本論文討論在三相交錯式降壓轉換器中使用的耦合電感的優化。為實現高效率和高功率密度，轉換器使用氮化鎵開關元件，降低高頻操作下的開關損耗，原本使用三個獨立電感，優化為整合耦合電感來減少磁性元件的數量。並分析在不同的工作週期下，耦合電感等效的電感感值、電感電流與耦合係數之間的關係。使用參數化決定鐵芯尺寸大小，在有限的電路板層數與電路面積大小下，選擇最佳的銅線損耗與鐵芯損耗的平衡點。並使用ANSYS的磁性模擬軟體Maxwell進行模擬，驗證鐵芯尺寸與外側柱峰值磁通是否符合設計。優化三相耦合電感鐵芯結構，透過增加鐵芯體積降低磁通密度，達到降低電感電流漣波和鐵芯損耗。使用數學計算軟體Mathcad計算出各相電感電流漣波，且使用電路模擬軟體SIMPLIS模擬各相電感電流，驗證計算與模擬的數值與波形是否符合。最終使用優化後的鐵芯結構實現切換頻率操作於500 kHz、輸入電壓為48 V、輸出電壓為40 V、輸出功率為500 W、最高效率為98.69%的降壓轉換器

This thesis discusses the optimization of the coupled inductor used in the three-phase interleaved buck converter. The converter uses wide bandgap devices to reduce switching losses under high-frequency oper-ation to achieve high efficiency and high power density. Initially, three independent inductors were used, which were optimized as integrated coupled inductors to reduce the number of magnetic components. Ana-lyze the relationship between the equivalent inductance value of the coupled inductor, the inductor current, and the coupling coefficient under different duty cycles. Use parameterization to determine the size of the ferrite core. Under the limited number of layers and circuit area, select the best balance point between copper loss and core loss, and use ANSYS's magnetic simulation software Maxwell to simulate and verify the core size and the peak magnetic flux of the outer leg conform to the design. Op-timize the structure of the three-phase coupled inductor ferrite core, re-duce the magnetic flux density by increasing the volume of the ferrite core, to reduce the inductor current ripple and the core loss. The mathe-matical calculation software Mathcad is used to calculate the inductor current ripple of each phase. The circuit simulation software SIMPLIS is used to simulate the inductor current of each phase to verify whether the calculated and simulated values and waveforms are consistent. Finally, the optimized core structure is used to implement a buck converter was achieved with a switching frequency operating at 500 kHz, an input voltage of 48 V, an output voltage of 40 V, an output power of 500 W, and a maximum efficiency of 98.69%.

[1] E. Ceuca, G. Brezeanu and V. Trifa, “Study for developing the energy recovering circuit for modern e-bike controller,” 2015 International Semiconductor Conference (CAS), 2015, pp. 245-248, doi: 10.1109/SMICND.2015.7355221.
[2] Z. Liu, X. Huang, M. Mu, Y. Yang, F. C. Lee and Q. Li, “Design and evaluation of GaN-based dual-phase interleaved MHz critical mode PFC converter,” 2014 IEEE Energy Conversion Congress and Exposition (ECCE), 2014, pp. 611-616, doi: 10.1109/ECCE.2014.6953451.
[3] X. Huang, Z. Liu, Q. Li and F. C. Lee, “Evaluation and Appli-cation of 600 V GaN HEMT in Cascode Structure,” in IEEE Transactions on Power Electronics, vol. 29, no. 5, pp. 2453-2461, May 2014, doi: 10.1109/TPEL.2013.2276127.
[4] U. K. Mishra, P. Parikh and Yi-Feng Wu, “AlGaN/GaN HEMTs-an overview of device operation and applications,” in Proceedings of the IEEE, vol. 90, no. 6, pp. 1022-1031, June 2002, doi: 10.1109/JPROC.2002.1021567.
[5] J. Millán, P. Godignon, X. Perpiñà, A. Pérez-Tomás and J. Re-bollo, “A Survey of Wide Bandgap Power Semiconductor De-vices,” in IEEE Transactions on Power Electronics, vol. 29, no. 5, pp. 2155-2163, May 2014, doi: 10.1109/TPEL.2013.2268900.
[6] J. Im aoka, M. Yamamoto, Y. Nakamura and T. Kawashima ,“Analysis of Output Capacitor Voltage Ripple in Multi Phase Transforme r Linked Boost Chopper circuit,” IEEJ Journal IA Vol. 2, No. 5, pp. 252 260 2013.
[7] J. Zhu and A. Pratt, “Capacitor Ripple Current in an Interleaved PFC Converter,” in IEEE Transactions on Power Electronics, vol. 24, no. 6, pp. 1506-1514, June 2009, doi: 10.1109/TPEL.2009.2014164.
[8] F. Yang, X. Ruan, Y. Yang and Z. Ye, “Interleaved Critical Cur-rent Mode Boost PFC Converter With Coupled Inductor,” in IEEE Transactions on Power Electronics, vol. 26, no. 9, pp. 2404-2413, Sept. 2011, doi: 10.1109/TPEL.2011.2106165.
[9] C. Wang, M. Xu, B. Lu and F. C. Lee, “New Architecture for MHz Switching Frequency PFC,” APEC 07 - Twenty-Second Annual IEEE Applied Power Electronics Conference and Expo-sition, 2007, pp. 179-185, doi: 10.1109/APEX.2007.357512.
[10] Y. -C. Liu et al., “Quarter-Turn Transformer Design and Optimi-zation for High Power Density 1-MHz LLC Resonant Converter,” in IEEE Transactions on Industrial Electronics, vol. 67, no. 2, pp. 1580-1591, Feb. 2020, doi: 10.1109/TIE.2019.2902821.
[11] Y. -C. Liu, C. Chen, K. -D. Chen, Y. -L. Syu and N. A. Dung, “High-Frequency and High-Efficiency Isolated Two-Stage Bidi-rectional DC–DC Converter for Residential Energy Storage Systems,” in IEEE Journal of Emerging and Selected Topics in Power Electronics, vol. 8, no. 3, pp. 1994-2006, Sept. 2020, doi: 10.1109/JESTPE.2019.2953117.
[12] C. Ting, Y. Syu, C. Chen, Y. Liu and H. Chiu, “Design and Im-plementation of a Novel Three Phase Interleaved Integrated Coupling Inductor,” 2018 IEEE International Power Electronics and Application Conference and Exposition (PEAC), 2018, pp. 1-7, doi: 10.1109/PEAC.2018.8590267.
[13] Liu, Yu-Chen, Chen Chen, Kai-De Chen, Yong-Long Syu, and Meng-Chi Tsai. 2019. “High-Frequency LLC Resonant Con-verter with GaN Devices and Integrated Magnetics” Energies 12, no. 9: 1781. https://doi.org/10.3390/en12091781
[14] Pit-Leong Wong, Peng Xu, P. Yang and F. C. Lee, “Performance improvements of interleaving VRMs with coupling inductors,” in IEEE Transactions on Power Electronics, vol. 16, no. 4, pp. 499-507, July 2001, doi: 10.1109/63.931059.
[15] M. Marinov, V. Valchev, R. Stoyanov and P. Andreev, “An Ap-proach to the Electrical Sizing of The Electric Motorcycle Drive,” 2018 20th International Symposium on Electrical Apparatus and Technologies (SIELA), 2018, pp. 1-4, doi: 10.1109/SIELA.2018.8447065.
[16] Comparing magnetic cores for power inductors. [Online]. Available：https://www.powerelectronictips.com/comparing-magnetic-cores-for-power-inductors-faq/
[17] J. Sibue, G. Meunier, J. Ferrieux, J. Roudet and R. Periot, “Modeling and Computation of Losses in Conductors and Magnetic Cores of a Large Air Gap Transformer Dedicated to Contactless Energy Transfer,” in IEEE Transactions on Magnetics, vol. 49, no. 1, pp. 586-590, Jan. 2013, doi: 10.1109/TMAG.2012.2211031.
[18] J. Schäfer, D. Bortis and J. W. Kolar, “Novel Highly Effi-cient/Compact Automotive PCB Winding Inductors Based on the Compensating Air-Gap Fringing Field Concept,” in IEEE Transactions on Power Electronics, vol. 35, no. 9, pp. 9617-9631, Sept. 2020, doi: 10.1109/TPEL.2020.2969295.
[19] X. Huang, F. C. Lee, Q. Li and W. Du, “High-Frequency High-Efficiency GaN-Based Interleaved CRM Bidirectional Buck/Boost Converter with Inverse Coupled Inductor,” in IEEE Transactions on Power Electronics, vol. 31, no. 6, pp. 4343-4352, June 2016, doi: 10.1109/TPEL.2015.2476482.
[20] Yang Yugang, Yan Dong and F. C. Lee, “A new coupled induc-tors design in 2-phase interleaving VRM,” 2009 IEEE 6th In-ternational Power Electronics and Motion Control Conference, 2009, pp. 344-350, doi: 10.1109/IPEMC.2009.5157410.
[21] Q. Li, Y. Dong, F. C. Lee and D. J. Gilham, “High-Density Low-Profile Coupled Inductor Design for Integrated Point-of-Load Converters,” in IEEE Transactions on Power Electronics, vol. 28, no. 1, pp. 547-554, Jan. 2013, doi: 10.1109/TPEL.2012.2196525.
[22] J. Imaoka, K. Okamoto, M. Shoyama, M. Noah, S. Kimura and M. Yamamoto, “A high-reliable magnetic design method for three-phase coupled inductor used in interleaved multi-phase boost converters,” 2017 IEEE Energy Conversion Congress and Exposition (ECCE), 2017, pp. 873-880, doi: 10.1109/ECCE.2017.8095877.
[23] Y. -C. Liu, C. Chen, Y. -C. Chung, M. -C. Tsai and K. A. Kathe-rine, “Integrated Magnetics Design for an Interleaved Three-Phase Buck Converter,” 2020 IEEE Energy Conversion Congress and Exposition (ECCE), 2020, pp. 4533-4538, doi: 10.1109/ECCE44975.2020.9235677.
[24] N. Lecic, G. Stojanovic, S. Djuric and E. Laboure, “Design and Analysis of Planar Symmetric Six-Phase Coupled Inductors,” in IEEE Transactions on Magnetics, vol. 51, no. 6, pp. 1-8, June 2015, Art no. 8400908, doi: 10.1109/TMAG.2014.2383358.
[25] S. Lu, M. Mu, Y. Jiao, F. C. Lee and Z. Zhao, “Coupled Inductors in Interleaved Multiphase Three-Level DC–DC Converter for High-Power Applications,” in IEEE Transactions on Power Electronics, vol. 31, no. 1, pp. 120-134, Jan. 2016, doi: 10.1109/TPEL.2015.2398572.
[26] 陳震，新型整合型三相交錯式耦合電感設計與研製，國立台灣科技大學電子工程系碩士論文，2016年。
[27] Santhos Ario Wibowo, Zhang Ting, Masashi Kono, Tetsuya Taura, Yasunori Kobori and Haruo Kobayashi, “Analysis of coupled inductors for low-ripple fast-response buck converter,” APCCAS 2008 - 2008 IEEE Asia Pacific Conference on Circuits and Systems, 2008, pp. 1860-1863, doi: 10.1109/APCCAS.2008.4746406.
[28] 3F36 datasheet. [Online]. Available：https://www.ferroxcube.com/upload/media/product/file/MDS/3f36.pdf
[29] 陳震，48 V-12 V高功率密度LLC諧振式轉換器之新型變壓器設計與研製，國立台灣科技大學電子工程系博士論文，2021年
[30] D. Lin, P. Zhou, W. N. Fu, Z. Badics and Z. J. Cendes, “A dy-namic core loss model for soft ferromagnetic and power ferrite materials in transient finite element analysis,” in IEEE Transac-tions on Magnetics, vol. 40, no. 2, pp. 1318-1321, March 2004, doi: 10.1109/TMAG.2004.825025.
[31] J. Muhlethaler, J. Biela, J. W. Kolar and A. Ecklebe, “Core Losses Under the DC Bias Condition Based on Steinmetz Parameters,” in IEEE Transactions on Power Electronics, vol. 27, no. 2, pp. 953-963, Feb. 2012, doi: 10.1109/TPEL.2011.2160971.
[32] Z. Ouyang, O. C. Thomsen and M. A. E. Andersen, “Optimal Design and Tradeoff Analysis of Planar Transformer in High-Power DC–DC Converters,” in IEEE Transactions on In-dustrial Electronics, vol. 59, no. 7, pp. 2800-2810, July 2012, doi: 10.1109/TIE.2010.2046005.