## 2 Theoretical Analysis and Proposed Hybrid IPT System
### Analysis and Implementation of the CC Charging Mode with the ZPA Operation  
Generally, for the analysis of an LCT composed of different combination forms, \(M\)-style and \(T\)-style models are used as shown in Figure 6. We consider that the theoretical analysis needs to utilize the \(T\)-type model to construct a \(\Pi\)-style model. In the proposed topology's CC mode, the compensation capacitor needs to be compensated by the LCT's leakage inductance to realize the ZPA adjustment. Meanwhile, the mutual inductance of the LCT and the secondary side should form a \(\Pi\)-type resonance network to achieve the CC output. Therefore, the \(T\)-style model is used in this study to analyze the proposed IPT systems. As shown in Figure 5, the proposed IPT system works in the CC mode when both ACS \(S_{1}\) and \(S_{2}\) are set in the \"on\" state. Figure 7 presents the proposed IPT charger's equivalent circuit. The overall resonant compensation circuit can be divided into three parts: 1 a \(T-\)style resonant network, 2 the ZPA adjustment, and 3 a \(\Pi\)-style resonant network. Figure 5: The proposed hybrid compensation topology’s circuit diagram. Figure 6: The equivalent model of the LCT: (**a**) \(M-\)type model; (**b**) \(T-\)type model. According to the characteristics of the 7-style resonance network, the input voltage source \(U_{AB}\) cascading with \(L_{1}\) and \(C_{p1}\) is simplified to a current source \(I_{p}\) as exhibited in Figure 8, which can be expressed as:  
\[I_{p}=\frac{U_{AB}}{j\omega L_{1}} \tag{8}\]  
Here, \(L_{1}\) and \(C_{p1}\) should satisfy \(\omega^{2}=1/(L_{1}C_{p1})\). When \(I_{IN}\) flowing in the transmitter coil works at the resonant frequency point, its magnitude is only affected by the input voltage on the transmitter side; it does not change with variations in the loads or the coupling coefficient \(k\) on the secondary side. This helps form a uniform and stable magnetic induction intensity during the transmission process. Then, after 2 the ZPA adjustment, \(I_{p}\) flows into the \(\Pi-\)style resonant network composed of \(M\), \(L_{s}-M\), \(C_{p2}\), and \(C_{p2}\). In practice, the leakage inductance \(L_{s}-M\) and \(C_{p2}\) can be regarded as one device, which may be an inductor \(L_{se}\) or a capacitor \(C_{pe}\). According to (5), when the sum of the impedances of the three resonant elements in the \(\Pi-\)style resonant network is equal to zero, a CC output independent of the load change can be obtained. The resonant condition of \(M\), \(C_{p2}\), \(L_{se}\), and \(C_{pe}\) can be given as follows:  
\[\omega^{2}=\frac{1}{MC_{p2}}\,+\,\frac{1}{MC_{pe}}\quad\text{or}\quad\omega^{ 2}=\frac{1}{C_{p2}(M+L_{se})} \tag{9}\]  
where \(M=k/\sqrt{L_{p}L_{s}}\). Therefore, Figure 8a can be further expressed as shown in Figure 8b. The output current \(I_{ab}\) is given as follows:  
\[I_{ab}=\frac{M\text{U}_{AB}}{j\omega L_{1}L_{2}} \tag{10}\]  
Thus, we can express the transconductance gain, \(G_{UII}\), as follows:  
\[G_{UII}=\left|\frac{I_{ab}}{U_{AB}}\right|=\frac{M}{j\omega L_{1}L_{2}} \tag{11}\]  
For reducing the HFI's VA rating while satisfying the conditions of (8) and (9), the equivalent input impedance can be given as follows:  
\[Z_{IN}=\frac{L_{1}L_{2}}{\omega^{2}M^{2}C_{p1}C_{p2}R_{sc}} \tag{12}\]  
Figure 8: Circuit conversion process for the CC mode: (**a**) Circuit before conversion; (**b**) simplified circuit. Figure 7: The proposed hybrid topology’s equivalent analytical circuit for the CC mode. The proposed IPT charger can achieve a load-independent CC output under the ZPA condition without constraining the LCT parameters. The output current can be adjusted by changing \(L_{1}\) and \(L_{2}\) to obtain the desired charging current. ### Analysis and Implementation of the CC Charging Mode with the ZPA Operation  
In this section, the objective is to operate in the CV mode under the ZPA constraint of the proposed hybrid-topology switching IPT system without adding passive compensated components.