Accurate Small-Signal Modeling for Charge-Controlled LLC Resonant Converter

In comparison with PWM converters, LLC resonant converters are gaining increasing popularity for cases in which efficiency and power density are at a premium. The regulation can be achieved by simple frequency control that changes the resonant tank impedance according to loading conditions. This control experiences a strong beat-frequency oscillation located at the difference between the switching frequency and resonant frequency, and therefore is difficult to compensate. The capacitor voltage is a good indicator of resonant tank energy at the instant where switching is taking place. This additional feedback effectively reduces the system order. However, the small-signal model is lacking. The recent breakthrough in resonant converter modeling is based on the extended describing function method, which takes into account all important contribution from harmonics. This paper extends this modeling for the capacitor-voltage-controlled LLC resonant converter. The corresponding equivalent circuit model is provided, and the comparison with the frequency control is discussed in detail.