# Analysis of AC DC Four-Switch Boost-Buck Battery Charger Converter for EV Applications
## 2 Circuit Operation  
This section will provide a detailed operation discussion on the AC/DC boost-buck PFC converter illustrated in Figure 2. The analyzed converter has been specifically designed to function in CCM, where the ripple current is significantly smaller than the average current. It is important to note that the analysis of the converter assumes ideal components, including capacitors, inductors, diodes, and MOSFETs. No equivalent series resistance (ESR) or other parasitic effects are taken into consideration.  
The sinusoidal input voltage is obtained from a passive 4 diodes' rectifier, which is connected to the grid input voltage, which leads to a rectified sine wave. Two modes of operation for this converter where the power can transfer from the input to the output port occur according to the needed input and output voltages.  
The first is the boost mode where output voltage is higher than input voltage. The switch \(Q_{1}\) and switch \(Q_{2}\) are the two primary switches for this mode. Figure 2(a) can illustrate the simplified model for the boost switching model. During this mode, the switch \(Q_{4}\) remains on while switch \(Q_{3}\) remains off throughout the entire period. In the boost mode, inductor \(L_{1}\) and \(L_{2}\) serve as the energy transfer component. The converter operates in CCM, and has two states. Switch \(Q_{2}\) is turned off while switch \(Q_{1}\) is turned on in the first state. Simultaneously, charging for inductors \(L_{1}\) and \(L_{2}\) is starting and the intermediate capacitor C discharges. In the second state, switch \(Q_{2}\) is turned on while switch \(Q_{1}\) is turned off, allowing inductor \(L_{1}\) and \(L_{2}\) to discharge their energy and charge the intermediate capacitor C and the output capacitor \(C_{o}\), respectively.  
The second mode is buck where output voltage is lower than input voltage. The switch \(Q_{3}\) and switch \(Q_{4}\) are the two primary switches for this mode. Figure 2(b) can illustrate the simplified model for the buck switching model. Conversely, switch \(Q_{1}\) remains off while switch \(Q_{2}\) remains on throughout the entire period. For this mode, the primary energy transfer component is inductor \(L_{2}\). As the converter operates in CCM, the first state happens when switch \(Q_{3}\) is turned off and switch \(Q_{4}\) is turned on. The intermediate capacitor C discharges to the output load and inductor \(L_{2}\) charges. The second state occurs when switch \(Q_{3}\) is turned on and switch \(Q_{4}\) is turned off. At that moment, the intermediate capacitor \(C\) charges up and inductor \(L_{2}\) begins to discharge.  
Due to the variable AC line input voltage, the converter operates in two distinct modes based on the output voltage requirements. Figure 4 shows the operation principle for the converters, wherein the converter operates in the boost mode when \(V_{o}>V_{g,p}\) for the whole double line period. However, the converter operates in the buck mode, when \(V_{o}<V_{g,p}\), for a portion of the double line. The rest of the period is working in the boost mode. Consequently, the converter utilizes approximately 75% of its operation in the boost mode and the remaining 25% operates in the buck mode.  
Figure 3: Simplified model for AC/DC boost-buck PFC converter at (**a**) boost mode; (**b**) buck mode.  
Figure 2: AC/DC boost-buck PFC converter.