## 1 Introduction  
With the rapid advancement of electronic devices, the demand for switching power supplies has surged significantly. Power factor correction (PFC) converters have been extensively utilized to mitigate input current distortion and ensure compliance with stringent harmonic standards. Certain commercial power supply products must comply with the IEC 61000-3-2 standard to mitigate the potential damage to the power grid caused by harmonic injection [1, 2, 3, 4, 5]. Among the various PFC converter topologies commonly used, the Boost converter is particularly favored because of its ability to achieve low input current ripple and maintain high efficiency. However, the Boost PFC converter faces several challenges, including high output voltage due to the need for the output voltage to exceed the peak input voltage, large input inrush current, and difficulty in achieving output short-circuit protection. These limitations restrict the applicability of the Boost PFC converter in certain scenarios [2, 3, 4]. The conventional Buck PFC converter offers advantages such as low voltage stress on the power switch and effective step-down conversion. Nevertheless, its operation is limited to lower voltage conditions. When the input voltage falls below the output voltage, a dead zone in the input current occurs, leading to a degraded power factor (PF) and increased total harmonic distortion (THD) of the input current. This restricted output voltage range further limits the applicability of the Buck PFC converter [5; 6; 7]. The Buck-Boost PFC converter offers inherent current shaping, cost-effectiveness, and the capability to perform both step-up and step-down conversions. However, compared to the traditional Boost and Buck converters, Buck-Boost PFC presents several drawbacks including low efficiency and high voltage stress of the main power switch due to the inductor only supplying energy to the load when the main switch is off, and the discontinuous input current leading to worse harmonic distortion in the power grid [8; 9]. The Cuk converter, introduced by [PERSON] in 1977 [10], features an input stage similar to a Boost converter, which provides the advantage of continuous input current and can be used for achieving PFC. The output stage of the Cuk converter resembles a Buck converter, enabling DC-DC conversion. Consequently, the Cuk converter generates minimal electromagnetic interference and output voltage ripple, which seems to be a better candidate in the basic PFC converter topology [11], leading to its widespread application in recent years. In [12], a Cuk PFC converter is used for driving brushless DC motors, which reduces system power consumption, achieves high efficiency, and also lowers costs. In [13], to improve the efficiency of the two-stage converters for electric bike battery charging, a switched inductor Cuk PFC converter was proposed. Compared to conventional two-stage converters, this topology offers advantages such as higher voltage gain, reduced current stress, and improved efficiency. In [14], a three-phase-isolated Cuk converter-based PFC rectifier is proposed. The converter operates in discontinuous output inductor current mode and requires only a simple voltage control loop to achieve PFC for the AC input. This design reduces the system cost while enhancing reliability and efficiency. Therefore, the Cuk PFC converter is widely used in many applications, but it still has some shortcomings. In [15], the harmonic balance method and Floquet theory are used to study the influence of intermediate capacitance on the slow-scale instability of operating in discontinuous capacitor voltage mode with a Cuk PFC converter. The research results show that with the increase in intermediate capacitance, the stability of the converter will be reduced due to period-doubling bifurcation, thereby reducing PF. The bridgeless Cuk PFC converter, by reducing the number of semiconductors in the circuit, lowers conduction losses and finds widespread application in various fields.