# Synchronous Rectification Method for CLLC Resonant Converters Based on State-Trajectory Models
## 1 Introduction  
A CLLC converter is a high-frequency, high-power, directional and bidirectional DC-DC converter, which has had a high research fever in academia and industry in recent years. The application areas of the CLLC converter include renewable energy systems, DC power distribution systems, electric vehicle vehicle-to-grid technology (V2G), On-Board Charger (OBC) systems, battery energy storage systems, and aspects of rail transportation and aerospace [1, 2, 3, 4, 5]. The CLLC converter is an isolated, symmetrical DC-DC converter with robust bidirectional power operation characteristics [6, 7]. However, a simple rectification using the body diode of the MOSFET can significantly reduce efficiency. Therefore, a SR technique must be introduced so that the current flows through the drain-source channel of the MOSFET instead of the body diode. SR reduces the conduction loss of the CLLC converter and significantly improves the overall efficiency and power density. The original SR strategy was implemented using a current sensor, which detects the current through the MOSFET, determines its direction, and subsequently adjusts the gate drive signal. Although this method exhibits high accuracy and stability, it requires an additional current transformer on the rectifier side, resulting in increased winding losses in the system. Meanwhile, due to the symmetry of the CLLC resonant converter, when the converter is not transferring energy, the LC circuit on the secondary side remains in resonance. This leads to the formation of oscillating currents on the secondary side, causing the MOSFETs to oscillate and compromising the stability of the circuit. In recent years, scholars have proposed numerous SR methods for CLLC resonant converters, broadly classified into sensor-based SR methods and sensorless SR methods. Sensor-based synchronous rectification methods are primarily divided into two categories: voltage-based and current-based approaches. The key to the voltage-based synchronous rectification method lies in accurately detecting the conduction state of the body diode, which is typically achieved through diode conduction detection circuits [8; 9], and some scholars carry out synchronous rectification by measuring the resonant inductor voltage [10]. The voltage-based SR method has certain limitations; when the current on the secondary side is zero, the drain voltage and inductor voltage oscillate [11], leading to errors in the SR signal. To address the issues associated with voltage-based SR methods, some scholars have proposed current-based SR methods [12; 13], and then SR through the current transformer is also problematic due to the inductor's inherent measurement errors, resulting in a relatively large phase shift detection error. This makes it unsuitable for high-frequency converter applications. Furthermore, for CLLC converters with bidirectional capability, sensors need to be added to both the primary and secondary sides, making sensor-based SR methods costly and difficult to implement on a large scale. The conventional sensor-based SR method is unsuitable for CLLC converters, necessitating the proposal of an accurate, stable, and low-cost synchronous rectification strategy. In parallel with advancements in converter modeling methods, many scholars have proposed sensorless SR methods. The sensorless SR method offers the advantage of it being possible to obtain the driving signal of SR by solving the mathematical model of the CLLC resonant converter. The literature [14; 15] derives the driving signal of SR by constructing a harmonic approximation (FHA) model. However, with the increase in the switching frequency, this sensorless SR method faces issues of low accuracy. To solve the problem of low accuracy, some scholars have proposed a sensorless SR method based on the time-domain model [16; 17; 18; 19], which significantly improves the accuracy. Still, the calculation process is complicated and relies on the look-up table method, which cannot update control parameters in real time, leading to control delays.