摘要

       近年来，随着航空航天、通信设备等各领域的快速发展，小型化、高效率的电源模块得到广泛应用，电源模块的发展将趋向于高频高效高功率密度。通过提高开关频率可以提高电源的功率密度，但会引起系统的开关损耗增加。为减小开关损耗，本文选取了能够实现软开关的LLC谐振变换器拓扑，但随着开关频率的进一步提高，开关损耗仍然比较大。为此，将新型半导体器件氮化镓(GaN)与LLC谐振变换器相结合，利用氮化镓具有体积小、导通速度快、通态电阻小等优势，在提高频率的同时降低开关损耗。此外，对高频变压器进行精心有效设计，可大大减小体积降低损耗，提高电源的整体效率。

         本文对GaN器件的导通机理、关键参数及驱动特性进行详细介绍。对LLC谐振变换器在不同工作频率范围内的工作模态进行分析，重点介绍了原边开关管实现零电压导通(ZVS)及副边整流管实现零电流关断(ZCS)的过程。根据基波分析法(FHA)建立等效电路模型，获得归一化增益函数。通过绘制其对应的曲线，分析不同参数对归一化增益的影响，对谐振回路主参数进行优化设计；此外，选用PCB平面变压器，可以进一步提高电源的效率和功率密度。

       为提高系统的稳态及动态性能，本文采用扩展描述函数法建立小信号模型，获得开环传递函数。考虑到数字控制会引起延时以及理想采样开关会引入增益之后，对开环传递函数进行修正。根据校正后的传递函数及伯德图，设计了内环为4P2Z补偿器，外环为PI补偿器的双闭环控制回路改善系统的动态特性，并搭建仿真模型进行验证。

       为更直观的表达本论题中补偿设计的有效性，本文根据设计参数搭建实验样机测试平台，并设置双PI补偿器的闭环控制作对照组。在输入电压和负载变化时对两种设计方案进行动态响应对比，实验结果与仿真结果一致，结果表明本文设计的动态响应速度更快、输出电压纹波更小，系统稳态及动态性能更好，还可在全工作范围内实现ZVS。此外，由不同输出功率下的效率曲线可知：系统转换效率最高可达95.22%，进一步验证了本文设计的合理性和正确性。

                                            ABSTRACT

          In recent years, with the rapid development of aerospace, communication equipment and other fields, miniaturized and high-efficiency power modules have been widely used and the development of power modules will tend to be high-frequency, high-efficiency and high-power density. The power density of the power supply can be increased by increasing the switching frequency, but it will cause the switching losses of the system to increase. In order to reduce the switching loss, the LLC resonant converter topology that can achieve soft switching is selected in this paper, but with the further increase of the switching frequency, the switching loss is still relatively large. To this end, a new semiconductor device gallium nitride (GaN) is combined with an LLC resonant converter, utilizing the advantages of gallium nitride, such as small size, fast turn-on speed and low on-state resistance, to reduce switching losses while increasing the frequency. In addition, the careful and effective design of the high-frequency transformer can greatly reduce the volume, reduce losses and improve the overall efficiency of the power supply.

      In this paper, the conduction mechanism, key parameters and driving characteristics of GaN devices are introduced in detail. The working modes of the LLC resonant converter in different operating frequency ranges are analyzed, and the process of zero-voltage switching (ZVS) for primary switch tube and zero-current switching (ZCS) for secondary rectifier tube is introduced emphatically. The equivalent circuit model is established based on First-Harmonic Approximation (FHA) and the normalized gain function is obtained. By drawing its corresponding curve, the influence of different parameters on the normalized gain is analyzed, and the main parameters of the resonant tank are optimized. In addition, the selection of PCB planar transformer can further improve the efficiency and power density of the power supply.

      In order to improve the steady-state and dynamic performance of the system, this paper adopts the extended description function method to establish a small-signal model and obtain the open-loop transfer function. The open-loop transfer function is modified to take into account the delay caused by digital control and the gain introduced by an ideal sampling switch. According to the corrected transfer function and Bode diagram, a double closed-loop control loop with a 4P2Z compensator in the inner loop and a PI compensator in the outer loop is designed to improve the dynamic characteristics of the system, and a simulation model is built for verification.

         In order to more intuitively express the effectiveness of the compensation design in this topic, this paper builds a test prototype test platform according to the design parameters and sets the closed-loop control of the double PI compensator as the control group. The dynamic responses of the two designs are compared when the input voltage and load change, and the experimental results are consistent with the simulation results. The results show that the dynamic response speed designed in this paper is faster, the output voltage ripple is smaller, the steady-state and dynamic performance of the system is better, and ZVS can be achieved in the full working range. In addition, the efficiency curves under different output powers show that the conversion efficiency of the system is up to 95.22%, which further verifies the rationality and correctness of the design in this paper.

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