基于纹波特性的白光LED器件动态及稳态光通量模型
There are increasing concerns about flicker as light-emitting diode (LED) source products enter the market, which is linked to the driver. In a passive circuit, the light output exhibits a sinusoidal function of rippled current's sinusoidal waveform. Color shifts and variations in luminous flux during dimming are generally unacceptable in general lighting. There are complex interconnections among white LED lighting system parameters, dynamic optical properties, ripple currents, LED light source device parameters, and LED driver parameters. However, the above issue lacks the necessary theory for clarifying the superiority. Therefore, an investigation of the illuminance and flicker variation of white LEDs driven by sinusoidal waveforms is presented in this paper. It incorporates factors such as illuminance, flicker index, percent flicker, voltage amplitude, frequency, amplification factor, and heatsink temperature into a relatively realistic model over dimming. This paper aims to present a method for designing LED systems with sinusoidal driving schemes that minimize flicker indexes and percent flicker variations systematically. In order to meet the flicker requirements set forth in IEEE Standard, the proposed model assists power supply engineers in controlling LED source and driver parameters.
Based on the interaction of photometric, electrical, and thermal factors of semiconductors, the maximum luminous flux, flicker index, and percent flicker of LED sources are modeled. Many parameters can affect luminous flux, flicker index, and percent flicker, including the heatsink temperature, the thermal resistance of the LED source, the heat dissipation coefficient, luminous efficacy, and driver parameters. A white LED lighting system has been used to demonstrate the proposed flicker modeling process. Light flicker analyzer (LFA-3000) shows the waveform of an LED system's light output with a sinusoidal wave of specified parameters. White LED system with different heatsink temperatures is electrically driven. A wideband amplifier (Texas Instruments ATA-122D) in the direct current (DC) component from the DC power supply adds the signal function (Gigol DG-500). The light output of the LED is captured from the detector (LFA-3000) using the high-speed signal amplifying function. The luminance of LED samples is measured after thermal stability with constant heatsink temperature from 25 ℃ to 85 ℃. The voltage amplitude ranges from 3 V to 5 V. The amplification factors vary from 2 dB to 6 dB. The frequency ranges from 100 Hz to 2000 Hz. LED source and photodetector are connected by the dark tube. There is a spacing of 20 cm between the source and the photodetector. Therefore, the ambient light does not influence the measurement results.
According to Eq. (8), heatsink temperature, and maximum electrical power, it is possible to predict the dynamic illumination of the LED source. A plot of the predicted and measured illumination variation is shown in Fig. 5. The results appear to be fairly in agreement. When the heatsink temperature is 30 ℃, the variation illumination of the LED source ranges from 2688 lx to 4512 lx, and the variation range is about 59.8%. Increasing the electrical power to 2.1 W results in a variation illumination range of 11252-21033 lx, with a variation range of around 53.2%. At a heatsink temperature of 85 ℃, the variation illumination is 2532-4399 lx at a maximum electrical power of 0.35 W, while the variation range is about 57.5%. As electrical power and heatsink temperature increase, there is a decrease in the variation range. This can be attributed to several reasons. First, with an increase in current density injected into the quantum well and junction temperature, the reduction of band gap and electron mobility will decrease. It means that the radiative recombination of electrons and holes in the potential well will decrease with increasing non-radiative recombination. The reduction of the internal quantum efficiency is caused by an increase in the number of electrons overflowing the potential well. As shown in Figs. 8 and 9, the average and maximum deviations between the calculations and measurements are about 7.1% and 12.8%, respectively. The illumination of white LED devices increases with increasing voltage amplitudes and amplification factors. It decreases with increasing frequency. When the voltage amplitude varies from 3 V to 3.5 V (amplification factors of 1 dB, heat sink temperature of 25 ℃, and frequency of 100 Hz), the illuminance increases from 3966 lx to 5889 lx, with a variation range of 32.6%. When the frequency changes from 100 Hz to 2000 Hz (amplification factors of 1 dB, heat sink temperature of 25 ℃, and voltage amplitude of 3 V), the illuminance decreases from 3966 lx to 2059 lx, with a variation range of 48.1%. When the heat sink temperature ranges from 25 ℃ to 65 ℃ (frequency of 100 Hz, amplification factors of 2 dB, and voltage amplitude of 4.5 V), the illuminance decreases from 13206 lx to 12904 lx, with a variation range of 2.3%. According to the proposed model, the deviations between theoretical and experimental results may be caused by the following factors: 1) the proposed model does not include the droop effect of multiple quantum wells and the nonlinear relationship between amplification factors of current ripple and carrier concentration; 2) the proposed model does not contain the relationship between Fermi energy level and voltage amplitude and cannot accurately predict threshold of carrier overflow potential well; 3) the proposed model does not contain the three-dimensional heat flow conduction and fails to accurately establish junction temperature of the device under different operating conditions. The ripple frequency of the LED device is 100-2000 Hz. Therefore, the allowable percent flicker is 0.3-66 according to IEEE standard 1789—2015 (Fig. 6). With a frequency of 100 Hz and maximum electrical power of 0.35 W, percent flicker is 0.276 and 0.289 under heatsink temperatures of 30 ℃ and 85 ℃, respectively. It is noted that the values of percent flicker are lower than the requirements of IEEE standard. When the maximum electrical power is increased to 2.1 W, the percent flicker increases to 0.341 and 0.356 under heatsink temperatures of 30 ℃ and 85 ℃, respectively. It should be pointed out that the values of percent flicker are higher than the requirements of IEEE standard.
A real-time LED measurement method is demonstrated in this paper, so as to analyze and develop dynamic light outputs in real time. The dynamic illuminance, percent flicker, and flicker index of LED sources can be calculated independently as a function of heatsink temperature, frequency, voltage amplitude, amplification factors, and electrical power. By using the proposed model, it is possible to convert the dynamic light output from LED sources into flicker indexes and percent flickers under different conditions. There is good agreement between measured and calculated optical and flicker results, even when measured at different heatsink temperatures and driver parameters. According to dynamic optical and flicker performance, the tool allows designers to optimize LED system designs. Therefore, researchers and engineers can determine dynamic illuminance and flicker index using the LED and driver datasheets instead of optical instruments.
1 引言
发光二极管(LED)因其高光效、无污染等优势逐渐取代白炽灯、荧光灯管,成为新一代绿色照明光源。LED光源作为半导体器件,对工作温度、电压及电流十分敏感,即微弱的电压、温度变化都会使其工作电流发生明显偏差。此外,传统的LED驱动都采用直流(DC)电源驱动,当其使用普通的市电供应时,必须配备整流变压器将交流转变为直流(AC/DC变换),这个过程会造成10%~20%的电能损耗,而附加整流设备也会增加LED灯具电路设计及散热设计的复杂度,进一步增加LED灯具的制作成本。由于纹波电流是产生频闪的决定性因素,为了稳定光通量输出,必须降低纹波电流的调制深度。根据电气与电子工程师协会(IEEE)发布的标准[1],频闪带来的风险与调制深度和闪烁频率有关,频率越高,允许的调制深度越大。该标准针对频闪带来的潜在健康问题给出了相应建议,并将频闪风险分为几个等级,目前市场上各类灯具都具有不同程度的频闪效应。因此,分析纹波电流对LED光学性能的影响,可以在保证LED高光效的条件下简化电路,提高开关电源功率因数[2]。
白光LED照明系统存在的纹波电流动态调制过程,将使LED器件的量子阱内产生交替的电场和温度效应,进而影响LED器件的光谱、波长以及内量子效率。在由二基色或三基色LED组成的白光照明系统中,波长的偏移,特别是氮化镓(GaN)基LED芯片峰值波长的变化将引起色度坐标移动,进而引起白光的颜色发生变化。GaN基材料具有非常强的压电极化效应,而极化效应对异质界面能带产生极强的调制和能带弯曲[3],产生量子限制斯塔克效应和局域态效应[4],随着渐变层中In含量的增大,载流子浓度以及极化电荷密度都增大,但极化电荷密度增幅较小,峰值功率谱密度的增长幅度随着In含量的增大逐渐减小,而功率谱密度随着渐变层顶层厚度的增加先增大后减小[5]。
由于LED系统的负载电流、散热器尺寸、器件结温之间存在内在联系,Pandey等首次报道了N极性InGaN/GaN纳米线亚微米LED在红色光谱中的发光现象[6],其突破了传统红色发光微型LED的效率限制,同时,通过采用InGaN有源区的原位退火工艺,将光发射强度提高超过一个数量级。Jiang等[7]采用钙钛矿发射层的界面和体控纳米晶体生长的方法,使得钙钛矿LED具有64756 cd/m2的高亮度,并实现了13.4%的外部量子效率。Shi等[8]提出并制备了基于InGaN/GaN多量子阱的垂直结构micro-LED光电探测器,首次利用基于GaN的micro-PD实现了超过10 Gbit/s的可见光通信。Pandey等[9]将InGaN/GaN 短周期超晶格结合到红色发射N极性纳米线异质结构中,实现无位错N极性InGaN/GaN纳米线的强红色发射特性(>620 nm)。基于能量传输引起的发光器件光学特性动态变化,Huang等[10]建立了LED灯具的电热光动力学系统模型。饶丰等[11]采用正向电压法测量双荧光粉转换型白色LED的结温,分析质心波长、半峰全宽、驱动电流和结温四者之间的变化规律,根据芯片的光谱特征参数,结合规律图计算得到实际结温。李奕等[12]利用实验获得的线性衰减率对相关性评价模型进行修正,解决了相关性评价模型因受到LED自身参数随环境温度变化的制约而无法对LED的平均发光强度及其发射波长进行有效定量评价的问题。Chen等[13-15]基于LED集成照明系统的非线性光学特性,通过分析器件在稳态及瞬态条件下的电功率、结温、光功率、光谱峰值波长、光谱半峰全宽、能量转换效率,建立白光LED动态光谱模型,利用该模型可准确预测白光LED器件在调光过程中的色温动态变化规律;在光电转换过程中研究白光LED光谱的非线性特性,同时建立符合无源驱动系统的动态光学模型,阐明探测响应谱与白光LED光谱之间响应区域的非线性变化规律。白光LED照明系统的动态光学特性、纹波电流、LED光源器件参数、驱动控制参数之间存在复杂的相互交叉问题,目前鲜有理论研究揭示上述变化规律。
本文提出一种基于纹波特性的白光LED器件动态和稳态光通量模型,在明确LED光源输出动态光通量、负载电功率、发光效率、热功率系数之间关系的基础上,动态改变LED光源输出光通量,并根据LED器件参数(频率、增益系数、电压幅值)以及驱动特性,评估白光LED照明系统的最佳工作点范围,进而分析照明系统闪烁指数、闪烁百分比、电压幅值、频率和LED光源参数之间的内在联系。所提模型可准确预估照明系统在不同纹波特性下白光LED器件的照度、闪烁指数、闪烁百分比。
2 正弦驱动白光LED器件动态和稳态光通量模型
2.1 LED光源输出最大光通量的工作点范围
式中:
光通量
当
设
将
如果
因此,该工作点下照明系统输出的最大光通量
从上述分析可知,照明系统的最大光通量
2.2 由正弦波形驱动的白光LED器件动态光通量模型
式中:
在
在正弦波形驱动下,最大光通量
一个周期内白光LED系统输出平均光通量
LED光源输出平均光通量
最小光通量
式中:
图 1. 正弦波形驱动LED光源的动态电功率和光输出。(a)动态电功率;(b)光输出
Fig. 1. Dynamic power and light output of LED light source driven by sinusoidal waveform. (a) Dynamic power; (b) light output
LED光源输出最小光通量
2.3 由正弦波形驱动的白光LED器件动态闪烁指数和闪烁百分比
通过分析正弦波形驱动LED光源的动态电功率和光输出特性,如
式中:
LED光源的闪烁百分比
因此,
将式(
将式(
由上述分析可知,闪烁指数和闪烁百分比与LED光源的器件参数(散热器温度
闪烁指数和闪烁百分比是由动态光通量变化规律决定的,与LED光源输出的最大光通量
2.4 白光LED器件稳态光通量与正弦波驱动参数的关系
在由正弦波形驱动的白光LED器件动态光通量模型中,白光LED器件在正弦波形驱动下,假设正弦波形驱动的电压幅度为唯一变量,其他参数为固定值,则白光LED器件输出的光通量与电压幅值之间关系为
式中:
开关电源中滤波电容、谐波注入方式、限流阻抗等因素导致LED器件两端的电压出现不同程度的波动,故本实验利用功率放大器来分析白光LED器件输出照度受纹波电流波动的影响,以此完善所提出的基于纹波特性的白光LED器件稳态光通量模型。在正弦波形驱动的白光LED器件动态光通量模型中,由于LED器件输出的电流值与所负载的功率增益系数呈正比例关系,因此白光LED器件输出的光通量与功率增益系数的关系可表示为
式中:
由于LED具有单向导电性,在交流电流驱动下,只有在正向偏压的周期内的LED才会被点亮,而驱动电流频率的变化,可能会造成光源的波动,进而产生光源的频闪效应,影响LED输出光通量的稳定性。此外,在实际的LED驱动电路中,其高频开关纹波分量在驱动电流总纹波中占据主要部分,故需对比不同频率对LED输出光通量的影响。通过分析由正弦波形驱动的白光LED器件动态光通量模型,发现白光LED器件负载频率与输出光通量呈正比例关系,进一步测试白光LED照度与频率之间的变化曲线,分析二者的变化趋势,得到白光LED器件输出的光通量与负载频率的关系为
式中:
当LED处于反向偏压时,PN结内的空间电荷层数增多,载流子的扩散运动减弱,量子阱内的载流子复合概率降低,导致其内量子效率降低,进而使得单个周期内输出的平均光通量减小。
基于正弦波形驱动的白光LED器件动态光通量模型,假设LED器件正弦波形驱动参数保持不变,热沉温度为唯一变量,得到其热沉温度-光通量的表达式为
式中:
一般情况下,LED芯片发射光子数量随着温度的升高而减少,这是因为随着LED结温升高,禁带宽度减小,电子迁移率减小,导致势阱中电子与空穴的辐射复合概率降低,非辐射复合的概率增大[17],使得LED的内量子效率下降。
2.5 由正弦波形驱动的白光LED器件稳态光通量特性
根据纹波特性参数(电压幅度、频率、增益系数)及热沉温度,分析白光LED器件的照度在不同工作条件下的变化规律,构建由4个变量组成的白光LED光通量系统模型,其模型表达式为
式中:
3 实验过程
目前电光源灯具种类可以分为两大类,即热辐射发光光源和气体放电发光光源,而依据灯具光的产生原理,电光源灯可分为白炽灯、卤钨灯、荧光灯、钠灯、汞灯、氖灯等。GaN基白光LED灯具是由GaN基蓝光LED芯片激发YAG∶Ce黄色荧光粉合成的白光照明灯具,其发光机理属于电致发光类型。由于LED器件的响应时间取决于载流子寿命,一般在纳秒数量级,因此白光LED照明系统的发光调制深度和纹波电流调制深度呈比例关系,LED器件的纹波特性将直接影响其动态光通量特性。
图 2. 不同类型白光照明灯具的动态光学特性[1]
Fig. 2. Dynamic optical characteristics of different types of white lighting fixtures[1]
白光LED器件通过暗管连接到光电探测器,因此环境对光电探测器的测量结果没有影响。白光LED器件的测量光学性能取决于光电探测器响应特性和LED光源的光谱功率分布。光电探测器响应强度随可见光波长线性增加,如
图 4. 白光LED器件的光谱功率分布和光电探测器响应特性
Fig. 4. Emission power of white LED device and photodetector responsivity
通过信号发生器控制输出正弦波的参数,使用TC-100温控设备对白光LED器件工作时的热沉温度进行控制;使用数字示波器测试白光LED器件负载的驱动波形;当白光LED样品负载电功率20 min后,器件内部达到热稳定状态,对其进行照度数据测量。
纹波电流会引起器件内部量子效率降低,进而导致其发光效率下降,热功耗上升,使得LED结温上升。在交流电流驱动时,其驱动电源的波形、幅度、频率与LED器件的动态光学特性存在紧密关系,因此需要分析照明系统闪烁指数、闪烁百分比、电压幅值、频率和LED光源参数的内在联系。
4 验证分析
由于白光LED器件的光通量
根据所提出的动态光学模型,即
图 5. LED光源的动态照度变化曲线。(a)(b)散热器温度为30 ℃和85 ℃条件下的测试值;(c)(d)散热器温度为30 ℃和85 ℃条件下的计算值
Fig. 5. Dynamic illumination curves of LED light source. (a) (b) Measured results with heatsink temperature of 30 ℃ and 85 ℃; (c) (d) calculated results with heatsink temperature of 30 ℃ and 85 ℃
图 6. 散热器温度为30 ℃和85 ℃条件下LED光源的闪烁百分比变化曲线。(a)测试值;(b)计算值
Fig. 6. Percent flicker versus maximum electrical power curves of LED light source with heatsink temperature of 30 ℃ and 85 ℃. (a) Measured results; (b) calculated results
图 7. 散热器温度为30 ℃和85 ℃条件下LED光源闪烁指数的变化曲线。(a)测试值;(b)计算值
Fig. 7. Flicker index versus maximum electrical power curves of LED light source with heatsink temperature of 30 ℃ and 85 ℃. (a) Measured results; (b) calculated results
为验证所提出模型的准确性,通过间隔性、随机性的条件取点对模型参数值的准确度进行验证。通过控制白光LED的负载纹波电压幅度、频率、增益系数以及热沉温度,测试不同工作状态下的照度值,根据所提出的光学模型,即
图 8. 在不同电压幅值、频率、功率增益系数下白光LED器件输出照度的变化曲线。(a)(c)测试值;(b)(d)计算值
Fig. 8. Illumination curves of white LED device under different voltage amplitudes, frequencies, and amplification factors. (a) (c) Measured results; (b) (d) calculated results
图 9. 白光LED器件在不同电压幅值、热沉温度、功率增益系数下照度变化曲线。(a)(c)测试值;(b)(d)计算值
Fig. 9. Illumination curves of white LED devices under different voltage amplitude, heatsink temperature, and amplification factor. (a) (c) Measured results; (b) (d) calculated results
5 结论
提出一种基于纹波特性的白光LED器件动态及稳态光通量理论模型,该理论模型可准确预估白光LED照明系统在不同纹波特性下的动态光学特性、闪烁指数、闪烁百分比。在分析白光LED光源输出动态光通量、负载电功率、发光效率、热功率系数之间关系的基础上,将讨论参数拓展到包含LED驱动控制器的参数(频率、增益系数、电压幅值)以及散热器温度,从而通过调节LED器件参数以及驱动特性,控制白光LED照明系统最佳工作点的范围,进而分析照明系统闪烁指数、闪烁百分比、电压幅值、频率和LED光源参数的内在规律。通过测试不同工作条件下LED照明器件的动态照度变化、闪烁指数以及闪烁百分比,并与计算值进行比较,二者的平均误差为7.1%,计算结果和测量结果之间具有良好的一致性,证明了所提出的基于纹波特性动态光电热一体化模型的有效性。该理论模型可为开关电源研发工程师提供无源驱动白光LED照明系统的设计思路。
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Article Outline
刘观洪, 张文杰, 陈焕庭, 林硕, 沈雪华, 林惠川, 陈景东, 张丽敏. 基于纹波特性的白光LED器件动态及稳态光通量模型[J]. 光学学报, 2023, 43(14): 1423001. Guanhong Liu, Wenjie Zhang, Huanting Chen, Shuo Lin, Xuehua Shen, Huichuan Lin, Jingdong Chen, Limin Zhang. Dynamic and Steady Luminous Flux Model for White LED Devices Based on Ripple Properties[J]. Acta Optica Sinica, 2023, 43(14): 1423001.