## 3 Results  
To verify the theoretical analysis above, the two modulation methods will be exemplified through a converter in the same application, whose specifications are listed in Table 1. It is a 600 W charger converter with an input of 120 V. The rated output voltage is 120 V, and the minimum output voltage is 84 V (70% of the rated value). The range of current in the CV stage is 0.5\(\sim\)5 A (10% to 100% rated current). Using the design procedures in the previous section, the converter is designed following the two methods, respectively. To be fair, the maximum capacitor voltage \(V_{cp}^{*}\) is selected at 1.5 times of input dc voltage, i.e., 180 V for both cases. The designed parameters are shown in Tables 2 and 3. For Method I, the switching frequency is selected at 100 kHz. Then, the resonant capacitance and inductance can be calculated by using (13) and (14), which in turn result in the resonance frequency of 77.68 kHz. The range of phase-shift angle \(\phi\) is 4.1\(\sim\)45.57\({}^{\circ}\). For Method II, the resonance frequency is selected at 80 kHz, and the maximum switching frequency is 108 kHz. For the sake of verification, the designed converter with proposed modulation was simulated in PSIM firstly. To approximate the actual implementation, non-ideal parameters are included in the simulation setup purposely. A dead-band of 2\({}^{\circ}\) is inserted into the gating signals. The on-state resistance of MOSFET is set at 50 m\(\Omega\), and the built-in barrier of anti-parallel diode is assumed to be 0.5 V.  
As shown in Figure 7, a simulation block diagram and two prototype converters with the two sets of designed parameters are also built and tested. IPP60R099P7 is used for all \begin{table}
\begin{tabular}{c c} \hline \hline Rated power & 600 W \\ \hline Input voltage & 120 V \\ ine Output voltage & 84\(\sim\)120 V \\ ine Output current & 0.5 A \(\sim\)5 A \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Specifications of the charger converter. \begin{table}
\begin{tabular}{c c} \hline \hline Transformer turns ratio & 1:1 \\ \hline Switching Frequency & 100 kHz \\ ine \(M_{min}\sim M_{max}\) & 0.7 \(\sim\) 1 \\ ine Resonant inductance \(L_{s}\) & 55.74 μH \\ ine Resonant capacitance \(C_{s}\) & 75.32 μF \\ ine Maximum phase-shift \(\phi_{max}\) & 45.57\({}^{\circ}\) \\ ine Minimum phase-shift \(\phi_{min}\) & 4.1\({}^{\circ}\) \\ \hline \hline \end{tabular}
\end{table} 
Table 2: The design parameters using CFVP. \begin{table}
\begin{tabular}{c c} \hline \hline Transformer turns ratio & 1:1 \\ \hline \(M_{min}\sim M_{max}\) & 0.7\(\sim\) 1 \\ ine Resonant inductance \(L_{s}\) & 45.60 μH \\ ine Resonant capacitance \(C_{s}\) & 86.81 nF \\ ine Maximum switching frequency & 108 kHz \\ ine Minimum switching frequency & 80 kHz \\ \hline \hline \end{tabular}
\end{table} 
Table 3: The design parameters using VF. MOSFET switches in the two bridges. The transformers are made with ETD49 ferrites core. The two inductors are made with PQ35 ferrites core. In Figures 8 and 9, waveforms of five cases obtained from simulation (left part) and experiment (right part) are illustrated for two modulation methods, respectively. The five cases are 70% rated voltage, 90% voltage in the CC stage, the rated/peak power case, 80% rated current, and 50% rated current in the CV stage. In each case, waveforms of \(v_{p},v_{s},v_{c},i_{r}\) (from top to bottom) are captured and shown together. Generally, the shape of those simulation waveforms has a close match with that of experimental ones in all cases. The first three cases correspond to points A, B and C in the CC stage. The output voltage rises from 84 V to 108 and 120 V, respectively, while the output current is always 5 A. It can be seen that the phase-shift \(\phi\) and switching frequency are kept constant in Figure 8a-c for Method I. For Method II, in Figure 9a-c, it is seen that the secondary side voltage is always synchronous with the resonant current, and the switching frequency is varied in this procedure.