# Hybrid Resonant Converter with Three Half-Bridge Legs for Wide Voltage Operation
## 2 Circuit Structure and Principle of Operation  
The circuit schematic of the developed circuit topology with wide voltage operation is shown in Figure 1. Three half-bridge legs (\(Q_{1}\)-\(Q_{6}\)) are used on the input side and one center-taped rectifier is used on the output side. Two resonant circuits (\(L_{r1}\), \(C_{r1}\), \(L_{r2}\) and \(C_{r2}\)) with one AC power switch \(S\) are used to accomplish series resonant operation with soft switching behavior for power switches. \(V_{in}\) (\(V_{o}\)) is the input (output) voltage and \(R_{o}\) is the output resistor. Transformer \(T\) has two primary and secondary winding sets with \(n_{p}\) and \(n_{s}\) winding turns, respectively. According to the switching states of \(Q_{1}\)-\(Q_{6}\) and \(S\), the developed converter can be operated under three input voltage ranges: \(V_{in,L}=V_{in,max}/8-V_{in,max}/4\), \(V_{in,M}=V_{in,max}/4\)-\(V_{in,max}/2\) and \(V_{in,H}=V_{in,max}/2\)-\(V_{in,max}\), as shown in Figure 2. Figure 2a gives the equivalent resonant circuit if \(V_{in}\) is under the low voltage range \(V_{in,L}\). To achieve the higher voltage gain in the proposed converter, \(Q_{5}\), \(Q_{6}\), and \(S\) are off. Only a full-bridge converter with \(Q_{1}\)-\(Q_{4}\), \(L_{r1}\), \(C_{r1}\), and \(T\) with \(n_{p}\) primary turns are operated on the input-side. The DC voltage gain of the resonant circuit in Figure 2a is \(V_{o}/V_{in,L}=G_{L}(f)n_{s}/n_{p}\), where \(G_{L}(f)\) is the voltage gain of the proposed converter in Figure 2a. Figure 2b illustrates the equivalent circuit if \(V_{in}\) is under the medium voltage range \(V_{in,M}\). In the medium voltage range, \(Q_{3}\) and \(Q_{4}\) are off. The resonant tank includes \(L_{r1}\), \(C_{r1}\), \(L_{r2}\), \(C_{r2}\), and transformer \(T\) with \(2n_{p}\) primary winding turns. The series resonant frequency of this equivalent circuit is also \(f_{r}=1/2\pi\sqrt{L_{r1}C_{r1}}\) due to \(C_{r1}=C_{r2}\) and \(L_{r1}=L_{r2}\). The DC voltage gain of the resonant circuit shown in Figure 2b is \(V_{o}/V_{in,M}=G_{M}(f)n_{s}/(2n_{p})\) due to the primary turns being \(2n_{p}\) instead of \(n_{p}\), where \(G_{M}(f)\) is the voltage gain of the proposed converter in Figure 2b. Figure 2c provides the equivalent circuit if \(V_{in}\) is under the high voltage range \(V_{in,H}\). In high voltage range, \(Q_{3}\), \(Q_{4}\), and \(Q_{5}\) are off and \(S\) and \(Q_{6}\) are on. The half-bridge resonant converter with the components \(Q_{1}\), \(Q_{2}\), \(L_{r1}\), \(C_{r1}\), \(L_{r2}\), \(C_{r2}\), and transformer \(T\) with \(2n_{p}\) primary winding turns is operated to achieve lower voltage gain. The series resonant frequency of this equivalent circuit is \(f_{r}=1/2\pi\sqrt{L_{r1}C_{r1}}\) with \(L_{r1}=L_{r2}\) and \(C_{r1}=C_{r2}\). Compared to the equivalent circuit in Figure 2b, the fundamental input voltage is \(V_{in}\)/2 in Figure 2c instead of \(V_{in}\) in Figure 2b. The DC voltage gain of the equivalent circuit in Figure 2c is \(V_{o}/V_{in,H}=G_{H}(f)n_{s}/(4n_{p})\), where \(G_{H}(f)\) is the voltage gain of the proposed converter in Figure 2c. Compared to the DC voltage gain under three different input voltage gains, it observes that \(V_{o}/V_{in,L}=2(V_{o}/V_{in,M})\) = \(4(V_{o}/V_{in,H})\) if \(G_{L}(f)=G_{M}(f)=G_{H}(f)\). Thus, the voltage gain of resonant circuit in Figure 2a is the largest compared to the resonant circuits in Figure 2b,c. Power switches \(Q_{1}\)-\(Q_{6}\) and \(S\) can be properly controlled from three equivalent circuits, as shown in Figure 2 to have 8:1 (\(V_{in,max}\) = 8\(V_{in,min}\)) wide voltage range operation. Figure 1: Circuit schematic of the developed converter. Figure 2: Circuit diagrams for different input voltage ranges: (**a**) low input voltage (\(V_{in,L}\) = \(V_{in,max}\)/8\(-V_{in,max}\)/4); (**b**) medium input voltage (\(V_{in,M}\) = \(V_{in,max}\)/4\(-V_{in,max}\)/2); (**c**) high input voltage (\(V_{in,H}\) = \(V_{in,max}\)/2\(-V_{in,max}\)).