Modeling resonant converters in a rotating, polar coordinate

The average concept, which extracts low frequency components of a signal, is widely adopted to model switching power converters. For resonant converters, the average concept fails due to the existence of a band-pass filter. The first small-signal equivalent circuit model for resonant converters, proposed by E. Yang, is based on fundamental approximation and harmonic balance theory. Although the model is accurate, the complex derivation and the mutual coupling in the equivalent circuit make the model lack of physical intuition. Recently, Y. Hsieh identified the rotating behavior of a resonant converter by studying the state plane and the property on a dq-plane was studied for the first time. A resonant converter on a dq-coordinate was shown to have high similarity to a conventional pulse-width-modulation (PWM) converter. Therefore, the simple average concept can be used for modeling. Nonetheless, the physical meaning of the mutual coupling between d and q axes is still unclear. This paper proposed a rotating, polar coordinate modeling for resonant converters. Compared to the dq-transformation based on the Cartesian coordinate, the radius in a polar coordinate represents the total energy of the resonant tank while the phase angle represents the leading or lagging information of the resonant tank current. Therefore, the proposed model is easy to derive and is rich in physical insight. The beat-frequency double pole and the resonance between the resonant tank and the output filter can be well explained with the proposed model.