本論文提出應用於數據中心48 V電壓調節模組的48 V-12 V隔離式直流-直流轉換器。本電路架構採用能夠在全負載範圍達到一次側開關零電壓切換ZVS，二次側開關零電流切換ZCS的全橋LLC串聯諧振轉換器，將開關的操作頻率固定在諧振點做為直流變壓器 (DC Transformer, DCX)，其中針對電路增益部分利用時域區間分析的推導，在諧振元件設計上能更好評估電路增益變化，利用更貼近實際情況的方式調整諧振元件參數以達到設計目標。由於在500 kHz的開關切換頻率下，開關切換損耗大幅上升，因此採用寬能隙元件氮化鎵取代傳統矽元件，以降低功率開關的損耗。針對變壓器一、二次側皆為低電壓大電流的規格，本文採用四分之一圈平板變壓器結構，在維持4：1 電壓轉換比下，一次側、二次側繞組的圈數將比傳統變壓器更少，具有更低直流銅線損耗的優勢。且針對變壓器繞組的並聯模式和排列方式進行探討及優化，同時將變壓器的尺寸大小利用參數化設計，在有限的電路面積下選擇最佳的鐵心損耗與銅線損耗的平衡點。並考慮氣隙間邊緣磁通對於繞組的影響，因此透過分散式氣隙的方式，在避免犧牲電路功率密度的同時，也能夠使邊緣磁通對銅線損耗的影響降低，維持電路效率。利用ANSYS 磁性模擬軟體Maxwell 驗證四分之一圈平板變壓器的電壓、電流轉換比與磁通密度分布是否符合設計理論，最終實現切換頻率操作於500 kHz、輸入電壓48 V、輸出電壓12 V、輸出功率為1200 W 且功率密度為7 W/cm3，最高效率可以達到96.55 %的LLC 串聯諧振式轉換器。

This thesis proposes a 48 V-12 V isolated DC-DC converter for 48 V voltage regulation modules in data centers. This circuit architecture uses a full-bridge LLC series resonant converter that can achieve ZVS on the primary side and ZCS on the secondary side in the range for a full load. The switching frequency of the switch is fixed at the resonance point as a DC transformer (DCX). Since the switching loss increases significantly when operating at high frequency, the MOSFET device is replaced by a GaN device to reduce the losses of the power switches. Aiming at the specification that the circuit is low-voltage and high-current, this thesis adopts a quarter-turn planar transformer structure. Under the condition of maintaining 4:1 turns of ratio, the number of turns of the windings will be less than the traditional one. In addition, the transformer windings' par-allel mode and winding arrangement are discussed and optimized, and the case with the smallest AC losses is finally selected as the transformer winding design. Besides, the size of the transformer is designed by pa-rameterization. Also, the influence of the fringing flux between the air gaps on the transformer winding is considered, so the copper loss is re-duced again through the distributed gap. The magnetic simulation soft-ware Maxwell of ANSYS is used to verify the magnetic components' conversion ratio and magnetic flux density distribution. Moreover, use the TIA to derive the gain curve to estimate the circuit's gain. Finally, an LLC series resonant converter with a switching frequency of 500 kHz, an input voltage of 48 V, an output voltage of 12 V, an output power of 1200 W and a power density of 7 W/cm3, and maximum efficiency of 96.55 % is realized.

[1] Energy Technology Area, “United States Data Center Energy Usage Report” [Online]. Available：https://eta.lbl.gov/publications/united-states-data-center-energy
[2] European Environment Agency, “United States Data Center Energy Usage Report” [Online]. Available：https://www.eea.europa.eu/data-and-maps/european-data-centres
[3] Efficiency in Data Centers [Online]. Available：https://www.comsoc.org/publications/tcn/2019-nov/energy-efficiency-data-centers
[4] World Internet Users Statistics [Online]. Available：https://www.internetworldstats.com/stats.htm
[5] IEEE.tv, “KeyTalk with Xin Li and Shuai Jiang: Google 48V Power Architecture – APEC 2017.” [Online]. Available：https://ieeetv.ieee.org/ieeetv-specials/keytalk-xin-li-and-shuai-jiang-google-48v-power-architecture-apec-2017?rf=events|114&
[6] R. Rong and R. Wang, “High efficiency 1.5kW 48V-12V DCDC Converter with Leadless MOSFET for Mild Hybrid Electric Vehi- cle,” PCIM Asia 2018; International Exhibition and Conference for Power Electronics, Intelligent Motion, Renewable Energy and En- ergy Management, Shanghai, China, 2018, pp. 1-6.
[7] L. Zhang and S. Chakraborty, “An Interleaved Series-Capacitor Tapped Buck Converter for High Step-Down DC/DC Application,” in IEEE Transactions on Power Electronics, vol. 34, no. 7, pp. 6565- 6574, July 2019,doi: 10.1109/TPEL.2018.2877309.
[8] Y. Zhang and M. de Rooij, “300 W 48V-12V Digitally Controlled 1/16 Brick DC-DC Converter Using GaN FETs,” PCIM Europe digi- tal days 2020; International Exhibition and Conference for Power Electronics, Intelligent Motion, Renewable Energy and Energy Man- agement, Germany, 2020, pp. 1-4.
[9] S. Webb and Y. Liu, “12 Switch Zero-Inductor Voltage Converter Topology,” 2019 IEEE Applied Power Electronics Conference and Exposition (APEC), 2019, pp. 2189-2196, doi: 10.1109/APEC.2019.8722328.
[10] Z. Ye, Y. Lei and R. C. N. Pilawa-Podgurski, “A Resonant Switched Capacitor Based 4-to-1 Bus Converter Achieving 2180 W/in3 Power Density and 98.9% Peak Efficiency,” 2018 IEEE Applied Power Electronics Conference and Exposition (APEC), 2018, pp. 121-126, doi: 10.1109/APEC.2018.8340997.
[11] Z. Ye, Y. Lei and R. C. N. Pilawa-Podgurski, “A 48-to-12 V Cas- caded Resonant Switched-Capacitor Converter for Data Centers with 99% Peak Efficiency and 2500 W/in3 Power Density,” 2019 IEEE Applied Power Electronics Conference and Exposition(APEC), Ana- heim, CA, USA, 2019, pp. 13-18, doi: 10.1109/APEC.2019.8721812.
[12] G. Sovik, T. Urkin, E. E. Masandilov and M. Mordechai Peretz, “Op- timal Self-Tuning Control for Data-Centers’ 48V-12V ZCS-STC,” 2020 IEEE Applied Power Electronics Conference and Exposition (APEC), New Orleans, LA, USA, 2020, pp. 455-462, doi: 10.1109/APEC39645.2020.9124129.
[13] S. Jiang, C. Nan, X. Li, C. Chung, and M. Yazdani, “Switched Tank Converters,” in Proc. IEEE Appl. Power Electron. Conf. Expo., San Antonio, TX, USA, 2018, pp. 81–90.
[14] Y. Ren, M. Xu, K. Yao and F. C. Lee, “Two-stage 48 V Power Pod Exploration for 64-bit Microprocessor,” Eighteenth Annual IEEE Ap- plied Power Electronics Conference and Exposition, 2003. APEC'03., Miami Beach, FL, USA, 2003, pp. 426-431 vol.1,doi:10.1109/APEC.2003.1179248.
[15] M. Ahmed, C. Fei, F. C. Lee and Q. Li, “High Efficiency Two-Stage 48V VRM with PCB Winding Matrix Transformer,” 2016 IEEE En- ergy Conversion Congress and Exposition (ECCE), Milwaukee, WI, 2016, pp. 1-8, doi: 10.1109/ECCE.2016.7855150.
[16] T. Liu, X. Wu and S. Yang, “1 MHz 48V-12V Regulated DCX with Single Transformer,” in IEEE Journal of Emerging and Selected Top- ics in Power Electronics, doi: 10.1109/JESTPE.2019.2955607.
[17] M. H. Ahmed, A. Nabih, F. C. Lee and Q. Li, “High-efficiency, High- density Isolated/Regulated 48V Bus Converter with a Novel Planar Magnetic Structure,” 2019 IEEE Applied Power Electronics Confer- ence and Exposition (APEC), Anaheim, CA, USA, 2019, pp. 468- 475, doi: 10.1109/APEC.2019.8722216.
[18] M. H. Ahmed, F. C. Lee and Q. Li, “Two-Stage 48V VRM With In- termediate Bus Voltage Optimization For Data Centers,” in IEEE Journal of Emerging and Selected Topics in Power Electronics, doi: 10.1109/JESTPE.2020.2976107.
[19] B. Yang, F. C. Lee, A. J. Zhang and G. S. Huang, “LLC Resonant Con- verter for Front end DC/DC Conversion,” APEC. Seventeenth Annual IEEE Applied Power Electronics Conference and Exposition (Cat. No.02CH37335), Dallas, TX, USA, 2002, pp. 1108-1112 vol.2.
[20] B. Yang, “Topology Investigation of Front End DC/DC Power Con- version for Distributed Power System,” PhD Disserta-tion, 2003.
[21] Power Supply Design Seminar, "Designing an LLC Resonant Half-Bridge Power Converter" [Online]. Available：https://www.ti.com/seclit/ml/slup263/slup263.pdf
[22] D. Zhou, X. Zhang, X. Liu, Y. Wang, D. Xu and H. Tian, "Design of LLC Converter Parameters Based on ZVS Characteristic Analy-sis," 2018 21st International Conference on Electrical Machines and Systems (ICEMS), 2018, pp. 2251-2255, doi: 10.23919/ICEMS.2018.8549063.
[23] E. S. Glitz and M. Ordonez, "MOSFET Power Loss Estimation in LLC Resonant Converters: Time Interval Analysis," in IEEE Transactions on Power Electronics, vol. 34, no. 12, pp. 11964-11980, Dec. 2019, doi: 10.1109/TPEL.2019.2909903.
[24] X. -R. Chen, K. -S. Liu, D. -W. Liu, Y. -C. Liu and H. -J. Chiu, "Analyze DC-DC 48V-12V High Power Density LLC Resonant Converter with the method of TIA and FHA," 2021 IEEE Interna-tional Future Energy Electronics Conference (IFEEC), 2021, pp. 1-4, doi: 10.1109/IFEEC53238.2021.9661665.
[25] W. Feng, F. C. Lee and P. Mattavelli, "Simplified Optimal Trajectory Control (SOTC) for LLC Resonant Converters," in IEEE Transac-tions on Power Electronics, vol. 28, no. 5, pp. 2415-2426, May 2013, doi: 10.1109/TPEL.2012.2212213.
[26] W. Jiang, J. Zhang, S. Shao, X. Wu and J. Zhang, "Constant Burst Frequency Control for LLC Converters with Trajectory Control," 2018 IEEE Energy Conversion Congress and Exposition (ECCE), 2018, pp. 6804-6808, doi: 10.1109/ECCE.2018.8557809.
[27] J. Millán, P. Godignon, X. Perpiñà, A. Pérez-Tomás and J. Rebollo, "A Survey of Wide Bandgap Power Semiconductor Devices," in IEEE Transactions on Power Electronics, vol. 29, no. 5, pp. 2155-2163, May 2014, doi: 10.1109/TPEL.2013.2268900.
[28] 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.
[29] D. Lin, P. Zhou, W. N.Fu, Z. Badics and Z. J. Cendes, “A Dynamic Core Loss Model for Soft Ferromagnetic and Power Ferrite Materials in Transient Finite Element Analysis,” in IEEE Transactions on Mag- netics, vol. 40, no. 2, pp. 1318-1321, March 2004, doi: 10.1109/TMAG.2004.825025.
[30] H. Cui and K. D. T. Ngo, “Transient Core-Loss Simulation for Fer- rites With Nonuniform Field in SPICE,” in IEEE Transactions on Power Electronics, vol. 34, no. 1, pp. 659-667, Jan. 2019, doi: 10.1109/TPEL.2018.2812856.
[31] Y. C. Liu, C Chen, K. D. Chen, Y. L. Syu, M. C. Tsai, “High-Frequency LLC Resonant Converter with GaN Devices and Integrated Magnetics,” Energies 2019, 12, 1781.
[32] C. Fei, W. Feng, F. C. Lee and Q. Li, “High-Efficiency High-Power- Density LLC Converter With an Integrated Pla-nar Matrix Trans- former for High-Output Current Applications,” in IEEE Transactions on Industrial Electronics, vol. 64, no. 11, pp. 9072-9082, Nov. 2017, doi: 10.1109/TIE.2017.2674599.
[33] D. Huang, S. Ji and F. C. Lee, "LLC Resonant Converter With Matrix Transformer," in IEEE Transactions on Power Elec-tronics, vol. 29, no. 8, pp. 4339-4347, Aug. 2014, doi: 10.1109/TPEL.2013.2292676.
[34] S. Wang, H. Wu, F. C. Lee and Q. Li, "Integrated Matrix Trans- former with Optimized PCB Winding for High-Efficiency High- Power-Density LLC Resonant Con-verter," 2019 IEEE Energy Con- version Congress and Ex-position (ECCE), 2019, pp. 6621-6627, doi: 10.1109/ECCE.2019.8911885.
[35] E. Rong, S. Li, R. Zhang, X. Du, Q. Min and S. Lu, "A Magnetic Inte- gration Half-turn Planar Transformer for LLC Resonant DC-DC Con- verters," 2018 IEEE Applied Power Elec-tronics Conference and Expo- sition (APEC), San Antonio, TX, 2018, pp. 484-488, doi: 10.1109/APEC.2018.8341055.
[36] M. K. Ranjram and D. J. Perreault, "Leveraging Multi-Phase and Frac- tional-Turn Integrated Planar Transformers for Miniaturiza-tion in Data Center Applications," 2020 IEEE 21st Workshop on Control andModeling for Power Electronics (COMPEL), 2020, pp. 1-8, doi: 10.1109/COMPEL49091.2020.9265752.
[37] Y. -C. Liu et al., "Design and development of a fractional-turn transformer for high power density LLC resonant converters," 2021 IEEE Applied Power Electronics Conference and Expo-sition (APEC), 2021, pp. 335-342, doi: 10.1109/APEC42165.2021.9487397.Y. C. Liu et al., "Design and Implementation of a Planar Transformer With Fractional Turns for High Power Density LLC Resonant Con- verters," in IEEE Transactions on Power Electronics, vol. 36, no. 5, pp. 5191-5203, May 2021, doi: 10.1109/TPEL.2020.3029001.
[38] Y. C. Liu et al., "Quarter-Turn Transformer Design and Opti-mization 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.
[39] M. H. Ahmed, F. C. Lee, Q. Li and M. d. Rooij, "Design Op-timiza- tion of Unregulated LLC Converter with Integrated Magnetics for Two-Stage 48V VRM," 2019 IEEE Energy Conversion Congress and Exposition (ECCE), 2019, pp. 521-528, doi: 10.1109/ECCE.2019.8912785.
[40] P. L. Dowell, "Effects of Eddy Currents in Transformer Wind-ings," in Proceedings of the Institution of Electrical Engineers, vol. 113, no. 8, pp. 1387-1394, August 1966, doi: 10.1049/piee.1966.0236.
[41] D. Maiti and S. K. Biswas, "A simple and generalized design pro-cedure for inductors in power electronics," 2012 IEEE International Conference on Power Electronics, Drives and Energy Systems (PEDES), 2012, pp. 1-5, doi: 10.1109/PEDES.2012.6484368.
[42] R. Jez, "Influence of the Distributed Air Gap on the Parameters of an Industrial Inductor," in IEEE Transactions on Magnetics, vol. 53, no. 11, pp. 1-5, Nov. 2017, Art no. 8401605, doi: 10.1109/TMAG.2017.2699120.
[43] S. Hao, Z. Zhang, J. Li and J. Han, "Analysis of Distributed Air Gap Parameters of Differential Mode Inductor Considering Core Loss and Saturation," 2019 22nd International Conference on Electrical Machines and Systems (ICEMS), 2019, pp. 1-5, doi: 10.1109/ICEMS.2019.8921879.
[44] Infineon Inc., “Resonant LLC Converter: Operation and Design 250W 33Vin 400Vout Design Example.” [Online]. Available：https://www.infineon.com/dgdl/Infineon-MOSFET_OptiMOS_reso- nant_LLC_converter_operation_and_design-AN-v01_00-EN.pdf?fileId=db3a30433acf32c9013ad11cddde01b6
[45] MPS Inc., “Application Note for an LLC Resonant Converter Using Resonant Controller HR1000A.” [Online]. Available：https://www.monolithicpower.cn/cn/documentview/productdocu- ment/index/version/2/document_type/Applica- tion%20Note/lang/en/sku/HR1000A/document_id/5926/
[46] C. Fei, M. H. Ahmed, F. C. Lee and Q. Li, "Two-Stage 48 V-12 V/6 V-1.8 V Voltage Regulator Module With Dynamic Bus Voltage Con- trol for Light-Load Efficiency Improvement," in IEEE Transactions on Power Electronics, vol. 32, no. 7, pp. 5628-5636, July 2017, doi: 10.1109/TPEL.2016.2605579.
[47] McLyman, C.W.T. (2011). Transformer and Inductor Design Handbook (4th ed.). CRC Press. https://doi.org/10.1201/b10865