Small-Signal Modeling of LLC Converters Using Homopolarity Cycle

The widespread use of the LLC converter in dc-dc applications has increased the importance of small-signal modeling to control the converter below- to above-resonant frequency. The analysis of LLC converters is complicated, since they process the electrical energy through a high-frequency resonant tank that causes excessive nonlinearity. As a result of this complexity, small-signal modeling of the LLC converter is traditionally performed using empirical methods, iterative simulation approaches, or theory limited to the vicinity of the resonant frequency. Often, such approaches may lead to limited insight (just empirical trends) or low accuracy below and above resonance. This article proposes a new average small-signal modeling technique for the LLC converter, and it is performed in the time domain. The proposed technique is based on the analysis of the homopolarity cycle and accurately predicts not only the small-signal dynamic behavior of the LLC converter at resonance, but also below and above resonance. By using the homopolarity cycle, the theoretical analysis of the LLC converter is significantly simplified to a level that the small-signal dynamic behavior of the LLC converter is expressed by two second-order circuit models. Experimental and simulation results of a 650-W LLC converter are provided to verify the theoretical analyses and accuracy of the circuit models. The results have shown that the proposed small-signal circuit models can accurately predict the small-signal dynamic behaviors of the LLC converter from below- to above-resonant operations.