Recently, LLC resonant converters have attracted significant research from industry and academia for AC–DC and DC–DC power conversion with high efficiency and remarkable power density. They are appealing candidates for numerous vehicular and renewable energy applications including battery chargers for electric vehicles and drivers of LED lights. This study introduces a mathematical model of LLC resonant half-bridge DC–DC converter, which captures its steady-state behaviours for both continuous conduction mode and discontinuous conduction mode operations. One major advantage of the proposed model lies in accurate estimation of the switching frequency of power switches under a wide range of parametric variations. This benefit is, however, not offered by the prevailing method based on the first harmonic approximation (FHA). The analytical derivations of the system's state-space model, as well as equations for calculating the switching frequency by FHA, are discussed in details. For illustration, a 340   W digitally controlled LLC resonant converter is targeted in this study. The simulation analyses of current and voltage waveforms for light and heavy load conditions are presented. Moreover, the experimental results, along with the comparison of switching frequency estimation for both methods, are demonstrated and discussed, which confirms the validity and effectiveness of the proposed model.

中文翻译：

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LLC谐振半桥DC-DC转换器的状态空间建模

最近，LLC谐振转换器已吸引了业界和学术界对AC-DC和DC-DC电源转换的高效能和非凡功率密度的重要研究。它们是众多车辆和可再生能源应用的诱人候选人，包括电动汽车的电池充电器和LED灯驱动器。本研究介绍了LLC谐振半桥DC-DC转换器的数学模型，该模型捕获了连续传导模式和非连续传导模式操作的稳态行为。提出的模型的一个主要优点在于，可以在各种参数变化范围内准确估算功率开关的开关频率。但是，基于一次谐波近似（FHA）的通用方法无法提供此好处。详细讨论了系统状态空间模型的解析推导以及通过FHA计算开关频率的公式。例如，一个340   本研究针对W数控LLC谐振转换器。给出了轻载和重载条件下电流和电压波形的仿真分析。此外，还对实验结果以及两种方法的开关频率估计进行了比较和讨论，从而证实了所提模型的有效性和有效性。