## 2 Operation Principle of the Conventional DCM-CRM Cuk PFC  
The main circuit configuration of the conventional DCM-CRM Cuk PFC converter is depicted in Figure 1. As illustrated, the main components include a rectifier bridge, an input LC filter \(L_{f}\) and C\({}_{f}\), two power diodes \(D_{0}\) and \(D_{1}\), a power switch \(S_{1}\), an input inductor \(L_{1}\), an output inductor \(L_{2}\) with auxiliary winding for zero current detection, an intermediate capacitor \(C_{1}\), and an output capacitor \(C_{2}\). The operating waveforms of the conventional DCM-CRM Cuk PFC converter are depicted in Figure 2. From top to bottom, the waveforms illustrate the switching drive signal \(V_{g}\), the input inductor current \(i_{L1}\), and the output inductor current \(i_{L2}\). The DCM-CRM Cuk PFC converter undergoes three distinct operating modes within each switching cycle. Mode I (0-\(t_{0}\)): During this interval, the drive signal \(V_{g}\) activates the switch, causing the voltage at the left terminal of the intermediate storage capacitor \(C_{1}\) to drop rapidly to zero. And since the voltage at the two ends of the capacitor cannot be changed abruptly, the voltage at the right end of the capacitor becomes negative. This results in the diode \(D_{1}\) being subjected to reverse voltage, thereby turning it off. The AC power source charges the input inductor \(L_{1}\) through diode \(D_{0}\) and switch \(S_{1}\). Simultaneously, the intermediate energy storage capacitor \(C_{1}\) powers the output inductor \(L_{2}\), output capacitor \(C_{2}\), and load via the \(S_{1}\). The increasing slopes of the currents flowing through the input and output inductors can be expressed as  
\[\frac{di_{L1}}{dt}=\frac{v_{\text{Rec}}}{L_{1}} \tag{1}\]  
\[\frac{di_{L2}}{dt}=\frac{V_{\text{C1}}-V_{0}}{L_{2}} \tag{2}\]  
where \(v_{\text{rec}}\) denotes the rectified voltage; \(V_{\text{C1}}\) represents the voltage across the intermediate capacitor \(C_{1}\); and \(V_{0}\) indicates the output voltage. Figure 1: Main power circuit of the conventional DCM-CRM Cuk PFC converter. Mode II (\(t_{0}\)-\(t_{1}\)): In this mode, the driving signal \(V_{\rm g}\) turns off the switch, while diode \(D_{0}\) remains in conduction. Diode \(D_{1}\) is subjected to a positive voltage, initiating conduction to provide access to the input circuit. The rectified voltage \(v_{\rm rec}\) and the input inductor \(L_{1}\) commence charging the intermediate capacitor \(C_{1}\) through \(D_{0}\) and \(D_{1}\). Meanwhile, the output capacitor \(C_{2}\) stores energy transferred from the output inductor \(L_{2}\). The rate of voltage decrease across both input and output inductors can be expressed as  
\[\frac{di_{L1}}{dt}=\frac{V_{\rm C1}-v_{\rm Rec}}{L_{1}} \tag{3}\]  
\[\frac{di_{L2}}{dt}=\frac{V_{\rm o}}{L_{2}} \tag{4}\]  
Mode III (\(t_{1}\)-\(t_{2}\)): The input inductor current \(i_{L1}\) drops to zero, causing diode \(D_{0}\) to turn off, while diode \(D_{1}\) remains conducting. During this phase, the output inductor \(L_{2}\) supplies the load through \(D_{1}\), forming the output circuit, and the current \(i_{L2}\) continues to decrease. When the output inductor current \(i_{L2}\) reaches zero, it is detected by the zero-crossing detection (ZCD) module. This triggers the driving signal \(V_{\rm g}\) to turn on the switch, transitioning \(L_{2}\) to CRM, and initiating the next operating cycle of the converter. According to Equation (1), during one switching cycle, the peak current \(i_{L1\_{\rm pk}}(t)\) through the input inductor \(L_{1}\) can be expressed as  
\[i_{L1\_{\rm pk}}(t)=\frac{V_{M}|\text{sin}(\omega t)|}{L_{1}}t_{\text{on}} \tag{5}\]  
where \(t_{\text{on}}\) is the turn-on time of switch \(S_{1}\) within one switching period, it is critical for determining the peak current \(i_{L1\_{\rm pk}}(t)\) through the input inductor \(L_{1}\). \(V_{\rm M}\) is the amplitude value of the AC input voltage. \(\omega\) is the angular frequency of the AC input voltage.