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不同驱动电流下的LED光谱模型

A model for LED spectra at dif ferent drive currents

A mathematical model for the spectra of monocolor light-emitting diodes (LEDs) and phosphor-coated white LEDs at different drive currents is established. The simulation program of the color rendering of a white light LED cluster is developed based on this model. The program can predict not only the spectral power distribution and color rendering index (CRI), but also the number of LEDs, drive currents, input power, and luminous efficacy of a white light LED cluster at a given color temperature according to the requirement of the luminous flux. The experimental results show that the relative spectral power distributions (SPDs) and chromaticity coordinates of the model LED are very close to that of the real LED at different drive currents. Moreover, the correlated color temperature (CCT), CRI, special color rendering index (R9) luminous flux, input power, and luminous efficacy of the white light LED cluster predicted by simulation are also very close to the measured values. Furthermore, a white/red cluster with high rendering (CCT = 2903 K, CRI = 91.3, R9 = 85) and a color temperature tunable warm-white/red/green/blule LED cluster with high rendering (CCT = 2700?6500 K, CRI > 90, R9 > 96) are created.

    OCIS codes: 230.3670, 330.1715.

    doi: 10.3788/COL20100811.1090.

    One of the most important characteristics of light sources for general lighting is color rendering. Color rendering is a property of a light source, which shows how natural the colors of objects look under the given illumination. If color rendering is poor, the light source will not be useful for general lighting. This is an important aspect to be considered in developing white light-emitting diodes (LEDs) for general lighting. To create white light from LEDs, two distinct approaches have been adopted: the use of individual primary-color LEDs (e.g., red, green, and blue, also known as RGB), and the combination of wavelength down-converting phosphor with a blue or ultraviolet LED. Color rendering index (CRI) can reach above 90 in any color temperature region from 2700 to 13000 K by matching the ratio of red and green phosphors and silica gel[1]. The light-extraction ef ficiency of LEDs has been improved by double-layer or multi-layer phosphor package structures[2]. The multichip RGB approach allows for high color rendering, chromaticity-point stabilization, and color adjustment[3?5]. However, the strong temperature dependence of performance and high cost are among its main disadvantages. It is possible to maintain precise and stable color temperature control using optical and thermal feedbacks[5]. Meanwhile, phosphor-coated white LEDs have the advantages of being relatively low cost and having great color stability over a wide range of temperatures[6]. These can also be tuned to achieve higher CRIs and luminous ef ficacies of radiation through dual-blue emitting active regions as opposed to single-blue white sources[7]. In order to analyze the numerous designs of white light LED clusters, mathematical models for relative spectral power distribution (SPD) of LEDs at a given drive current have been developed[3?5]. However, the drive current af fects the peak wavelength, half spectral width of the monocolor LED, the relative SPD of the phosphor-coated white LED, and the color rendering of white light LED clusters. Thus, simulated programs developed by these mod-els cannot predict the drive currents, luminous flux, input power, and luminous ef ficacy of white light LED clusters. In this letter, the mathematical model for the spectra of monocolor LEDs and phosphor-coated white LEDs at dif ferent drive currents is established, and the simulation program of the color rendering of the white light LED cluster is developed based on this model. The simulations and verifications of the two white light LED clusters are also presented.

   Based on the established mathematical model for the spectra of monocolor LED, its relative SPD, SLED(λ, λ0, ?λ), is given by

   SLED(λ, λ0, ?λ) = [g(λ, λ0, ?λ) + k1g(λ, λ0, ?λ) k2 ] /(1 + k1), (1)

    where

    λ0 is the peak wavelength, ?λ1 is the left half spectral width which is 2 ∫ λ0 380 nm SLED(λ)dλ, ?λ2 is the right half spectral width which is 2 ∫ 780 nm λ0 SLED(λ)dλ, ?λ0 is the half spectral width which is [(?λ1 + ?λ2)/2], and ki (i = 1,2) represents the characteristic parameters of the spectral shape. Figure 1 shows an example of this LED model compared with the SPD of a typical blue LED. The average residual sum of squares, Chi2/DoF, for the model and real SPDs of blue LED is 1×10?6 . The dif ference of the chromaticity coordinates ( √ u, v) of the model and those of real blue LED, dC = (?u) 2 + (?v) 2, is 6×10?7 .

Fig. 3. Curve of ?λ0 versus IF for a typical blue LED

    LED drive current af fects the peak wavelength and half spectral width of monocolor LED. The functional relationship of the peak wavelength λ0 and the drive current IF, λ0 (IF), is given by

   λ0(IF) = Aλ0 exp(Bλ0 IF) + Cλ0 , (2)

   where Aλ0 , Bλ0 , and Cλ0 are function parameters of λ0(IF). The curve of λ0 versus IF for a typical blue LED is shown in Fig. 2. Chi2/DoF for the curve of λ0 versus IF of blue LED is 1×10?2 .

   The functional relationship of the half spectral width ?λ0 and the drive current IF, ?λ0(IF), is given by

   ?λ0(IF) = A?λ + B?λIF, (3)

   where A?λ and B?λ are the function parameters of ?λ0(IF). ?λ1 and ?λ2 can also be expressed by Eq. (3). The curve of ?λ0 versus IF for a typical blue LED is shown in Fig. 3. Chi2/DoF for the curve of ?λ0 versus IF of blue LED is 1×10?3 .

    In this letter, the LED drive current af fects the characteristic parameters ki (i=1,2) of the spectral shape  for monocolor LED. The functional relationship between the characteristic parameter ki and the drive current IF, ki(IF), is given by

  ki(IF) = Ai exp(BiIF) + Ci , (4)

   where Ai , Bi , and Ci are the function parameters of ki(IF).

    Four monocolor LEDs (red, yellow, green, and blue) were tested. Their parameters are shown in Table 1. Chi2/DoF for the model and real SPDs of these LEDs at dif ferent drive currents are shown in Table 2. dCs of the model and real LEDs at dif ferent drive currents are shown in Table 3. The results show that the SPDs and chromaticity coordinates of the model LED are very close to those of real LED.

     A mathematical model for the spectra of phosphorcoated white LED was established in this work. The relative SPD of phosphor-coated white LED, SW(λ), is given by

      SW(λ) = SB(λ) + SF(λ), (5)

    where SW (λ), SB(λ), and SF (λ) are the white, blue, and fluorescence spectra of phosphor-coated white LED, respectively. SB(λ) can be expressed by Eq. (1). SF(λ) can be determined by 475 ∑ 380 [SW(λ) ? SB(λ)]2 → min. SW(λ), SB(λ), and SF(λ) of a typical phosphor-coated white LED are shown in Fig. 4. Chi2/DoF for the model and real SPDs of the LED is 3×10?5 and dC of the model and real white LEDs is 1×10?4 .

     The drive current also af fects the relative SPD of phosphor-coated white LED. Equations (2)–(4) can be applied to the blue spectrum of phosphor-coated white LED. The functional relationship of the fluorescence spectrum SF(λ) and the drive current IF, SF(λ,IF), is given by

 

SF(λ, IF) = SF(λ, IFmax) + AF exp(BFIF), (6)

     where AF and BF are the function parameters of SF(λ, IF). Chi2/DoF for the model and real SPDs of phosphorcoated white LEDs at dif ferent drive currents are shown in Table 4. dCs of the model and real phosphor-coated white LEDs at dif ferent drive currents are shown in Table 5. The results show that the SPDs and chromaticity coordinates of model white light LED are very close to those of the real white light LED.

   

 

    To predict the drive current of LED at a given luminous flux, the functional relationship between the drive current IF and luminous flux Φ, IF(Φ), is given by IF(Φ) = kIΦ γ (1 + cIΦ 2 ), (7) where kI , cI , and γ are the function parameters of IF(Φ). The curve of IF versus Φ for a typical white LED is shown in Fig. 5. Chi2/DoF for the curve of IF versus Φ for a typical white LED is 6×10?2 . To predict the input power of LED at a given luminous flux, the functional relationship between the input power Pin and luminous flux Φ, Pin(Φ), is given by Pin(Φ) = kPΦ γ 0 (1 + cPΦ 2 ), (8)

    where kP, cP, and γ 0 are the function parameters of Pin(Φ). The curve of Pin versus Φ for a typical white LED is shown in Fig. 6. Chi2/DoF for the curve of Pin versus Φ for a typical white LED is 2×10?4 .

    To analyze the possible performance of the white light LED cluster, a simulation program was developed according to the principles of additive color mixture and the Commission International del’ Eclairage (CIE) method of measuring and specifying color rendering properties of light sources. The simulation program can predict the SPD of phosphor-coated white LEDs by spectra mixture of blue chip, yellow, green, and red phosphor according to the requirements of the CCT and CRI. Thus,the program can predict not only the SPDs, chromaticity coordinates, and CRIs, but also the number of LEDs (N), drive currents (IF), input power (Pin), and the luminous ef ficacy (η) according to the requirements of the CCT and luminous flux (Φ).

 

    To validate the simulation for phosphor-coated white LED, a real warm-white LED (CCT = 3183 K, u = 0.2429, v = 0.3487, CRI = 80.4, excitation wavelength λ0 = 451.0 nm) was simulated by our program. The simulated and measured SPD and CRIs of phosphor-coated white LED are shown in Figs. 7 and 8, respectively. The simulation results show that the predicted spectra are very close to the real spectra of the warm-white LED, and that the predicted CRIs are almost equal to the measured values.

   To validate simulation for the white light cluster, white/red LED (W/R cluster) and warmwhite/red/green/blue LED (WW/R/G/B cluster) were tested in our laboratory.

   The W/R clusters with white light LEDs (excited wavelength λ0 = 450.0 nm, CCT = 4587 K, Φ = 95.1 lm, Pin = 1.15 W, and η = 82.7 lm/W at IF = 350 mA) and red LEDs (λ0 = 631.9 nm, Φ = 37.6 lm, Pin = 0.75 W, and η = 50.1 lm/W at IF = 350 mA) were simulated according to CCT = 2900 K and Φ = 450 lm. The predicted numbers of white light and red LEDs were four and three, respectively, while the predicted drive currents of white light and red LEDs were 350 and 220 mA, respectively.The predicted and measured SPDs and CRIs of the W/R cluster are shown in Figs. 9 and 10, respectively. The CCT, CRI, Φ, Pin, and η of the W/R cluster are shown in Table 6.

   The WW/R/G/B clusters (Pin = 8 W) with the WW LEDs (excited wavelength λ0 = 454.0 nm, CCT = 3162 K, Φ = 79.2 lm, Pin = 1.21 W, and η = 65.5 lm/W at IF = 350 mA), the red LEDs (λ0 = 633.6 nm, Φ = 32.7 lm, Pin = 0.75 W, and η = 43.6 lm/W at IF =350 mA), the green LEDs (λ0 = 522.9 nm, Φ = 45.2 lm, Pin = 1.08 W, and η = 41.9 lm/W at IF = 350 mA), and the blue LEDs (λ0 = 454.3 nm, Φ = 12.8 lm, Pin = 1.21 W, and η = 10.6 lm/W at IF = 350 mA) were simulated. The predicted and measured results are shown in Table 7.

    The experimental results show that the correlated color temperature, CRIs, luminous flux, input power, and luminous ef ficacy of white light LED cluster predicted using simulation are very close to the measured values. Furthermore, CRI and R9 of the W/R and WW/R/G/B clusters are over 90. This result is the first to be created successfully in a laboratory as far as we know.

     In conclusion, a mathematical model for spectra of monocolor and phosphor-coated white LEDs at dif ferent drive currents is established. The simulation program of the color rendering of the white light LED cluster is developed based on this model. The program can predict both the SPDs and CRIs, as well as the numbers of LEDs, drive currents, input power, and luminous ef ficacy of a white light LED cluster at a given color temperature according to the requirement of luminous flux. As far as we know, our laboratory is the first to create successfully the W/R cluster with high rendering (CCT = 2903 K, CRI = 91.3, R9 = 85) and a color temperature tunable WW/R/G/B cluster with high rendering (CCT = 2700–6500 K, CRI > 90, R9 > 96).

      This work was supported by the Shanghai Science and Technology Committee under Grant No. 09DZ1141100.


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