Extended Phasor Analysis-Based Unified Approach to Accurate Small-Signal Modeling of $LLC$ Resonant Converters

Resonant converters have become a popular choice for power-dense and efficient operation with applications ranging from the telecom industry to electric vehicle (EV) battery charging. However, the modeling procedure of these converters remains challenging as some of the state variables vary sinusoidally and have significant switching frequency components. Most of the efforts in the literature describing the small-signal dynamics of resonant converters either involve intense calculations or do not offer any analytical control-to-output transfer function, which is important for the ease in controller design. Further, as more elements are added to the resonant tank to extend the soft-switching range and operation flexibility, the modeling process becomes increasingly complicated. Additionally, distinct transfer functions need to be derived for different operating regions and the uniformity in the model is absent. This paper presents a modeling procedure based on extended phasor analysis simplifying the modeling procedure. The entire resonant tank is modeled by a single thevenin equivalent impedance making the procedure generalizable to multi-element resonant tanks. The same set of assumptions hold across all operating regions for the model, resulting in a unified transfer function. To validate the effectiveness of the proposed method, a reduced order small-signal model of LLC resonant converter, valid for all switching frequencies of operation, is derived and experimentally verified in a 500W, 50kHz LLC resonant converter laboratory prototype.