## 1 Introduction  
Since traditional wired power supply methods limit the flexibility of electrical equipment and have potential safety hazards, inductive power transfer (IPT) is proposed to provide flexible and reliable power transmission. Inductive power transfer is a technology using electromagnetic fields or electromagnetic waves to transmit electrical energy contcatiessly. Due to the inherent advantages of IPT, it has significant research value and broad application prospects. At present, IPT has been applied in various industrial applications, such as portable electronic devices [1, 2], light-emitting diode (LED) lighting applications [3, 4], biomedical implants [5, 6], electric vehicles [7, 8], unmanned aerial vehicles [9, 10], underwater applications [11], etc. Lithium-ion batteries are widely used as energy storage devices due to their safety, good high-temperature performance, extended service life, and high energy density [12]. It is well known that the load of the battery continues to increase during battery charging. To ensure battery performance and prolong battery life, an IPT system with stable constant current output (CCO) and constant voltage output (CVO) should be designed according to the battery charging law. Figure 1 shows a typical battery charging curve. Generally, the battery is first charged in CC mode. As the battery load continues to increase, the battery charging voltage increases. Once the charging voltage reaches a preset value, the system switches to CV mode. The charging current of the battery then gradually decreases until charging is completed. In recent years, scholars have made many innovative attempts to design an IPT system with CCO and CVO functions. In general, IPT systems have four basic topologies, namely, series-series (SS), series-parallel (SP), parallel-series (PS), and parallel-parallel (PP) [13]. It has been proven that under specific parameters, SS and PS can provide load-independent CCO characteristics, while SP and PP can provide load-independent CVO characteristics [14, 15]. To realize reliable CCO and CVO functions, in [13], the aforementioned four basic topologies are combined, and hybrid topologies combining SS and PS, and SP and PP, respectively, are proposed. In addition, refs. [16; 17; 18; 19] all achieved CCO and CVO characteristics with ZPA operation by designing different hybrid topologies. However, the proposed structures in [13; 16; 17; 18; 19] must introduce additional AC switches and compensation elements, which increases the cost and size of the systems. Therefore, the hybrid topology switching method is not the optimal solution for achieving CCO and CVO characteristics. In view of this, the authors in [20] proposed a method to achieve CCO and CVO characteristics by changing the operating frequency. Although complex topology switching is not required, SS topology can only achieve purely resistive input impedance in CC mode. In CV mode, ZPA operation cannot be satisfied, which will inevitably lead to massive power loss. In [21], the authors proposed an S/S/P topology that can provide CCO and CVO characteristics at two frequencies. Unfortunately, the volume, weight, and cost of the receiver are increased due to a bulky filter inductor behind the rectifier in this system. In [22], [PERSON] et al. deduced and verified that a dual LCC topology could realize CCO and CVO characteristics at two frequency points. However, due to the large number of compensation components derived from this topology, this solution suffers from the same structural drawbacks as [21]. In [23], the authors presented a new three-coil parameter design approach to achieve CCO and CVO by modifying the frequency. In addition, [PERSON] et al. [24] comprehensively analyzed a four-coil IPT system and realized CCO and CVO functions at two distinct frequency points. However, the three-coil IPT system in [23] and the four-coil IPT system in [24] both have a rigorous mutual inductance relationship, which increases the design difficulty and instability of the system.