# Synchronous Rectification Method for CLLC Resonant Converters Based on State-Trajectory Models
## 4 Discussion
### Verification of Accuracy  
Figure 14 shows the main waveforms of the converter at an input voltage of 200 V and an output voltage of 200 V, operating at the resonance point. As can be seen from the figure, the synchronous rectifier signal is consistent with the ideal conduction state. There is no premature shutdown or advance conduction of the rectifier, which proves the accuracy and effectiveness of the present method at the resonance point. To verify the accuracy of the synchronous rectification scheme in both forward and reverse directions under under-resonance and over-resonance states, the CLLC resonant converter was operated in a resonant state. The forward and reverse operations of the CLLC resonant converter were validated. Figure 15a illustrates the key waveforms of the converter in forward operation with an input voltage of 200 V and an output voltage of 250 V. Figure 15b depicts the key waveforms of the converter in reverse operation with an input voltage of 250 V and an output voltage of 300 V.  
Figure 16a presents the key waveforms of the converter in under-resonant mode during forward operation with an input voltage of 200 V and an output voltage of 160 V. Figure 16b shows the key waveforms of reverse operation in under-resonant mode, with an input voltage of 160 V and an output voltage of 130 V. From the above waveforms, it can be observed that the synchronous rectifier signal aligns with the ideal conduction state. There is no instance of the rectifier tube shutting down prematurely or conducting ahead of time, which confirms the accuracy of the proposed method. \begin{table}
\begin{tabular}{c c} \hline \hline
**Parameters** & **Values** \\ \hline \(V_{\text{in}}\) & 200 V \\ \(V_{\text{o}}\) & 160\(\sim\)250 V \\ \(L_{\tau 1}\) and \(L_{\tau 2}\) & 32.25 \(\upmu\)H:32.25 \(\upmu\)H \\ \(C_{\tau 1}\) and \(C_{\tau 2}\) & 78.56 nF:78.56 nF \\ \(L_{\text{m}}\) & 167.7 \(\upmu\)H \\ \(f_{s}\) & 70\(\sim\)130 KHz \\ \(n\) & 1 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Experimental prototype parameters. Figure 13: Comparison of calculated and simulated SR gate drive signal duty cycle in the below-resonant region for the proposed synchronous rectification scheme. Figure 14: SR waveforms for forward operation of the CLLC resonant converter in the under-resonant state. Figure 15: SR waveforms for forward and reverse operation of the CLLC resonant converter in the under-resonant state. (**a**) Forward operation. (**b**) Reverse operation. Figure 17 illustrates the dynamic waveform of the switching current during forward operation in the under-resonant state, with an output voltage of 250 V and an output current changing from 4 A to 1 A. The figure demonstrates that the proposed synchronous rectification scheme exhibits excellent dynamic performance in the under-resonant state. Figure 16: SR waveforms for forward and reverse operation of the CLLC resonant converter in the over-resonant state. (**a**) Forward operation. (**b**) Reverse operation. Figure 17: CLLC resonant converter under-resonant state switching load SR waveform, input voltage 200 V, output voltage 250 V, output current 4 A switching to 1 A. (**A–C**) are enlarged diagrams of the corresponding points. Figure 18 depicts the dynamic waveform of the switching current during forward operation in the over-resonant state, with an output voltage of 160 V and an output current changing from 3.5 A to 1 A. From the figure, it can be observed that the over-resonant state also demonstrates a good dynamic performance. However, a slight error in the over-resonant state may lead to a minor degradation in the rectifier performance. Nevertheless, the proposed synchronous rectification scheme maintains high dynamic performance and accuracy. As shown in Table 3, the proposed SR method is compared with other SR methods reported in the literature. The proposed method achieves accurate synchronous rectification with low complexity, broader applicability, and without the need for additional auxiliary circuits or sensors.