# Analysis of a Three-Level Bidirectional ZVS Resonant Converter
## 3 Circuit Operation
The ac equivalent resistance \(R_{ac,L}\) at the rated power is obtained in Equation (14). Figure 3:1  
The circuit parameters \(C_{r}\) = \(1/2\pi Q_{1}f_{r}R_{ac,L}\approx 50\) nF and \(L_{r}\) = \(1/\left(2\pi f_{r}\right)^{2}C_{r}\approx 50\) uH under \(f_{r}\) = 100 kHz. The actual resonant inductance and capacitance are \(C_{r}\) = 47 nF and \(L_{r}\) = 54 uH and the magnetizing inductance \(L_{m}\) = \(K_{1}L_{r}\) = 540 uH. The theoretical primary \(rms\) current is calculated as:  
Figure 3:2  
The theoretical minimum switching frequency is obtained as \(f_{sw,\min}~{}=~{}1/2\pi\sqrt{C_{r}(L_{r}+L_{m})}~{}\approx 30\) kHz. The minimum switching frequency will result in the maximum \(rms\) magnetizing current. Figure 3:3  
Therefore, the \(rms\) resonant inductor current is obtained in Equation (17). Figure 3:4  
The flying capacitor \(C_{f}\) is used to realize voltage balance of \(C_{H1}\) and \(C_{H2}\) so that \(V_{CH1}\) = \(V_{CH2}\) = \(V_{H}\)/2. The theoretical voltage stresses of power semiconductors can be calculated as \(v_{51,stress}\) = \(..\) = \(v_{54,stress}\) = \(V_{H,max}\)/2 = 400 V and \(v_{Q1,stress}\) = \(..\) = \(v_{Q4,stress}\) = \(V_{L,max}\) = 52 V. The switch currents approximate \(I_{S1,rms}\) = \(..\) = \(I_{S4,rms}\)\(\approx\)\(I_{Lr,rms}\)/ \(\sqrt{2}\)\(\approx\) 3.2 A and \(I_{Q1,rms}\) = \(..\) = \(I_{Q4,rms}\)\(\approx\)\(\pi I_{o}\)/4 \(\approx\) 23.6 A. Power devices \(S_{1}\)\(\sim\)\(S_{4}\) are implemented using IRG4 PC40W with 600 V/20 A rating. Power switches \(Q_{1}\)\(\sim\)\(Q_{4}\) are implemented using IRFB3307 with 75 V/150 A rating. \(S_{ac}\) is implemented using two G20N50C with 500 V/20 A rating. The parallel inductor \(L_{b}\) is selected as 230 uH and \(K_{2}\) = \(L_{b}\)/\(L_{r}\) = 4.25 under reverse power flow operation. The clamp diodes \(D_{a}\) and \(D_{b}\) are implemented with ultrafast recovery diodes HFA15 TB60 PBF with 600 V/15 A rating. The other circuit parameters used in the prototype are \(C_{H1}\) = \(C_{H2}\) = 330 uF/400 V, \(C_{f}\) = 2.2 uF/630 V and \(C_{L}\) = 4400 uF/100 V. The parameters and specifications used in the laboratory prototype are given in Figure 3:5  
Figures 6-10 provide the test results for forward power operation and Figures 11-14 provide the measured waveforms for reverse power operation. The PWM signals of \(S_{1}\)-\(S_{4}\) at 100% load are presented in Figure 3:6 \(S_{1}\) (\(S_{3}\)) and \(S_{2}\) (\(S_{4}\)) have the same gate-to-source voltage signals. The converter at \(V_{H}\) = 750 V input has less switching frequency than \(V_{H}\) = 800 V input condition. Figure 7 gives the experimental results of leg voltage \(v_{ab}\), \(i_{L}\), and \(v_{C}\), at 100% load. It can be seen that the measured waveforms \(i_{L}\), and \(v_{C}\) are almost the sinusoidal waves due to \(f_{sw}\) close to \(f_{r}\) for both 750 V and 800 V inputs. Figure 8 shows the experimental results of \(V_{CH1}\), \(V_{CH2}\), \(V_{C\!f}\), \(V_{Da}\) and \(V_{D\!b}\). The dc voltage differences between \(V_{CH1}\), \(V_{CH2}\) and \(V_{C\!f}\) are about 5V. Figure 9 demonstrates the switch currents of \(Q_{I}\)-\(Q_{4}\) at 100% load. Figure 10 illustrates the PWM waveforms of \(S_{1}\)-\(S_{4}\) at 20% load. It can observe that \(S_{1}\)-\(S_{4}\) all turn on under ZVS at 20% load. Figure 11 gives the PWM signals of \(Q_{1}\)-\(Q_{4}\) under backward power operation and different input voltages. Power devices \(Q_{1}\) (\(Q_{2}\)) and \(Q_{4}\) (\(Q_{3}\)) have the same gate-to-source voltage signals. Figure 12 illustrates the measured results of \(i_{Lr}\), \(i_{Lb}\) and \(v_{C}\), under for reverse power operation. The parallel inductor current \(i_{Lb}\) is similar to the magnetizing current on conventional _LLC_ resonant converter to achieve voltage step-up capability. Figure 13 shows the measured capacitor voltages \(V_{C\!f}\), \(V_{CH1}\) and \(V_{CH2}\) on the high voltage side. These three voltages \(V_{CH1}\), \(V_{CH2}\) and \(V_{C\!f}\) are almost balanced with about 7 V voltage difference.