in a quantitative estimate of luminous efficacy (4.1) is doable. At the end of 2009 the wall-plug efficiencies for Blue (450 nm), Green (520 nm), and Red (615 nm) LEDs stood at 50-55%, 21%, and 35%, respectively.

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WHITE LED EFFICIENCY

By now the reader may have already recognized a relationship between our original ε,
the fraction of electrical energy converted into light, and η[SUB]v[/SUB], the luminous efficacy of radiation.
This relation is

(5.1) ε = F[SUB]LED[/SUB] / η[SUB]v[/SUB]

where F[SUB]LED [/SUB]equals the White LED luminous flux value in units of lumens, an important LED characteristic
found in all LED data sheets.

Together with our just arrived at estimate of η[SUB]e[/SUB], evaluation of the integrals
in (4.2) yields a numerical value for η[SUB]v[/SUB].

This means that for the first time a rational and unambiguous method for calculating LED power dissipation PD is computable.
Because V(&#955 is a known, standard function it can be fit to a curve.
As a first approximation a normal distribution Gaussian was used.

This fits V(&#955 using three parameters: amplitude, center wavelength λ0,
and width σ.
The expression is

(5.2) amplitude · (1/σ (O) 2&#960 ·{ exp{-(λ-λ0)[SUP]2[/SUP]/2σ[SUP]2 [/SUP]}

and the curve width, full width at half-maximum (FWHM) equals 2(O) 2ln[SUP]2[/SUP]·σ.
Using parameter values amplitude = 110, center wavelength = 556, and σ = 44 (so that FWHM = 104 nm) a reasonable fit was
achieved (Figure 4).

By no means is this the only possible fitting expression or the best one. Certainly the model of (5.2) doesn’t provide a suitable description of bare, monochromatic LED emission. However,white LEDs generating light by the Stokes shift of a blue LED emitting into a phosphor do attempt to
mimic this model as do combinations of RGB LEDs or RGBA LEDs. Alternative fitting expressions under investigation are


(5.3)
amplitude ·exp{-a(-b+x)2
amplitude ·exp{-ax[SUP]2 [/SUP]+bx[SUP]3[/SUP]}


For now the Gaussian fit is the one taken for V(&#955. Next we need an expression for the spectral
distribution of the LED source S(&#955. Our model for the spectral distribution of a white LED is the
radiance expression of a blackbody:

(5.4) S(λ,T) = C[SUB]1[/SUB] / [ exp(C[SUB]2[/SUB]/&#955 – 1]·λ

(Calculations were performed using Wolfram Mathematica8 )

....................


Here C[SUB]1[/SUB] is the first radiation constant, C[SUB]2[/SUB] is the second radiation constant, T is the LED “color
temperature” (K) and λ is the LED wavelength.

The constants are defined as follows:

C[SUB]1[/SUB] = 2πhc[SUP]2[/SUP] =119.104x10[SUP]18 [/SUP](W/m2)(1/nm)(1/sr)

and

C[SUB]2[/SUB] = hc/kBλT = 143.88x10[SUP]5[/SUP] (nm·K).

If the integrals of (4.2) are a little too abstract, Figure 5 illustrates pictorially the

∫ V(&#955S(&#955 dλ calculation.

The integral in the denominator of (4.2), ∫ S(&#955 dλ, is a constant times T4 (LED Color Temperature to the fourth power)
and by itself is known as Wien’s Law.

So using (5.2) for V(&#955 and (5.4) for S(&#955 we are in a position to evaluate K, the luminous efficacy of radiation.

We then use that value in (4.1) together with known values of LED wall-plug efficiencies to
obtain a numerical value for ηv. This series of calculations needs to be performed for each LED ColorTemperature of interest.

The numerical value ε needed in the calculation of LED heat dissipation (3.2) is then found using


(5.5) ε = F[SUB]LED[/SUB] / η[SUB]v[/SUB] = F[SUB]LED[/SUB] / η[SUB]e[/SUB] · K ≈ F[SUB]LED[/SUB] / 0.5 · K.


Equation (5.5) provides an unambiguous method for answering the question

‘What size heat sink is required for my White LED?’.

Plugging the ε value calculated in (5.5) into equation (3.2) provides the answer.
To create a practical implementation of this method equation (5.5) has been put into graphical form.
Rather than evaluate V(&#955 and S(&#955 integrals the user is more naturally going to implement the method using Figure 5.
Two examples of this method are given in the next section.
.................




EXAMPLE APPLICATIONS

Here we apply the method described above to LEDs from two manufacturers:

(1)a Cree XP-G XLamp (XPGWHT-L1-0000-00FE4) in the “R3” group
with a Color Temperature of 5,000K,operating at 350 mA where its Vf(typ) = 3.0V;

and

(2) an OSRAM OSLON SSL (LCW CQDP.PC-KTLP-5L7N-1)
with a Color Temperature of 4,000K, operating at 350 mA where its Vf(typ) = 3.2.V.

Example 1
From the Cree data sheet the LED’s Luminous Flux equals 122 lm.

Using Figure 5 we see that 5000K
corresponds to a ½*K value ≈ 215.

Dividing 122 by 215 yields ε = 0.56. (*56% radiometric efficiency )
From (3.2) the heat requiring dissipation is given by the (1-&#949·(Vf · I) term. So

P[SUB]D [/SUB]≈ (1-0.56)(3.0*0.350) = 0.46W.

Example 2
From the OSRAM data sheet the LED’s Luminous Flux equals 97-121 lm, so let’s choose 110 lm.
UsingFigure 5 we see that 4000K corresponds to a ½*K value ≈ 145.

Dividing 110 by 145 yields ε = 0.76. (*76%!!! radiometric efficiency !!! )

From (3.2) the heat requiring dissipation is given by the (1-&#949·(V[SUB]f[/SUB] · I) term.

SoP[SUB]D[/SUB] ≈ (1-0.76)(3.2*0.350) = 0.27W.


Summary
A method for computing White LED power dissipation has been derived. An easy-to-use graphical
implementation has also been presented. With this method an accurate answer to the simple question
‘What size heat sink is required for my White LED?’ is available. By knowing accurately the LED heat
dissipation requirement a more informed choice of heat sink can be made by the LED user.

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stardustsailor said:

P.S :

What about LCW CQ7P .CC at 2700°K ....???
With 61-76 lm (@350mA Bins JTKP ) or 65-82 lm (@350mA bins JUKQ )...

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stardustsailor said:

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MrFlux said:

You know where to find the spectrum? I'm looking at page 11 of these specs but it doesn't even mention the color temperature.

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guod said:

The RGB Values are more a neutral white
did you sample the Graph from the datasheet for this numbers?

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