## 2 Theoretical Analysis and Proposed Hybrid IPT System  
### The Principle of Constant Voltage/Current Outputs of Second- and Third-Order Resonant Networks  
In the IPT system, the LCT's coupling coefficient \(k\) is small, resulting in a large amount of inductive reactive power. To reduce it, a compensation network must be added. Meanwhile, CC or CV output characteristics independent of the output impedance can be realized by using the passive resonant network. Figure 3a shows a \(\Gamma\)-style resonant network with a CV output driven by a current source, and Figure 3b shows a \(\Gamma\)-style resonant network with a CC output driven by a voltage source. In Figure 3a, \(I_{\text{IN}}\) represents a CC source; \(Z_{\Gamma 1}\) and \(Z_{\Gamma 2}\) represent the impedances of the compensation components; \(Z_{\text{R}}\) represents the load impedance; the load voltage \(U_{\text{o}}\) and input impedance \(Z_{\Gamma IN}\) are expressed as follows:  
\[\left\{ \begin{array}{l}U_{\text{o}}=\dfrac{Z_{\Gamma 1}Z_{R}l_{IN}}{Z_{ \Gamma 1}+Z_{\Gamma 2}+Z_{R}}\\ Z_{\Gamma IN}=(Z_{R}+Z_{\Gamma 2})||Z_{\Gamma 2}=X^{2}/Z_{R}-Z_{\Gamma 1}\end{array} \right. \tag{1}\]  
where \(Z_{\Gamma 1}=jX_{\Gamma 1}\) and \(Z_{\Gamma 2}=-jX_{\Gamma 2}\). To achieve a CV output, \(Z_{\Gamma 1}+Z_{\Gamma 2}\) should be equal to 0, and the output voltage can be represented as follows: \(U_{\text{o}}=Z_{\Gamma 1}I_{\text{IN}}=-Z_{\Gamma 2}I_{\text{IN}}\). Additionally, the output voltage should be independent of the dynamic loads. Thus, the CC\(-\)source input should include the impedance \(Z_{\Gamma 1}\) to neutralize the impedance in the \(\Gamma\) resonant network. The \(\Gamma\)-style resonant network has a CV output. In Figure 3b, \(U_{\text{IN}}\) represents a CV source, and \(Z_{\Gamma 1}\) and \(Z_{\Gamma 2}\) represent the impedances of the resonant components. The output current \(I_{\text{o}}\) and input impedance \(Z_{\mathcal{T}IN}\) can be represented as follows:  
\[\left\{ \begin{array}{l}I_{\text{o}}=\dfrac{Z_{\Gamma 2}U_{\text{IN}}}{Z_{ \Gamma 1}Z_{\Gamma 2}+(Z_{\Gamma 1}+Z_{\Gamma 2})Z_{R}}\\ Z_{\Gamma IN}=Z_{R}//(-jX)+jX=X^{2}/(Z_{R}-jX)\end{array} \right. \tag{2}\]  
where \(Z_{\Gamma 1}=jX_{\Gamma 1}\) and \(Z_{\Gamma 2}=-jX_{\Gamma 2}\). Clearly, to satisfy the load-independent purely resistive CC output, only when \(Z_{\Gamma 1}+Z_{\Gamma 2}=0\) and \(Z_{R}\) contains \(Z_{\Gamma 1}\), the output current \(I_{\text{o}}\) can be expressed as: \(I_{\text{o}}=U_{\text{IN}}/Z_{\Gamma 1}=-U_{\text{IN}}/Z_{\Gamma 2}\). Figure 3: (a) A \(\Gamma\)-style resonant network; (b) A \(\Gamma\)-style resonant network. In addition to the second-order resonant network, by combining the \(\Gamma\)-style and \(\mathcal{T}\)-style resonant networks, we can obtain a third \(-\)order \(\Pi\)-style resonant network as shown in Figure 4.  
According to [PERSON]'s current law, the \(\Pi\)-style resonant network can be described as:  
\[I_{o}=\frac{Z_{\Pi\Pi}Z_{\Pi 3}I_{IN}}{(Z_{\Pi\Pi}+Z_{var\Pi 2})Z_{\Pi 3}+(Z_{ \Pi\Pi}+Z_{\Pi 2}+Z_{\Pi 3})Z_{R}} \tag{3}\]  
Hence, the transconductance \(G_{\Pi I}\), which is defined as the ratio of the output current \(I_{o}\) of the rectifier to the input current \(I_{IN}\) of the high-frequency inverter (HFI), can be determined as:  
\[G_{\Pi I}=\left|\frac{I_{o}}{I_{IN}}\right|=\left|\frac{Z_{\Pi \Pi}Z_{\Pi 3}}{(Z_{\Pi 1}+Z_{\Pi 2})Z_{\Pi 3}+(Z_{\Pi\Pi}+Z_{\Pi 2}+Z_{\Pi 3 })Z_{R}}\right| \tag{4}\]  
When the three resonant components in the \(\Pi-\)style resonant network satisfy the resonant condition \(Z_{\Pi 1}+Z_{\Pi 2}+Z_{\Pi 3}=0\), a CC output independent of the dynamic loads can be expressed:  
\[G_{\Pi I}=\frac{Z_{\Pi 1}}{Z_{\Pi 1}+Z_{\Pi 2}}=-\frac{Z_{\Pi 1}}{Z_{\Pi 3}} \tag{5}\]  
Similarly, the voltage transfer gain \(G_{IV}\), i.e., the ratio of the output voltage \(U_{o}\) to the input current \(I_{IN}\), and the input transfer impedance \(Z_{\Pi IN}\) are expressed as follows:  
\[\left\{