# Hybrid LLC Converter with Wide Range of Zero-Voltage Switching and Wide Input Voltage Operation
## 3 Circuit Analysis and Principle of Operation  
From the ON-OFF states of \(\rm S_{ac1}\) and \(\rm S_{ac2}\) in Figure 2b-d, the proposed LLC converter can be controlled under three voltage input regions: \(\rm V_{in-H}\): 400 V-200 V (high voltage region), \(\rm V_{in-M}\): 200 V-100 V (medium voltage region) and \(\rm V_{in-L}\): 100 V-50 V (low voltage region). When \(\rm V_{in}\) is in the high voltage, the converter only needs low voltage gain to control load voltage. Therefore, \(\rm S_{ac1}\) turns on and \(\rm S_{ac2}\), \(\rm S_{1}\) and \(\rm S_{2}\) turn off. The half bridge LLC resonant circuit and low secondary turns are used in Figure 2b. \(\rm S_{3}\) and \(\rm S_{4}\) are operated with frequency control. According to the resonant circuit by \(\rm L_{r}\), \(\rm C_{r}\)  
Figure 2: Circuit schematics (**a**) the proposed converter (**b**) high voltage input region (200 V–400 V) (**c**) medium voltage input region (100 V–200 V) (**d**) low voltage input region (50 V–100 V). \(\rm L_{m}\) and \(\rm R_{o}\), the voltage gain under high voltage input region is \(\rm V_{o}/V_{in-H}=n_{s}G_{ac}(f_{sw})/n_{p}\), where \(G_{ac}(f)\) is the transfer function by \(\rm L_{r}\), \(\rm C_{r}\), \(\rm L_{m}\) and \(\rm R_{o}\). The LLC converter has four or six operating modes under \(f_{sw}\) (switching frequency) \(>\) or \(<\rm f_{r}\) (resonant frequency). Since the converter is designed to have wide voltage gain, \(f_{sw}\) is always less than or close to \(\rm f_{r}\). Therefore, the zero-voltage switching (ZVS) of \(\rm S_{3}\) and \(\rm S_{4}\) and zero-current switching (ZCS) of \(\rm D_{3}\) and \(\rm D_{4}\) are accomplished. The PWM waveforms of LLC converter operated for high voltage region are illustrated in Figure 3a and the Figure 3b-g provide the equivalent circuits for modes 1-6 for one switching cycle. **Mode 1 [t\({}_{0}\), t\({}_{1}\)]:** At \(\rm t_{0}\), \(\rm v_{CS4}=0\). The current \(\rm i_{Lr}\) flows through \(\rm D_{S4}\) and \(\rm S_{4}\) turns on at this instant to have ZCS operation. The secondary current is positive so that \(\rm D_{3}\) is conducting and capacitor \(\rm C_{o1}\) is charged. The components \(\rm C_{r}\) and \(\rm L_{r}\) are naturally resonant and the resonant frequency \(\rm f_{r}\approx 1/2\pi\sqrt{\rm L_{r}C_{r}}\). **Mode 2 [t\({}_{1}\), t\({}_{2}\)]:** Since \(\rm f_{r}>f_{sw}\), \(\rm i_{03}\) is decreased to zero at \(\rm t_{1}\) with ZCS operation and \(\rm i_{Lr}(t_{1})=i_{Lm}(t_{1})\). Thus, the load current \(\rm I_{o}\) will discharge \(\rm C_{o1}\) and \(\rm C_{o2}\). The current \(\rm i_{Lm}(t_{2})\) is obtained \(\rm i_{Lm}(t_{2})\approx(n_{p}V_{o})/(8n_{s}L_{m}f_{sw})\). **Mode 3 [t\({}_{2}\), t\({}_{3}\)]:** Power device \(\rm S_{4}\) turns off at \(\rm t_{2}\). \(\rm i_{Lr}(t_{2})\) will discharge (charge) \(\rm C_{S3}\) (\(\rm C_{S4}\)). Due to \(\rm i_{Lr}(t_{2})<i_{Lm}(t_{2})\), \(\rm D_{4}\) will naturally conduct and capacitor voltage \(\rm v_{C02}\) is increased. **Mode 4 [t\({}_{3}\), t\({}_{4}\)]:** At the start of this mode, the capacitor voltage \(\rm v_{CS3}=0\). \(\rm i_{Lr}(t_{3})\) is positive and \(\rm D_{S3}\) is conducting so that \(\rm S_{3}\) can turn on at this instant to accomplish ZVS. In mode 4, the resonant tank transfers power from input terminal \(\rm V_{in}\) to output terminal \(\rm V_{o}\). **Mode 5 [t\({}_{4}\), t\({}_{3}\)]:** The diode current \(\rm i_{D4}\) will naturally turn off at \(\rm t_{4}\) due to \(\rm f_{r}>f_{sw}\). In this mode, the load current \(\rm I_{o}\) discharges \(\rm C_{o1}\) and \(\rm C_{o2}\). The current \(\rm i_{Lm}(t_{5})\) is obtained \(\rm i_{Lm}(t_{5})\approx-(n_{p}V_{o})/(8n_{s}L_{m}f_{sw})\). **Mode 6 [ts, \(\rm T_{sw}\) + t\({}_{0}\)]:**\(S_{3}\) turns off at the start of this mode. \(\rm i_{Lr}(t_{5})\) discharge (charge) \(\rm C_{S4}\) (\(\rm C_{S3}\)) and \(\rm D_{3}\) start conducting. To achieve zero-voltage switching of \(\rm S_{4}\), \(\rm|i_{Lm}(t_{5})|\) must be greater than \(\rm V_{in-H}\sqrt{2C_{oss}/(L_{m}+L_{r})}\). At the end of this mode, \(\rm v_{CS4}=0\).