## 3 Operating Principle and Performance of DCM-CRM Cuk PFC Converter Utilizing VI Control
### Operation Principle of DCM-CRM Cuk PFC Converter Based on Variable Inductor Control  
Observing the input current Equation (7), if the input inductor of the DCM-CRM Cuk PFC converter can be a variable inductor whose inductance varies according to the following Formula (24), the input current will be an ideal sinusoid.  
\[L_{V}=\frac{L_{\text{initial}}}{[1-\frac{V_{M}}{V_{\text{C1}}}[\sin(\omega t)]]} \tag{24}\]  
where \(L_{\text{initial}}\) is a constant value.  
Based on the variable inductance in Expression (24), a DCM-CRM Cuk PFC converter utilizing variable inductor control is proposed as illustrated in Figure 5. This converter replaces the conventional input inductor with a variable inductor and integrates a calculation unit and a control unit to dynamically adjust the input inductance of the converter. The main power circuit components of the proposed DCM-CRM Cuk PFC converter are almost identical to the conventional DCM-CRM Cuk converter, except for replacing the constant input inductor with a variable input inductor.  
The control circuit of the proposed converter primarily comprises an output regulation circuit, a calculation unit of the variable inductor to obtain the value of input variable inductor \(L_{V}\), and a variable inductor control circuit to control the bias current flowing through the bias winding of outer legs. The output regulation circuit utilizes voltage mode control, while the calculation unit of the variable inductor is achieved by a digital control board with an STM32 microcontroller. The variable inductor control circuit primarily includes an operational amplifier, a power Mosfet \(S_{2}\), and a bias resistor \(R_{\text{bias}}\).  
The output error signal is generated by amplifying the difference between the feedback signal of the output voltage sampling circuit and the reference voltage \(V_{\text{ref}}\). This error signal is then fed to the negative input of the comparator. When the output inductor current drops to zero moment, ZCD auxiliary winding voltage experiences a high to low jump variation. At this time, the RS flip-flop detects the level variation of ZCD auxiliary winding at this moment, then \(S_{1}\) is turned on, and then the current source \(I_{\text{dc}}\) by charging the capacitor \(C_{3}\) so that the capacitor voltage continues to rise until it exceeds the error signal. Furthermore,  
Figure 5: Control circuit for DCM-CRM Cuk PFC Converter with variable inductor.  
the RS flip-flop output is low level to make the switch off, so the output inductor current \(i_{\text{L2}}\) is linearly down, and so on. The inductance of the input variable inductor \(L_{V}\) is determined by the calculation result of the calculation unit of the variable inductor with the input signal of the sampled rectified input voltage and the calculated intermediate capacitor voltage. The bias voltage of the input signal of the variable inductor control circuit is converted from the digital output signal of the calculation unit of the variable inductor unit to an analog signal by the DAC block. This bias voltage \(V_{\text{bias}}\) is then converted into a bias current \(i_{\text{bias}}\) by a voltage-controlled current source comprising an operational amplifier, a bias resistor \(R_{\text{bias}}\), and a MOSFET \(S_{2}\) operating in saturation mode. The resulting bias current \(i_{\text{bias}}\) is subsequently injected into the auxiliary winding of the variable input inductor \(L_{V}\) through the variable inductor control circuit, thereby achieving the desired inductance value.  
The proposed converter is operated in DCM-CRM mode. Figure 6 shows the key waveforms of the output inductor current \(i_{\text{L2}}\) and the input inductor current \(i_{\text{LV}}\) as well as the timing of the switch drive signal during the half-line cycle. The \(L_{V}\) operates in the DCM mode and the output inductor \(L_{2}\) operates in the CRM mode.