Methods for optimal operation of light emitting diodes

LED illumination systems are formed with a suitable choice of LED and/or heatsink, such that an optimum operating power is identified using computer modeling for a desired output luminous flux, given the constraints of the rated power of the LED and the heatsink.

FIELD OF THE INVENTION

This invention relates to light emitting diodes (LEDs) and to systems formed from multiple LEDs that maximizes the luminous flux output from a given thermal design of LED system.

BACKGROUND OF THE INVENTION

A light emitting diode (LED) is a semiconductor device that emits light when a current is passed through it in a forward direction. Many types of LEDs are known that emit light in various wavelengths including infra-red, visible and ultra-violet regions. Many applications for LEDs are known including as indicator lights of various colors, for use in advertising displays, and in video displays.

In the past LEDs have tended to be lower power devices that produce relatively low power outputs and have not been used for general illumination purposes. More recently, however, high-power LED devices have become known that can provide an alternative to incandescent and fluorescent light sources. LED devices produce more light per watt than incandescent light sources and may therefore be useful as energy efficient light sources, while they have a number of advantages over fluorescent light sources including being easier to dim and not requiring the use of potentially toxic and polluting elements such as mercury to create the plasma that is the source of fluorescent light.

Light emitting diodes (LEDs) have therefore emerged as promising lighting devices for the future. However, LEDs are still primarily restricted to decorative, display and signaling applications so far and have not yet entered the market for general illumination to any great extent.

In photometry, one important factor that is commonly used for comparing different lighting devices is the luminous efficacy (lumen per Watt). One major hindrance to the widespread use of LEDs in general illumination applications is that the luminous flux of LEDs decreases with the junction temperature of the LEDs. The luminous efficacy of various LEDs typically decreases by approximately 0.2% to 1% per decree Celsius rise in temperature. Due to the aging effect, the actual degradation of luminous efficacy could be higher than this quoted figures. Accelerated aging tests show that the light output can drop by a further 45%. For aged LEDs, the efficacy degradation rate could be up to 1% per ° C. In some applications such as automobile headlights and compact lamps, the ambient temperature could be very high and the size of the heatsink is limited. The drop in luminous efficacy due to thermal problem would be serious, resulting in reduction of luminous output.

FIG. 1shows a conventional LED9. At the heart of the LED device is a light emitting semiconductor material such as InGaN though other materials will be known to those skilled in the art. In the example ofFIG. 1a light-emitting InGaN chip1is mounted on a silicon substrate2and is connected to electrodes such as cathode3through gold wires4and solder connection5. The light-emitting chip1is covered by a silicone encapsulant6and a plastic lens7.

When a LED of the type shown inFIG. 1is used to generate light a substantial amount of heat is generated that will damage the light-emitting chip if not removed. Therefore a heat sink must be provided and beneath the light-emitting chip1is a heatsink slug8. In practice when used to provide a source of light for illumination, conventionally multiple LEDs are provided to form a LED system10as shown inFIG. 2where multiple LEDs11are provided on a single heatsink12.

SUMMARY OF THE INVENTION

According to the present invention there is provided a method of forming an LED illumination system comprising a single or a plurality of LEDs on a heatsink with a desired output flux, comprising the steps of: (a) modeling on a computer the luminous flux emitted by said LED system as a function of the thermal resistance of said heatsink and the power applied to each LED, and (b) selecting an LED system such that the maximum luminous flux is emitted at a power equal to or below a rated power of said LED system provided that said maximum luminous flux is equal to or greater than the desired output flux, or (c) selecting an LED such that the rated power of said LED system is below the power at which the maximum luminous flux is emitted, provided that the flux emitted by said LED system at said rated power is equal to or greater than the desired output flux.

Preferably, in option (c) the rated power is at between 80% and 96% of the power at which maximum flux would be output.

Viewed from another aspect the present invention provides a method of forming an LED illumination system comprising a single or a plurality of LEDs on a heatsink with a desired output flux, comprising the steps of: (a) modeling on a computer the luminous flux emitted by said LED system as a function of the thermal resistance of said heatsink and the power applied to each LED, and (b) selecting a heatsink having a thermal resistance such that the maximum luminous flux is emitted at a power equal to or below a rated power of said LEDs, or (c) selecting a heatsink having a thermal resistance such that the rated power of said LED system is below the power at which the maximum luminous flux is emitted, provided that the flux emitted by said LED system at said rated power is equal to or greater than the desired output flux.

Preferably in step (c) the rated power is at between 80% and 96% of the power at which maximum flux would be output.

Viewed from another broad aspect the present invention provides an LED illumination system comprising a plurality of LEDs on a heatsink, wherein said heatsink has a thermal resistance such that the maximum luminous flux is emitted at a power below a rated power of said LEDs.

According to the present invention there is also provided a method of forming an LED illumination system comprising a plurality of LEDs on a heatsink with a desired output flux, comprising the steps of: (a) selecting an LED system such that the maximum luminous flux is emitted at a power below a rated power of said LED system provided that said maximum luminous flux is equal to or greater than the desired output flux, or (b) selecting an LED such that the rated power of said LED system is below the power at which the maximum luminous flux is emitted, provided that the flux emitted by said LED system at said rated power is equal to or greater than the desired output flux.

Viewed from a still further aspect the present invention provides a method of forming an LED illumination system comprising a plurality of LEDs on a heatsink with a desired output flux, comprising the steps of: (a) selecting a heatsink having a thermal resistance such that the maximum luminous flux is emitted at a power below a rated power of said LEDs, or (b) selecting a heatsink having a thermal resistance such that the rated power of said LED system is below the power at which the maximum luminous flux is emitted, provided that the flux emitted by said LED system at said rated power is equal to or greater than the desired output flux.

DETAILED DESCRIPTION OF PREFERRED EMBODIMENTS

To increase the light emitted from a conventional LED system it is necessary to increase the current applied to the LED. Continuing to increase the LED power will have diminishing returns, however, as the increasing temperature of the LED will reduce its efficiency and potentially damage the LED. The heatsink is therefore important as it is essential for heat to be carried away from the LED so as not to cause it any damage. The light emitted by a LED will increase with applied current provided that the heat produced can be removed, but for any individual LED design there will come a point where increasing power applied to the LED will not result in greater light being emitted because heat is no longer being effectively removed. Identifying the relationship between power applied and light emitted is an important aspect of the present invention.

Let φvbe the total luminous flux of an LED system consisting of N LED devices.
φv=N×E×Pd(1)
where E is efficacy (lumen/Watt) and Pdis the real power of one LED (W)

It is well known that the efficacy (E) of LEDs will decrease with increasing junction temperature of the LEDs.FIG. 3shows a typical relationship provided by an LED manufacturer. It can be seen that:
E=Eo└1+ke(Tj−To)┘ forTj≦ToandE≦0  (2)
where Eois the rated efficacy at the rated temperature To(typically 25° C.) and keis the relative reduction of efficacy with increase in temperature. For example, if E reduces by 20% over a temperature increase of 100° C., then ke=0.002.

In general, the LED power can be defined as Pd=Vd×Id, where Vdand Idare the diode voltage and current respectively. But only part of the power will be dissipated as heat. Thus, the heat generated in one LED is defined as:
Pheat=khPd=khVdId(3)
where khis a constant less than 1.

Now consider a typical relationship of the heatsink temperature and the heat generated in the LED system as shown inFIG. 4. A simplified dynamic thermal equivalent circuit of a LED system is shown inFIG. 5(a), assuming that (i) the N LEDs are placed on the same heatsink with thermal resistance of Rhs, (ii) each LED has a junction to case thermal resistance Rjcand (iii) a thermal conductor with electrical isolation (such as heatsink compound) is used to isolate the LEDs from the heatsink and which has a thermal resistance of Rins. A distributed thermal model is used for the heatsink due to its relatively large size. The corresponding thermal capacitances are needed if dynamic response is to be studied.

Under steady-state conditions, the thermal model can be further simplified into a steady-state model as shown inFIG. 5(b). In practice, a heat sink compound or equivalent may be used between the LEDs and the heat sink to ensure good thermal contact. The thermal resistance of such thermal conductor/electric insulator is relatively small when compared with Rjcof LEDs and is neglected inFIG. 5(b) and the following equations.

Based on the model inFIG. 5(b), the steady-state heatsink temperature can be expressed as:
Ths=Ta+Rhs(NPheat)=Ta+Rhs(NkhPd)  (4)
where Ta=ambient temperature.

FromFIGS. 5(b) and (4), the junction of each LED is therefore:
Tj=Ths+Rjc(Pheat)=Ths+Rjc(khPd)  (5a)
Tj=Ta+(Rjc+NRhs)khPd(5b)

Equation (7a) can also be expressed as follows:
φ=NEo{Pd+[ke(T−To)]Pd+kekh(Rjc+NRhs)Pd2}  (7b)

Several important observations can be made from equations (7a) and (7b).1. Equation (7) relates the luminous flux (φv) to the electrical power of the LED (Pd) and the thermal resistance of the heatsink (Rhs) and the LED junction (Rjc) together. It is an equation that integrates the photometric, electrical and thermal aspects of the LED system together.2. For a given heatsink (that may be restricted in size by a specific application), the operating point Pd* at which maximum φvoccurs can be determined. Alternatively where there is flexibility in designing the heatsink, the equations can be used for thermal design to optimize the size of the heatsink (Rhs) for a given LED array.3. Because keis negative and less than 1, (7) is in the form of φv=α1Pd−α2Pd2where a1and a2are two positive coefficients. As Pdis increased from zero, φvincreases almost linearly because the second term is negligible when Pdis small. As Pdincreases, the second negative term which is proportional to the square of Pdwill reduce φvsignificantly. After reaching the maximum point, the φvwill drop faster as Pdand Rjcincrease (due to the increasing significance of the negative terms in (7b)). This means that the parabola of φvis not symmetrical. Since the luminous flux function is a parabola and therefore has a maximum value, this maximum point can be obtained from

By differentiating (7) with respect to Pd,

It should be noted that the first two terms on the right hand side of (8) do not have derivatives, while the remaining three terms do. Strictly speaking, ke, khand Rjcare not constant. It must be noted that Rjcwill indeed increase significantly with lamp power.

The above equations can usefully be simplified for practical applications. As a first approximation, it is assumed that ke, kh, and Rjcare constant for the time being. It is known that khwill reduce slightly for a few percent under dimming conditions. From LED manufacturer data sheets the degradation of the efficacy with junction temperature is usually assumed to be linear and thus keis assumed to be constant. This assumption is acceptable for keand kh, and will be relaxed to accommodate the changing nature of Rjcin the analysis later. Based on this assumption, (8) can be simplified as:

Therefore, maximum-φvpoint can be obtained by putting

ⅆϕvⅆPd=0⁢⁢and⁢⁢Pd*=-[1+ke⁡(Ta-To)]2⁢ke⁢kh⁡(Rjc+NRhs)(10)
where Pd* is the led power at which maximum φvoccurs. (Note that keis a negative value.)

From (3), the corresponding LED current at which maximum φvoccurs can be obtained as:

Several significant observations can be made from (10) and (11).1. Equations (10) and (11) relate the optimal Pdand Id, respectively, to the thermal design of the LED system (i.e., thermal resistance of the heatsink Rhsand Rjc).2. The maximum luminous flux will occur approximately at a lamp power Pd* specified in (10). This Pd* will shift to a lower value if (Rjc+NRhs) is increased. This leads to the possibility that the Pd* may occur at a power level that is less than the rated power Pd(rated)of the LED.3. Based on the above comment, one should expect that the Pd* could be shifted to higher power level if a larger heatsink with lower Rhsis used.4. For many applications such as head lamps of vehicles and compact lamps for replacement of incandescent lamps, the size of the heatsink is highly restricted and the ambient temperature is high. In these cases, there is a high possibility that Pd* (at which maximum luminous flux is produced) will occur at a power level less than the rated power.

In practice, Rjcof the LED increases with lamp power. Therefore, a vigorous equation can be obtained from (8) as:

The function of Rjcis highly complex and it depends on several factors such as thermal resistance of the heatsink, ambient temperature, the LED size and mounting structure and even the orientation of the heatsink. Equation (7b) in fact provides the physical meaning of effects of the temperature-dependent Rjc. Since Rjcincreases with lamp power Pd, the two negative terms (with kewhich is negative) in (7b) will accelerate the reduction of the luminous flux as Pdincreases. This effect should be noticeable when Pdexceeds the Pd*, resulting in a slightly asymmetric parabolic luminous flux function.

In order to verify the theory two types of LEDs are used: 3 W cool white LEDs and 5 W cool white LEDs from Luxeon K2 Star series. They are mounted on several heatsinks with thermal resistances of 6.3° C./W, 3.9° C./W and 2.2° C./W so that experiments can be performed to evaluate their luminous output under different lamp power operations.

Since the junction-to-case thermal resistance Rjcis a complex and nonlinear function of the lamp heat dissipation Pheat(which is equal to khPd) and the thermal design of the mounting structure, the theoretical prediction is based on a simplified linear function as follows:
Rjc=Rjco(1+kjcPd)  (13)
where Rjcois the rated junction-to-case thermal resistance at 25° C. and kjcis a positive coefficient. A typical linear approximation of Rjcis shown inFIG. 6.

If equation (13) is used in (7b), a more accurate luminous flux equation can be derived as:
φv=NEo{[1+ke(T−To)]Pd+[kekh(Rjco+NRhs)]Pd2+[kekhkjcRjco]Pd3}  (7c)
A Tests on 3 WLEDs
(i) On a Heatsink with Thermal Resistance of 6.3° C./W

A group of eight identical Luxeon K2 Cool-white 3 W LEDs are mounted on a standard heatsink with a thermal resistance of 6.3° C./W. The efficacy of the LEDs is measured at rated power in an integrating sphere. The parameters required for the equation (7) are:
ke=−0.005, kh=0.85, Ta=28° C.,T0=25° C.,E0=41 Lumen/Watt,N=8, Rhs=6.3° C./WRjco=10° C.//W andkjc=0.1° C./W2.

Now two equations can be derived from (7). If the Rjcis assumed to be constant as a first approximation (i.e., Rjc=Rjco)
φv=323.08×Pd−84.2×Pd2(14)

If Rjcis assumed to obey (13),
φv=323.08×Pd−84.2×Pd2−1.39Pd3(15)

The luminous flux is measured in an integrating sphere. The measured total luminous flux for eight LEDs is used for comparison with calculated values. The measured and calculated total luminous flux values are plotted, not against the total power sum of eight LEDs but against one LED power because the eight LEDs are identical and are connected in series. Using the power of one LED in the x-axis allows one to check easily if the optimal operating point is at the rated LED power or not. The measured results and calculated results from (14) and (15) are plotted inFIG. 7. Several points should be noted:1. The theoretical curves generally have the same trends as the measured curve. This confirms the validity of the general theory.2. The maximum lumen/Watt point occurs at about Pd=1.9 W, which is less than the rated power of 3 W. This result shows that the general theory can predict accurately the Pd* operating point which may not be the rated power. Equation (10) indicates that a large NRhsterm will shift Pd* to the low power level of the LED.3. The two negative terms in this example can also be seen in (15). The asymmetry after the peak luminous output point is more noticeable in the theoretical curve obtained from (15) than from (14). Comparison of (14) and (15) shows that the effect of the variation of Rjc, which is reflected in the extra third term in (15) is the reason for the obvious asymmetry of φv.4. In summary, the simplified model (7b), which is the basis for (14), has the form of φv=α1Pd−α2Pd2, while the more vigorous model (7c), which is the basis for (15), has the form of φ=α1Pd−α2Pd2−α3Pd2. Therefore, the model in (7c) is more accurate than the model (7b) particularly when Pdhas exceeded Pd*. However, since both simplified and vigorous models are accurate enough for the power less than Pd*, which is also the recommended useable power range of LEDs, both equations can be used in the design optimization procedure to be explained.

Based on (6), the efficacy function can also be obtained.
E=40.39−10.52PdassumingRjcis constant  (16)
E=40.39−10.52Pd−0.17Pd2assumingRjcobeys (13)  (17)

The measured efficacy values and the calculated values from (16) and (17) are displayed inFIG. 6. It is noted that the calculated values are consistent with measurements. The results obtained from (17) are more accurate than those from (16) when Pdis large.

(ii) On a Heatsink with Thermal Resistance of 4.5° C./W

Eight identical 3 W LEDs are mounted on a larger heatsink with thermal resistance of 4.5° C./W. The measured and calculated total luminous output as a function of single LED power Pdare shown inFIG. 9. It is noted that the calculated values are generally consistent with measurements, except at very low power where the light output is low and the relative measurement error is large. The Pd* is 2.4 W at an efficacy of 21 lumens/Watt in this case. The use of a larger heatsink with a smaller thermal resistance means that the NRhsterm in the denominator of (10) is smaller than that in the previous case (with Rhs=6.3° C./W). Therefore, Pd* has increased from 1.9 W to 2.4 W as expected from (10) and the efficacy from 21 lumens/Watt to 23 lumens/Watt.

The corresponding measured and calculated efficacy are shown inFIG. 10and it can be seen that they are in good agreement.

(iii) On a Heatsink with Thermal Resistance of 2.2° C./W

Another eight 3 W LEDs are mounted on an even larger heatsink with thermal resistance of 2.2° C./W for evaluation. The measured and calculated luminous output as a function of LED power Pdare shown inFIG. 11and the corresponding results of the efficacy are included inFIG. 12.

The theoretical Pd* is now about 3.5 W, which is higher than the rated power of 3 W. This again confirms the prediction by the theory (10) that Pd* will shift to the higher power level with a decreasing term of NRhs(i.e., a larger heatsink with a lower Rhs). Therefore, the theory can be used to design the optimal heatsink for a particular operating power. On the other hand, it can also be used to predict the optimal operating power for a given heatsink.

B Tests on 5 W LEDs

In order to ensure that the theory can be applied to other LEDs, 5 W LEDs are used for evaluation. They are mounted on two heatsinks with thermal resistance of 6.8° C./W and 10° C./W respectively.

(i) On a Heatsink with Thermal Resistance of 10° C./W

Two 5 W LEDs are mounted on a heatsink with thermal resistance of 10° C./W. For the theoretical calculation, the parameters used in (10) are ke=−0.00355, kh=0.85, Ta=28° C., T0=25° C., E0=38 Lum/W, N=2, Rhs=10° C./W, Rjc=13° C./W and kjc=0.13° C./W2. Fitting these parameters into (7) and assuming that Rjcwill rise linearly with temperature, the luminous flux equation and the efficacy equation are expressed as (18) and (19), respectively, and they are plotted with practical measurements inFIG. 13andFIG. 14, respectively. Despite only two 5 W LEDs being used, the theoretical predictions based on the averaged values are in general agreement with the measurements.
φv=75.2Pd−7.572d−0.296Pd(18)
E=37.6−3.78Pd−0.149Pd2(19)
(ii) On a Heatsink with Thermal Resistance of 6.8° C./W

The previous experiments are repeated by mounting the two 5 W LEDs on a larger heatsink with a thermal resistance of 6.8° C./W.FIG. 15andFIG. 16show the comparisons of the measured and calculated luminous flux and efficacy, respectively. In general, calculated and measured results are in good agreement. Comparisons of the peak luminous flux inFIG. 13andFIG. 14confirm once again that using a larger heatsink (with lower thermal resistance) can shift the optimal operating point to a higher lamp power level. For the heatsink with Rhs=10° C./W, the optimal point occurs at about 3.8 W. For the heatsink with Rhs=6.8° C./W, this optimal point has shifted to about 6 W.

An important conclusion can be drawn from these results. The peak luminous flux (i.e., maximum φv) occurs at a LED power Pd* that depends on the thermal design (i.e., the heatsink thermal resistance). In general, the larger the heatsink (the lower the heatsink thermal resistance or the better the cooling effects), the higher the peak luminous flux can be achieved. Since operating the LEDs at a power higher than their rated power will shorten the lifetime of LEDs drastically, the theory can be used to project the maximum luminous flux for a given thermal design. It can also be used to predict the optimal thermal design for maximum luminous flux output if the LEDs are designed to operate at rated power.

Pd* can be controlled by using different heatsinks with different thermal resistance. For a larger heatsink, Rhsbecomes small and therefore Pd* will be shifted to the higher power level as shown inFIG. 17, where the values of Pd* are labeled as A, B, C and D as the size of heatsink (or cooling effect) increases. By assuming Rhs=0, a theoretical limit can be plotted as shown inFIG. 17. It is important to note that the operating LED power must not exceed the rated LED power (Prated) otherwise the lifetime of the LED will be shortened. Therefore, the intersection points of these curves with the rated power limit indicate how the light output can be maximized.

It should be noted that a reduction of Rhscorresponds to an increase in the cooling effect. One way to achieve increased cooling is to increase the size of the heatsink. InFIG. 17, it can be seen that two curves with maximum points marked by C and D have relatively high luminous flux at the rated power. The curve with maximum point D has a smaller Rhsand thus a larger heatsink than that with maximum point C. The increase of luminous flux at the rated power from using curve C to curve D is small, but the increase in the size of the heatsink is much larger in proportion.

Three important points are highlighted here:1. The maximum φvis the point of inflexion of the luminous flux function (7b) or (7c). As Pdincreases from zero, the positive slope of the curve

(i.e.,ⅆϕvⅆPd)
is gradually decreasing to zero when the peak of the curve is reached. A large positive slope means that a relatively small increase of Pdcan result in a relatively large increase of φv. So the initial linear portion of the curve results in good efficacy. As Pdis moved to the region at and around Pd*, the slope is zero or relatively small. Therefore, a relatively large increase in Pdwill give a relatively small increase in φv.2. The LED power Pdmust not exceed the rated LED power Pd(rated). Otherwise, the lifetime of the LED will be shortened. Therefore, the intersection points of these curves with the rated power limit should indicate how the light output can be maximized. The intersection points of these curves and the rated power line are denoted as “a”, “b”, “c” and “d” as shown inFIG. 17.3. The values of φvat “c” and “d” are higher than that at “b”. But the curve with peak φvat D requires a much larger heatsink than that with peak φvat C. The difference of φvat “c” and “d” may not be significant enough to justify an increase in cost and size of the heatsink.

The following rules are proposed as an optimization.

The function of the luminous flux φvversus LED power Pdis a parabolic curve with a maximum point. The operating point Pdshould be chosen at or below the maximum point Pd*. This means that for a given luminous flux output, the lower LED power should be chosen. Within this recommended power range, either (7) or (14) can provide sufficiently accurate predictions.

If the thermal design is restricted by limited space for the heatsink so that the Pd* occurs at a power less than or equal to the rated power P(rated), then the LED system should be operated at Pd* for each LED device. [For example, points A and B are optimal operating points for the respective curves as their Pd* values do not exceed P(rated).]

If the thermal design is flexible, then the LED system should be designed in such a way that (i) the theoretical maximum φvpoint (or Pd*) occurs at a power higher than P(rated)of the LED and (ii) the intersection point of the theoretical φv−Pdcurve and the rated power line should have a value of about 80% to 96% of the theoretical maximum φvvalue. The rated power should be chosen as the operating power for each LED.

Rule 3 is an important idea. Where the theoretical maximum (Pd* for maximum φv) occurs at a point higher than the rated power, one should still operate the LED system at the rated power. As can be seen fromFIGS. 17 and 18the slope of the curve shows that as Pd* is approached the increase in luminous flux becomes very small and in terms of efficiency the gain in flux is not worth the additional power used. By using Δφv|pu=0.04˜0.20 of the maximum φvpoint in the curve the 4%-20% range for Δφvfrom the maximum φvpoint offers a good compromise of the light output and the size and thus cost of the heatsink.

If forced cooling is applied, the φv−Pdcurve will change dynamically. This can be visualized as having a dynamically changing thermal resistance Rhs. The optimal operating point should follow the three rules explained previously. It should be kept along the operating lines as highlighted in the bold solid lines inFIG. 19in order to maximize the luminous flux output.

FIG. 20shows schematically an apparatus that may be used in embodiments of the invention. The apparatus comprises a microprocessor control unit (MCU)20that performs functions to be described below, database21, user input means22which may be a keyboard, touchscreen or any other means that enables a user to display data, and output display means23which may be a screen, print out or any other means for data output to be communicated to a user. Database21includes details obtained from datasheets of the physical and electrical parameters of all known commercially available LEDs. This database may be provided directly as part of the apparatus or may a database kept elsewhere and accessed remotely. A user will input selected parameters of a desired LED lighting system using input means22. These parameters will include at least the desired luminous flux output required from the system, and may further include any other parameters that the user wishes to fix, including for example the number N of LEDs and the size of the heatsink if that is fixed.

MCU20is programmed to carry out the steps shown in the flowcharts ofFIGS. 21 and 22. Beginning withFIG. 21, a user may input a required flux output φv. The MCU may then select a candidate LED from the database and calculated the maximum flux that the LED is capable of achieving from Eq. 7 above. If this maximum flux is obtained at a power below the rated power, and if this maximum flux is equal to or greater than the required flux, then such an LED is capable of being used in an LED system meeting the desired flux output and the process can stop. If the answer to either question is negative, i.e., if the maximum flux would only be obtained at a power greater than the rated power, or if the maximum flux is insufficient, then another LED is chosen and the process repeats.

If no LED can be found by the process ofFIG. 21, either after a number of attempts or after all LEDs in the database have been exhausted, the MCU runs the process ofFIG. 22(or alternatively a user may go directly to the process ofFIG. 22if preferred). This process corresponds to the situation where the peak of the flux output occurs at a power above the rated power. In such cases, as discussed above, it is preferable to select an LED with a peak flux output such that the maximum rated power is between 80% and 96% of the power at which the maximum flux is obtained. As can be seen from lines C and D inFIG. 17the output of these lines where they cross the rated power is higher than the equivalent flux of an LED that has its peak flux output exactly when operated at the rated power (the condition of line B). InFIG. 21a peak output is calculated by the MCU at a power higher than a rated power and then various LEDs are chosen from the database until one is found where the flux output φvat the rated power is equal to or greater than the required power φreq.