# Hybrid Resonant Converter with Three Half-Bridge Legs for Wide Voltage Operation
## 2 Circuit Structure and Principle of Operation
The DC voltage gain for the medium voltage  
Figure 3: Proposed direct current (DC) converter under low input voltage range: (**a**) pulse-width modulation (PWM) waveforms; (**b**) state 1; (**c**) state 2; (**d**) state 3; (**e**) state 4; (**f**) state 5; (**g**) state 6.  
range is \(V_{o}/V_{in,M}=G_{M}(f)n_{s}/(2n_{p})\). Comparing the DC voltage gains for low and medium voltage ranges, one can observe that \(V_{o}/V_{in,L}=2(V_{o}/V_{in,M})\) under \(G_{L}(f)=G_{M}(f)\). This means the proposed converter has less DC voltage gain at the medium input voltage range operation. The theoretical PWM waveforms and the equivalent circuits are given in Figure 4.  
**State 1 [\(t_{0}\)-\(t_{1}\)]:** At time \(t_{0}\), the capacitor voltages of \(v_{CQ1}\) and \(v_{CQ6}\) are zero. \(D_{Q1}\) and \(D_{Q6}\) are forward biased due to \(i_{Lr1}(t_{0})\) being negative. \(Q_{1}\) and \(Q_{6}\) can turn on after \(t_{0}\) to achieve zero-voltage switching. In this state, \(C_{r1}\), \(C_{r2}\), \(L_{r1}\), and \(L_{r2}\) are naturally resonant with series resonant frequency \(f_{r}=1/2\pi\sqrt{L_{r1}C_{r1}}\) due to \(L_{r1}=L_{r2}\) and \(C_{r1}=C_{r2}\), and the energy is transferred from \(V_{in}\) to \(R_{o}\). Due to \(D_{1}\) being forward biased, the magnetizing voltage \(v_{Lm1}=v_{Lm2}=(n_{p}/n_{s})V_{o}\) and \(i_{Lm1}\) and \(i_{Lm2}\) increase. **State 2 [\(t_{1}\)-\(t_{2}\)]:** If \(f_{sw}\) (the switching frequency) \(<\)\(f_{r}\) (series resonant frequency), then \(i_{Lm1}=i_{Lr1}\) and \(i_{Lm2}=i_{Lr2}\) at \(t=t_{1}\). Thus, \(D_{1}\) is off without reverse recovery current loss. In this state, the circuit components \(C_{r1}\), \(L_{r1}\), \(C_{r2}\), \(L_{r2}\), \(L_{m1}\), and \(L_{m2}\) are naturally resonant. **State 3 [\(t_{2}\)-\(t_{3}\)]:** Power switches \(Q_{1}\) and \(Q_{6}\) turn off at \(t=t_{2}\). \(C_{Q1}\) and \(C_{Q6}\) are charged and \(C_{Q2}\) and \(C_{Q5}\) are discharged due to \(i_{Lr1}(t_{2})>0\). Because \(i_{Lr1}<i_{Lm1}\) after \(t_{2}\), the diode \(D_{2}\) is forward biased. **State 4 [\(t_{3}\)-\(t_{4}\)]:\(v_{CQ2}\) and \(v_{CQ5}\) are decreased to zero at \(t=t_{3}\). Because \(i_{Lr1}(t_{3})>0\), the body diodes \(D_{Q2}\) and \(D_{Q5}\) are conducting. \(Q_{2}\) and \(Q_{5}\) can be turned on after \(t_{3}\) to have zero-voltage switching. In this state, \(C_{r1}\), \(L_{r1}\), \(C_{r2}\), and \(L_{r2}\) are naturally resonant with series resonant frequency \(f_{r}=1/2\pi\sqrt{L_{r1}C_{r1}}\) and the energy is transferred from \(V_{in}\) to \(R_{o}\). Due to \(D_{2}\) being forward biased, the magnetizing voltage \(v_{Lm1}=v_{Lm2}=-(n_{p}/n_{s})V_{o}\) and \(i_{Lm1}\) and \(i_{Lm2}\) decrease in state 4. **State 5 [\(t_{4}\)-\(t_{5}\)]:** At time \(t_{4}\), \(i_{Lm1}\) equals \(i_{Lr1}\) and \(i_{Lm2}\) equals \(i_{Lr2}\). Therefore, \(D_{2}\) becomes off. Hence, the components \(L_{r1}\), \(L_{r2}\), \(C_{r1}\), \(C_{r2}\)\(L_{m1}\), and \(L_{m2}\) are naturally resonant. **State 6 [\(t_{5}\)-\(T_{sw}\) + \(t_{0}\)]:** Power switches \(Q_{2}\) and \(Q_{5}\) are turned off at \(t=t_{5}\). \(C_{Q1}\) (\(C_{Q2}\)) and \(C_{Q6}\) (\(C_{Q5}\)) are discharged (charged) due to \(i_{Lr1}(t_{5})<0\). Because \(i_{Lr1}(t_{5})\) is greater than \(i_{Lm1}(t_{5})\), the diode \(D_{1}\) is forward biased. At \(t=T_{sw}\)+\(t_{0}\), \(v_{CQ1}=v_{CQ6}=0\). Figure 4: \(Cont.\)  
High Input Voltage Range (\(Q_{3}\)-\(Q_{4}\) off, \(V_{in,H}=V_{in,max}\)/2-\(V_{in,max}\))  
Figure 2c shows the sub-circuit when \(V_{in}\) is in the high voltage range (\(V_{in,max}\)/2-\(V_{in,max}\)). Power switches \(Q_{3}\)-\(Q_{5}\) are turned off, and \(S\) and \(Q_{6}\) are always on. The half-bridge resonant circuit with the components \(L_{r1}\), \(L_{r2}\), \(C_{r1}\), \(C_{r2}\), and transformer \(T\) with \(2n_{p}\) primary winding turns is operated to regulate the load voltage. Because \(C_{r1}=C_{r2}\) and \(L_{r1}=L_{r2}\), the series resonant frequencies for three input voltage ranges in Figure 2 are identical.