Discrete-Time Modeling Framework for Analysis of LLC Converters over a Wide Frequency Range

Abstract

LLC converters offer high efficiency, low electro-magnetic interference (EMI) and high power density using soft switching, which makes them an attractive solution for data center, electric vehicle and renewable energy applications. While operating over a wide range of input/output voltages and power level, the switching frequency <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$f_{\text{sw}}$</tex> may vary around the resonant frequency <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$f_{r}$</tex> under pulse frequency modulation (PFM) or may be maintained at <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$f_{r}$</tex> using phase shift modulation (PSM) within some limits. Nevertheless, for varying voltage gain and power level, the LLC converter often undergoes structural changes with reduced system dimension, making it difficult in identifying suitable modeling techniques. Small-signal models using first-order-harmonic approximation (FHA) are widely used, which work fine while operating well near <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$f_{r}$</tex> ; however, the model validity remains a serious concern with increasing harmonic contents when <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$f_{\text{sw}}$</tex> deviates from <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$f_{r}$</tex> . This digest proposes a unified discrete-time (DT) framework for the derivation of accurate large-signal and small-signal models of an LLC converter by taking into consideration the dimensional change over the entire frequency range. Large-signal models are shown to perfectly capture the actual switch simulation for three possible configurations depending on the relationship between <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$f_{\text{sw}}$</tex> and <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$f_{r}$</tex> . A 2.5 k W LLC resonant converter hardware prototype is developed and the accuracy of the proposed large-signal models is validated using experimental results, which show close agreement with the analytical prediction. Finally, the proposed discrete-time small-signal models are verified with the SIMetrix/SIMPLIS simulation in the frequency domain and are also compared with traditional Extended Describing Function (EDF) method.