# Hybrid Resonant Converter with Three Half-Bridge Legs for Wide Voltage Operation
## 2 Circuit Structure and Principle of Operation
Low Input Voltage Range (\(S\), \(Q_{5}\), and \(Q_{6}\) off, \(V_{in,L}=V_{in,max}/8\)-\(V_{in,max}/4\))  
If the input voltage \(V_{in}\) is between \(V_{in,max}/8\) and \(V_{in,max}/4\), \(S\), \(Q_{5}\), and \(Q_{6}\) are turned off and only \(Q_{1}\).\(Q_{4}\) are operated to realize the high voltage gain shown in Figure 2a compared to the other two equivalent circuits (Figure 2b,c). The input-side is a full-bridge resonant converter and the output-side is a center-tapped diode rectifier. The DC voltage gain for low input voltage range is \(V_{o}/V_{in,L}=G_{L}(f)n_{s}/n_{p}\). The theoretical pulse-width modulation (PWM) waveforms and the equivalent circuits for six operating states are provided in Figure 3 if \(f_{sw}\) (switching frequency) is less than \(f_{r}\) (series resonant frequency). **State 1 [\(t_{0}\)-\(t_{1}\)]:** At \(t=t_{0}\), \(v_{\text{CQ1}}=v_{\text{CQ4}}=0\). Then \(D_{Q1}\) and \(D_{Q4}\) are conducting due to \(i_{Lr1}(t_{0})<0\). \(Q_{1}\) and \(Q_{4}\) turn on after \(t_{0}\) to have soft switching operation. In this time interval, \(L_{r}\) and \(C_{r}\) are naturally resonant to deliver power to the load side. Because the diode \(D_{1}\) is conducting, the magnetizing voltage \(v_{Lm1}=nV_{o}\), where \(n=n_{p}/n_{s}\), and \(i_{Lm1}\) increases. **State 2 [\(t_{1}\)-\(t_{2}\)]:** If \(f_{sw}<f_{r}\), then \(i_{D1}\) decreases to zero at time \(t_{1}\) and \(D_{1}\) is reverse biased without the reverse recovery current. In this state, \(L_{r1}\), \(L_{m1}\), and \(C_{r1}\) are naturally resonant with the resonant frequency \(f_{p}=1/2\pi\sqrt{(L_{r1}+L_{m1})C_{r1}}\). **State 3 [\(t_{2}\)-\(t_{3}\)]:** At time \(t_{2}\), \(Q_{1}\) and \(Q_{4}\) turn off. \(C_{Q1}\) (\(C_{Q2}\)) and \(C_{Q4}\) (\(C_{Q3}\)) are charged (discharged) due to \(i_{Lr1}(t_{2})\) being positive. In this state, \(D_{2}\) is forward biased due to \(i_{Lr1}<i_{Lm1}\) and the magnetizing voltage \(v_{Lm1}\) equals \(-nV_{o}\). **State 4 [\(t_{3}\)-\(t_{4}\)]:** At time \(t_{3}\), \(v_{\text{CQ2}}=v_{\text{CQ3}}=0\). \(D_{Q2}\) and \(D_{Q3}\) are conducting owing to \(i_{Lr1}(t_{3})>0\). \(Q_{2}\) and \(Q_{3}\) turn on after \(t_{3}\) to realize the soft switching operation. In this time interval, \(L_{r}\) and \(C_{r}\) are naturally resonant to deliver power to load side. Because the diode \(D_{2}\) is forward biased on the secondary side, the magnetizing voltage \(v_{Lm1}=-nV_{o}\) and \(i_{Lm1}\) decreases. **State 5 [\(t_{4}\)-\(t_{5}\)]:** At time \(t_{4}\), \(i_{D2}\) is decreased to zero so that \(D_{2}\) is off. In this state, \(L_{r1}\), \(L_{m1}\), and \(C_{r1}\) are naturally resonant. **State 6 [\(t_{5}\)-\(T_{sw}\) + \(t_{0}\)]:** At time \(t_{5}\), power switches \(Q_{2}\) and \(Q_{3}\) are turned off. \(C_{Q1}\) (\(C_{Q2}\)) and \(C_{Q4}\) (\(C_{\text{Q3}}\)) are discharged (charged) due to \(i_{Lr1}(t_{5})\) is negative. In this state, \(D_{1}\) is forward biased owing to \(i_{Lr1}>i_{Lm1}\) and the magnetizing voltage \(v_{Lm1}=nV_{o}\) and \(i_{Lm1}\) increases. At \(T_{sw}+t_{0}\), \(v_{\text{CQ1}}=v_{\text{CQ4}}=0\) and the converter goes to state 1 for the next switching period. Figure 3: \(Cont.\)  
Medium Input Voltage Range (\(Q_{3}\) and \(Q_{4}\) off, \(V_{in,M}=V_{in,max}\)/4-\(V_{in,max}\)/2)  
The proposed converter for the medium input voltage (\(V_{in}=V_{in,max}\)/4-\(V_{in,max}\)/2) operation is illustrated in Figure 2b. Under the medium voltage range, power switches \(Q_{3}\) and \(Q_{4}\) turn off and AC switch \(S\) is always on. The full-bridge resonant circuit is adopted on the input-side with the resonant components \(L_{r1}\), \(L_{r2}\), \(C_{r1}\), \(C_{r2}\), and transformer \(T\) with \(2n_{p}\) primary winding turns. Because \(C_{r1}=C_{r2}\) and \(L_{r1}=L_{r2}\), the series resonant frequencies at the medium input voltage operation (Figure 2b) and the low input voltage operation (Figure 2a) are identical.