Enhanced Small-Signal Modeling for Charge-Controlled Resonant Converters

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Charge control for resonant converters introduces an inner feedback loop that improves the system dynamic characteristics. However, small-signal modeling is not as straightforward with charge-controlled resonant converters as it is with current mode hard-switching topologies, due to the nature of resonant behavior. Conventional small-signal models for charge-controlled resonant converters are developed based on the converter input and output energy balance. This simplified approach overlooks the dynamics of the magnetizing inductor current and generates errors in small-signal frequency response. To improve the analytical model and enable high-bandwidth design, this article proposes a new methodology for modeling charge-controlled resonant converters. The energy stored in the resonant tank is analyzed using the theory of extended describing function, which accounts for the effect of the magnetizing current. This methodology applies to a wide range of charge control variants, such as bang-bang charge control and hybrid-hysteretic control. To demonstrate the modeling procedure, this article considers a high-order, five resonant-component half-bridge CLLC resonant converter as a case study. The proposed analytical model is applied to a 1 kW, 400-V/3.3-A power supply prototype for simulation and experimental validation. The proposed model successfully predicts the frequency response of the resonant converter across frequency and load conditions, providing rapid frequency-domain evaluation in the design process.