# Single-Stage Step-Down Power Factor Corrector without Full-Bridge Rectifier
## 3 Operating Principle  
The operating principle of the proposed single-stage step-down power factor corrector without a full bridge is analyzed, and then the corresponding related theoretical derivation is followed. For analysis convenience, the following assumptions are made first:  
1. All power switches, diodes, inductors, and capacitors are viewed as ideal components. 2. The value of the output capacitor \(C_{o}\) is large enough so that the voltage across \(C_{o}\) is stabilized at some output voltage. 3. The converter is operated in steady state under DCM. Based on the above assumptions, the illustrated waveforms of the inductor voltage and current in DCM are shown in Figure 4.  
State \(1\) [\(0\leq t\leq dT_{s}\)]: As shown in Figure 5, when the input voltage \(v_{in}\) is in a positive half-cycle, the switch \(S_{1}\) is turned on. The input current \(i_{in}\) flows through the switch \(S_{1}\), the body diode of the switch \(S_{2}\), the diodes \(D_{1}\) and \(D_{3}\), the output inductor \(L\), and the output capacitor \(C_{o}\). During this state, the voltage across the output inductor \(L\), called \(v_{L}\), is the input voltage \(v_{in}\) minus the output voltage \(V_{o}\), so the output inductor \(L\) is in magnetization mode and hence the inductor current \(i_{L}\) rises linearly. At the same time, the input power supply charges the output capacitor \(C_{o}\) and provides energy to the load \(R\). Moreover, the corresponding time experienced in this state is \(dT_{s}\). In the following, for the first three states, the switch \(S_{2}\) is always off, whereas for the last three states, the switch \(S_{1}\) is always off. As a result, the dead-time effect on switches [41] does not be considered for the proposed rectifier in the actual applications. Figure 4: Illustrated waveforms of inductor voltage and current in DCM in a positive half-cycle. Figure 3: System configuration. State 2 \([dT_{s}\leq t\leq T_{s}]\): As shown in Figure 6, when the input voltage \(v_{in}\) is in a positive half-cycle, the switch \(S_{1}\) is cut off, the input current \(i_{in}\) is zero, the diodes \(D_{1},D_{2},D_{3}\), and \(D_{4}\) conduct, and the inductor current \(i_{L}\) continues to flow through these four diodes. During this state, the voltage across the output inductor \(L\) is zero minus the output voltage \(V_{o}\), so the output inductor \(L\) is in demagnetization mode and hence the inductor current decreases linearly. At the same time, the output capacitor \(C_{o}\) and the output inductor \(L\) provide energy to the load \(R\). Moreover, the corresponding time experienced in this state is \(\Delta_{1}T_{s}\). State 3 \([(d+\Delta_{1})T_{s}\leq t\leq T_{s}]\): As shown in Figure 7, when the input voltage \(v_{in}\) is in a positive half-cycle, the switch \(S_{1}\) is still off and the diodes \(D_{1}\), \(D_{2}\), \(D_{3}\), and \(D_{4}\) are all cut off. During this state, there is no current flowing through the inductor \(L\). At the same time, the energy required for the load \(R\) is supplied by the output capacitor \(C_{o}\). Moreover, the corresponding time experienced in this state is \(\Delta_{2}T_{s}\). State 4 \([0\leq t\leq dT_{s}]\): As shown in Figure 8, when the input voltage is in a negative half-cycle, the switch \(S_{2}\) is turned on, and the input current \(i_{in}\) flows through the switch  
Figure 5: State 1. Figure 6: State 2. Figure 7: State 3. \(S_{2}\), the body diode of the switch \(S_{1}\), the diodes \(D_{2}\) and \(D_{4}\), the output inductor \(L\), and the output capacitor \(C_{o}\). During this state, the voltage across the output inductor \(L\), called \(v_{L}\), is the input voltage \(v_{in}\) minus the output voltage \(V_{o}\), so the output inductor \(L\) is in magnetization mode and hence the inductor current \(i_{L}\) rises linearly. At the same time, the input power supply charges the output capacitor \(C_{o}\) and provides energy to the load \(R\). Moreover, the corresponding time experienced in this state is \(DT_{s}\).