本論文分別提出單迴路控制與雙迴路控制升壓型驅動電路之發光二極體陣列最佳化組合設計，並驗證及推導各系統轉移函數。由於發光二極體驅動電路為達到較寬之調光範圍，在不同負載條件下，分別操作於連續電流模式與非連續電流模式。因此，本論文所分析升壓型驅動電路之發光二極體陣列最佳化組合設計亦會分為連續電流與非連續電流兩種模式。
為了簡單且準確地描述發光二極體陣列之電壓對電流曲線，本論文係利用發光二極體之Datasheet所提供之電壓對電流曲線以三點法直接建構其等效模型。同時，利用此一模型推導發光二極體之等效直流與小訊號模型，並以實測驗證其準確性。
基於電路效率之考量，在連續電流模式之單迴路控制壓型驅動電路中，是以最大效率功率傳輸做為發光二極體陣列最佳化設計之依據；在非連續模式之峰值電流控制壓型驅動電路中，是以電路之功率損耗做為發光二極體陣列最佳化設計之依據。
為了消除在責任周期大於50%時所產生之次諧波振盪電流問題，其連續電流模式雙迴路控制升壓型驅動電路須外加斜率補償，但其斜率補償之大小對於系統之暫態特性有很嚴重的影響。因此，基於改善暫態響應之問題，其最佳化發光二極體陣列可被求得。
最後，實做一個具15×8發光二極體陣列之連續電流模式雙迴路控制升壓型驅動雛型電路，以驗證本論文所提之理論。

This thesis presents the design of optimal LED array combination for boost drivers with single-loop and dual-loop control, respectively. The system transfer functions are derived from the corresponding equivalent circuit model to predict the system performance with different LED arrays, including control-to output current gain, and effect of harmonic oscillation. Due to the demand of wide dimming range, the boost LED driver operates in continuous current mode (CCM) and discontinuous current mode (DCM), which means that the design of optimal LED array combination for boost drivers are also divided into two operating modes: CCM and DCM, respectively.
In order to simply and precisely curve-fit the V-I characteristic curve of the N×M LED array, the model of N×M LED array is constructed based on the 3-point approach from the V-I curve in the LED datasheet. According to the proposed LED model, the equivalent DC and small-signal models can be derived and verified with the measured results.
Based on the circuit efficiency, the optimal LED array combination can be obtained with the concept of the maximum-efficiency power transferring in CCM single-loop boost LED driver. In DCM peak current mode controlled boost LED driver, the optimal LED array combination is obtained based on the power consumptions of the circuit.
In order to alleviate the sub-harmonic oscillation as the duty-cycle greater than 50%, the CCM dual-loop boost driver has to add the slope compensation. However, different values of the slope compensation affect the transient response of the system. Thus, the optimal design of the LED array combination is based on improving the transient response.
Finally, the prototype circuit of dual-loop CCM boost driver with 15×8 LED array is built to validate the optimal combination of the LED array.

[1] R. N. Hall, G. E. Fenner, J. D. Kingsley, T. J. Soltys and R. O. Carlson, “Coherent light emission from GaAs junctions,” Phys. Rev. Lett., vol. 9, no. 9, pp. 366-368, Nov. 1962.
[2] Peter Baureis, “Compact modeling of electrical, thermal and optical LED behavior,” Proceedings of ESSDERC, pp. 145-148, Sept. 2005.
[3] Mark Jordan, “Single Inductor, Tiny buck-boost converter provides 95% efficiency in Lithium-lon to 3.3V applications,” , Design Notes, 2002.
[4] N. Narendran and Y. Gu, “Life of LED-based white light sources,” IEEE Journal of Display Technology, vol. 1, pp. 167-171, Sept. 2005.
[5] N. Narendran, J. D. Bullough, N. Maliyagoda and A. Bierman, “What is useful life for white light LEDs”, JIES., vol. 30, no. 1, pp. 57-67, 2001.
[6] H. J. Chiu and S. J. Cheng, “LED backlight driving system for large-scale LCD panels,” IEEE Trans. Ind. Electron., vol. 54, no. 5, pp. 2751-2760, Aug. 2007.
[7] Hino and K. Iwamoto, “LED pulse response analysis considering the distributed CR constant in the peripheral junction,” IEEE Trans. Electron. Dev., vol. 26, no. 8, pp. 1238-1242, Aug. 1979.
[8] E. Fred Schubert, Light-Emitting Diodes. Cambridge University Press, Inc., 2003.
[9] Ray-Lee Lin, “Piezoelectric Transformer Characterization and Application of Electric Ballast,” Ph.D. dissertation, Univ. of Virginia Polytechnic Institute and State, Virginia, Nov. 2001.
[10] Steve Winder, Power Supplies for LED Driving. Butterworth-Heinemann Press, Inc., 2008.
[11] Jian Fang, Zhiping Lu, Zehong Li and Zhaoji Li, “A new flyback converter with primary side detection and peak current mode control,” IEEE Communications, Circuits and Systems, vol. 2, pp. 1707-1710, Jun. 2002.
[12] A. Fontan, S. Ollero, E. de la Cruz and J. Sebastian, “Peak current mode control applied to the forward converter with active clamp,” PESC., vol. 1, pp. 45-51, May. 1998.
[13] Guisong Huang, Alpha J. Zhang and Yilei Gu, “LLC series resonant DC-to-DC converter.” U.S. Patent 6344979, 2001.
[14] Ned Mohan, Tore M. Undeland and William P. Robbins, Power Electronics: Converters, Applications, and Design. John Wiley & Sons, Inc., 2003.
[15] Muhammad H. Rashid, Power Electronics: Circuits, Devices, and Applications. Pearson Education, Inc., 2004.
[16] “Modeling, analysis, and compensation of the current-mode converter,” Texas Instruments Inc., Application Note U-97, 1999.
[17] Hsieh, Chun-Yu Chen and Ke-Horng, “Boost DC-DC converter with charge-recycling (CR) and fast reference tracking (FRT) techniques for high-efficiency and low-cost LED driver,” IEEE Solid-State Circuits Conf., pp. 358-361, Sept. 2008.
[18] Xiaoru Xu and Xiaobo Wu, “High dimming ratio LED driver with fast transient boost converter,” IEEE PESC., pp. 4192-4195, Jun. 2008.
[19] Ray-Lee Lin and Yi-Fan Chen, “Equivalent circuit model of light-emitting-diode for system analysis of lighting drivers,” IEEE Conference on IAS Annual Meeting, pp. 1-5, Oct. 2009.
[20] Datasheets, “LNL-190UW-4H: SMD LED,” LIGHTOP Technology Co., 2007.
[21] Ray-Lee Lin, Chia-Chun Lee, and Shun-Yao Liu, “Taylor Series Expression Based Equivalent Circuit Models of LEDs for Analysis of LED Driver System,” IEEE Conference on IAS Annual Meeting, pp. 1-7, Oct. 2011.
[22] Heinz van der Broeck, Georg Saüerlander and Matthias Wendt, “Power driver topologies and control schemes for LEDs,” IEEE APEC., pp. 1319-1325, Mar. 2007.
[23] V. Vorperian, “Simplified analysis of PWM converters using model of PWM switch part I: continuous conduction mode,” IEEE Trans. Power Electron., vol. 26, no. 3, pp. 490-496, May. 1990.
[24] Ray-Lee Lin, Chia-Chun Lee, and Yi-Chun Chang, “Optimal Design of LED Array for Single-loop CCM Buck-Boost LED Driver,” IEEE Conference on IAS Annual Meeting, pp. 9-13, Oct. 2011.
[25] K.S. Kostov and J.J. Kyyra, “Genetic algorithm optimization of peak current mode controlled buck converter,” IEEE Mid-Summer Workshop on Soft Computing in Industrial Applications, pp. 111-116, Jun. 2005.
[26] Raymond B. Ridley, “A New Small-signal Model for Current-mode Control,” Ph.D. dissertation, Univ. of Virginia Polytechnic Institute and State, Virginia, Nov. 1990.
[27] Maniktala Sanjaya, Switching Power Supplies A to Z. Maryland Heights: Newnes, 2006.
[28] Datasheets, “UCC38C43: BiCMOS low-power current-mode PWM controller,” Texas Instruments Incorporated, 2001.
[29] V. Vorperian, “Simplified analysis of PWM converters using model of PWM switch part II: discontinuous conduction mode,” IEEE Trans. on Power Electron., vol. 26, no. 3, pp. 497-505, May. 1990.