Extended Describing Function Method Based On An LLC Resonant Converter Modeling

The development of power electronic technology led to the development of switching power supply. The traditional PWM converter with hard-switching mode has failed to meet people’s requirements on power supply of small size, light weight, low EMI noise, high efficiency, high power density and so on. The appearance of soft-switching technology was to solve this problem. Common soft switching converters were resonant converter, multi-resonant converter, quasi-resonant converter and soft switching PWM converter. LLC resonant converter have been widely used as a multi-resonant converter since its input voltage and load variations range were wide, its primary and secondary side switches were easy to achieve soft switching, its voltage stress is small, etc. But its small signal modeling technology was not mature. It was difficult to build a complete and systemic model since generalized averaging method can only built piecewise linear average model. The mathematical derivation of J.Groves method was more complex and a large number simulation of the model was time consuming. In this paper, a small-signal model of LLC resonant converter was established based on extended description method that combined with research methods of predecessors. The main content are as follows:1) The working states of a studied LLC resonant converter topology were analyzed. The equivalent circuit model of LLC resonant converter was given under the assumptions.2) According to the given equivalent circuit, the state equations LLC resonant converter was derived. Finally we get the small-signal model and small-signal circuit of LLC resonant converter by extended describing function.3) The steady-state solution and DC voltage gain characteristics of LLC resonant converter were obtained among the process of modeling.4) The frequency characteristics of control to output variable were given at different frequencies and different circuit parameters with PSpice.The effect of main parameters like switching frequency, input voltage, the duty cycle, the quality factor and the load on the frequency characteristics were analyzed.5) A power supply prototype was designed that based on the circuit parameters optimizated by simulation analysis. And the experimental analysis was also carried out.