# Analysis and Implementation of a Hybrid DC Converter with Wide Voltage Variation
## 4 Circuit Characteristics and Design Example
If 60 V \(\leq V_{in}\) < 120 V (low voltage range), then the full-bridge resonant circuit is operated on the left-hand side and the half-wave diode rectifier is used on the right-hand side of the converter, as shown in Figure 1b. If 120 V \(\leq V_{in}\) < 240 V (medium voltage range), then the half-bridge resonant circuit is operated on the left-hand side and half-wave diode rectifier is used on the right-hand side of the converter, as shown in Figure 1c. If 240 V \(\leq V_{in}\) < 480 V (high voltage range), then the half-bridge resonant circuit and full-wave diode rectifier are is operated on the left-hand side and right-hand side of the converter, respectively, as shown in Figure 1d. Due to the gains of the four mode operations in (8)-(11) having a similar transfer function, the circuit parameters in the laboratory prototype are obtained from low voltage range input (\(V_{in}\) = 60 V-120 V) under forward power flow. In the prototype design, the minimum voltage gain \(\mid M_{ac,FL}\mid_{min}\) is set at unity under \(V_{in}\) = 120 V and \(V_{o}\) = 40 V. The turn-ratio \(n\) of \(T\) is obtained from Equation (8) and given in Equation (12). \[ \begin{array}{ll}n=\Big{|}M_{ac,F,L}\Big{|}_{min}\times\frac{2V_{in,max}}{V_ {o,min}}=1\times\frac{2\times 120}{40}=6.\end{array}  \tag{12}\]  
The transformer \(T\) is implemented by magnetic core PC40/EE55 with 22 turns on the primary side and 4 turns on the secondary side. Thus, the actual turn-ratio \(n\) = 22/4 = 5.5. The maximum and minimum voltage gains at low voltage range input conditions are given in (13) and (14). \[ \begin{array}{ll}\Big{|}G_{ac,F,L}\Big{|}_{max}=\frac{nV_{o,max}}{2V_{in, min}}=\frac{5.5\times 52}{2\times 60}\approx 2.38.\end{array}  \tag{13}\]  
\[ \begin{array}{ll}\Big{|}G_{ac,F,L}\Big{|}_{min}=\frac{nV_{o,min}}{2V_{in,max}}= \frac{5.5\times 40}{2\times 120}\approx 0.92.\end{array}  \tag{14}\]  
The gain curves of the transfer function at the low voltage range input condition under \(K_{F}\) = 5 are plotted in Figure 6. Since the maximum voltage gain at \(V_{in}\) = 60 V and \(V_{o}\) = 52 V is 2.38 in (13), the quality factor \(Q_{F,h}\) = 0.2 is selected to have a peak voltage gain (= 2.5),which is greater than \(\mid G_{ac,FL}\mid max\) = 2.38. Therefore, the switching frequency index \(F_{F}\) is created and obtained under \(V_{in}\) = 60 V-120 V and \(V_{o}\) = 40 V-52 V. Then, the equivalent resistance \(R_{o,e,h}\) at full load is obtained as  
\[R_{o,e,h}=\frac{2n^{2}}{\pi^{2}}R_{o}=\frac{2\times 5.5^{2}}{3.14159^{2}}\times \frac{52}{7.7}\approx 41.4\ \Omega. \tag{15}\]  
The resonant components on the primary-side of the converter are calculated in Equations (16) and (17). \[C_{r,1}=1/(2\pi Q_{F,h}f_{r,1}R_{o,e,h})\approx 192\ \mathrm{nF}. \tag{16}\]  
\[L_{r,1}=Q_{F,h}R_{o,e,h}/(2\pi f_{r,1})\approx 13\ \mathrm{\mu H}. \tag{17}\]  
Since \(K_{F}\) = 5, the magnetizing inductance \(L_{m,1}\) = \(K_{F}L_{r,1}\) = 65 \(\mathrm{\mu H}\). The resonant components on the secondary-side of the converter are \(L_{r,2}\) = \(L_{r,1}/n^{2}\approx\) 0.43 \(\mathrm{\mu H}\) and \(C_{r,2}\) = \(n^{2}C_{r,1}\approx\) 5.8 \(\mathrm{\mu F}\). Magnetic cores PC40/EER35 are used to implement \(L_{r,1}\) and \(L_{r,2}\). \(S_{1}\)-\(S_{4}\) and \(S_{ac1}\) are implemented by power switches FGH60N60 with a 600 V/60 A rating, \(S_{5}\)-\(S_{8}\) and \(S_{ac2}\) are implemented by power switches P80 NF12 with a 120 V/80 A rating. The capacitances are \(C_{1}\) = \(C_{2}\) = 560 \(\mathrm{\mu F}\)/400 V, \(C_{3}\) = \(C_{4}\) = 220 \(\mathrm{\mu F}\)/100 V, and \(C_{o}\) = 660 \(\mathrm{\mu F}\)/100 V. Table 1 gives the circuit parameters used in the prototype circuit. Figure 6: Gain curves of the converter at low voltage range input.