# Hybrid Resonant Converter with Three Half-Bridge Legs for Wide Voltage Operation
## 4 Design Procedures and Test Results  
The design procedures and test results of the presented circuit are verified in this section. A laboratory circuit was built and the electric specifications were \(V_{in}=50\)-\(400~{}\mathrm{V}\), \(V_{o}=48~{}\mathrm{V}\), and \(I_{o,max}=10~{}\mathrm{A}\). The series resonant frequency was designed at \(150~{}\mathrm{kHz}\). Due to \(L_{r1}=L_{r2}\) and \(C_{r1}=C_{r2}\), the series resonant frequencies for all three equivalent circuits shown in Figure 2 were identical and designed at \(150~{}\mathrm{kHz}\). According to the voltage transfer function in Equation (5), the gain curves of the developed resonant converter with different input voltage ranges are given in Figure 7. The transition voltage \(V_{in,tran\,1}\) between the low and medium input voltage ranges was designed at \(100~{}\mathrm{V}\) with \(\pm 5~{}\mathrm{V}\) voltage  
Figure 6: Equivalent circuit of the resonant tank. tolerance. Similarly, the transition voltage \(V_{in,tran\,2}\) between the medium and high input voltage ranges was designed at 200 V with \(\pm 5\) V voltage tolerance. From Equation (6), one can observe that the voltage gain at the high input voltage range was about two (four) times of the voltage gain at the medium (low) input voltage range. The design procedures for three equivalent resonant circuits were almost identical. Therefore, the prototype circuit was designed at the low input voltage range to simplify the design consideration. The minimum voltage gain \(G_{ac,min}\) at the series resonant frequency was designed as unity and the transition voltage \(V_{in,trans\,1}\) = 100 V. The turns ratio \(n_{1}\) = \(n_{p}\)/\(n_{s}\) can be calculated from Equation (5) and expressed in Equation (7):  
\[n_{1}=G_{ac,min}\times V_{in,tran\,1}/V_{o}=1\times 100/48\approx 2.08. \tag{7}\]  
Transformer \(T\) is implemented by the TDK (Tokyo Electric Chemical Industry Co., Ltd., Tokyo, Japan) magnetic core with \(\Delta B\) = 0.4 _tesla_ and \(A_{e}\) = 354 mm\({}^{2}\). The series resonant frequency was selected at 150 kHz. The primary turns of transformer are obtained in Equation (8):  
\[n_{p,min}>n_{1}V_{o}/[f_{sw}\Delta BA_{e}]=2.08\times 48/[150000\times 0.4\times 0.000354]\approx 4.7. \tag{8}\]  
The actual primary turns and secondary turns in the prototype circuit were \(n_{p}\) = 8 and \(n_{s}\) = 4. The equivalent resistance \(R_{eq}\) at the rated power is given in Equation (9):  
\[R_{eq}=8n_{1}^{2}R_{o}/\pi^{2}=8\times 2^{2}\times(48/10)/3.14159^{2}=15.56\ \Omega. \tag{9}\]  
The inductor ratio \(l_{n}=L_{m1}\)/\(L_{r1}\) = 3 and quality factor \(x\) = 0.25 were selected in the prototype circuit. \(L_{r1}\) and \(L_{r2}\) are obtained from Equation (10) and \(C_{r1}\) and \(C_{r2}\) are calculated in Equation (11):  
\[L_{r1}=L_{r2}=\frac{xR_{eq}}{[2\pi f_{r}]}=4.13\ \mu\mathrm{H}, \tag{10}\]  
\[C_{r1}=C_{r2}=\frac{1}{4\pi^{2}L_{r1}f_{r}^{2}}\approx 273\ \mathrm{nF}. \tag{11}\]  
The magnetizing inductors \(L_{m1}\) and \(L_{m2}\) are expressed in Equation (12):  
\[L_{m1}=L_{m2}=l_{n}\times L_{r1}\approx 12.4\ \mu\mathrm{H}. \tag{12}\]  
The voltage stress of power MOSFETs (metal-oxide-semiconductor field-effect transistor) \(Q_{1}\)-\(Q_{6}\) and switch \(S\) was the maximum input voltage \(V_{in,max}\) = 400 V. The theoretical voltage ratings of the rectifier diodes \(D_{1}\) and \(D_{2}\) were 2\(V_{o}\) = 98 V. Figure 8 shows the control block of the signals \(Q_{1}\)-\(Q_{6}\) and \(S\). Two Schmitt trigger comparators were used for transition voltages 100 and 200 V to select the correct range of input voltage. Figure 9 and Table 1 give the photographs and all circuit components used in the prototype circuit, respectively. Figure 9a shows the photograph of the prototype circuit. The control board for selecting the correct range of input voltage and the consequent bridge configuration is given in Figure 9b. The experimental setup, including the test equipment, is provided in Figure 9c.