## 4 Simulation and Experiment  
The proposed compensation method was implemented in the Altera Cyclone IV FPGA of a digitally controlled ARSI prototype using the parameters listed in Table 2. Figure 8 shows the photograph of the prototype, which consists of a FPGA (Altera Corporation EP4 CE22E22C7N) control board, a switching power supply, a MOSFET driver and a power circuit. In addition, the method is also verified in the simulation using Saber. Figure 9 shows the open-loop control diagram of the ARSI with proposed dead-time effect compensation. FPGA samples the output current in each switching cycle. Then the mode judgement is completed according to Table 1. The voltage error can be calculated from Equation (38). Therefore, the voltage error can be compensated in the reference voltage. As for the auxiliary current control, the on-time of the auxiliary switches can be calculated after the mode judgement. Finally, the gate signals of the switches can be generated from the compensated reference voltage and the on-time of the auxiliary switches. The compensation method is based on the model of the voltage error. The more accurate the model, the more precise the compensation result. Figure 10 shows the calculated voltage error vs. output current according to Equation (38). The voltage error only occurs in the HLM. A voltage error about 1.2 V occurs at the threshold current 3A. As the output current increases, the voltage error decreases first before increasing. \begin{table}
\begin{tabular}{c c} \hline \hline
**Parameter** & **Value** \\ \hline DC voltage \(V_{s}\) & 80 V \\ Switching frequency \(f_{s}\) & 200 kHz \\ Dead-time \(t_{dead}\) & 0.5 us \\ Load & 3.7 \(\Omega\), 4.87 mH \\ Resonant inductor \(L_{r}\) & 4.4 uH \\ Resonant capacitor \(C_{r}\) & 4.7 nF \\ Threshold current \(I_{th}\) & 3 A \\ \(I_{boost}\) & 4 A \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Parameters of the circuit. Figure 8: Photograph of the prototype. Figure 11 shows the resonant time vs. the switching current both in the calculation and simulation, where the switching current of AZVS is \(I_{\text{boost}}\) and the switching current of NZVS is \(i_{o}\). The resonant time of AZVS is nonlinear related to the switching current. When the switching current is high enough, the resonant time of AZVS is close to that of NZVS. The calculation of the resonant time is in good agreement with the simulation results, which is related to the voltage error. Figure 12 shows the output voltage and current of the hard-switching inverter when the modulation index is 0.4 in an open-loop configuration. To measure the output voltage \(v_{o}\), a filter is added to attenuate the carrier harmonics of the pole voltage \(v_{ab}\). A serious distortion occurs both in the output current and voltage due to the long dead-time of 0.5 \(\mu\)s.  
Figure 10: Average voltage error vs. output current in the calculation. Figure 9: Open-loop control diagram of the ARSI with proposed dead-time effect compensation. Figures 13 and 14 show the simulation and experimental results of ARSI without dead-time compensation, respectively, when the modulation index is 0.4 in an open-loop configuration. The auxiliary circuit is operated twice with bidirectional current in a switching cycle in the LLM. An obvious distortion occurs in the output voltage at the mode switching point. However, the distortion of the output current and voltage is less than that of the hard-switching inverter in Figure 12, owing to the absence of blanking delay error in the ARSI. Figure 13b shows the voltage error between the actual output voltage and ideal output voltage. The simulation results are in good agreement with the experimental results. Figure 11: Resonant time vs. the switching current both in the calculation and simulation. Figure 12: Output voltage and current of the hard-switching inverter when the modulation index is 0.4 in an open-loop configuration. (**a**) simulation results; (**b**) experimental results. the calculation results in Figure 10 without consideration of the ripple.