## 2 Basic Principle  
### Fundamentals  
Figure 1 shows the diagram of the IPT system. To simplify the circuit diagram, line resistance, core resistance, and parasitic parameters are not shown in this figure. A full-bridge inverter comprising four MOSFETs (\(Q_{1}\)-\(Q_{4}\)) was utilized to convert a direct current (DC) link voltage into an alternating current (AC) square wave voltage. \(U_{s}\) is the equivalent AC input voltage of the compensation topology. According to [29], \(U_{s}\) can be calculated as follows:  
\[U_{s}=\frac{4U_{\text{DC}}}{\pi}\sum_{n=1,3,5...}\frac{\sin(n\phi)}{n} \tag{1}\]  
Generally, only the fundamental harmonic (\(n=1\)) is considered in the IPT converter system because high-order harmonics are filtered in the IPT converter circuit, which appear in the high-order harmonics of a high-impedance circuit. M represents the mutual inductance between the two pads. \(C_{r}\) and \(C_{s}\) represent the resonance capacitors in the primary and secondary coils, respectively. As illustrated in Figure 1, a loosely coupled transformer (LCT) works as an ideal transformer model. The coupling coefficient \(k\) of the LCT and its effective turn ratio are defined in (2) and (3). A bridge rectifier consists of four diodes (\(D_{1}\)-\(D_{4}\)) to rectify the sinusoidal AC voltage flowing from the IPT converter to the DC battery-charging voltage. \(R_{L}\) and \(C_{o}\) represent the DC output load and the output filter capacitance, respectively. \(U_{o}\) and \(I_{o}\) are the output voltage and output current, respectively. The following equations can be derived from [31]:  
\[k=\frac{M}{\sqrt{L_{p}L_{s}}} \tag{2}\]  
\[n=k\sqrt{\frac{L_{p}}{L_{s}}} \tag{3}\]  
\[\left\{\begin{array}{l}U_{L}=\frac{\pi}{2\sqrt{2}}U_{o}\\ I_{L}=\frac{2\sqrt{2}}{\pi}I_{o}\end{array}\right. \tag{4}\]  
where \(U_{L}\) and \(I_{L}\) represent the root-mean-square (RMS) values of \(U_{o}\) and \(I_{o}\), respectively. Based on (4), the relationship between \(R_{L}\) and \(R_{o}\) is given as follows:  
\[R_{o}=\frac{8}{\pi^{2}}R_{L} \tag{5}\]  
Figure 1: IPT system.  
In order to prevent faults caused by overvoltage and overcurrent, protection and wireless communication devices with low latency are required, which lead to increased cost and volume.  
\begin{table}
\begin{tabular}{c c c} \hline \hline
**Symbols** & **Parameters** & **Values** \\ \hline \(U_{s}\) & DC link voltage & 96 V \\ \(f\) & Operation frequency & 85 kHz \\ \(P_{o,max}\) & Maximum-output power & 400 W \\ \(U_{L}\) & Load voltage range & 0–35.1 V \\ \(I_{L,short}\) & Load current under short-circuit & 23.4 A \\ \(k\) & Coupling coefficient & 0.324 \\ \(L_{p}\) & Primary self-inductance & 56.76 uH \\ \(L_{s}\) & Secondary self-inductance & 6.628 uH \\ \(L_{R}\) & Primary leakage inductance & 38.421 uH \\ \(C_{r}\) & Leakage resonance capacitor & 91.1 nF \\ \(R_{L}\) & Load resistance & 0.46–2000 \(\Omega\) \\ \(R_{LP}\) & AC resistance of \(L_{p}\) & 58.7 m\(\Omega\) \\ \(R_{Ls}\) & AC resistance of \(L_{s}\) & 19.2 m\(\Omega\) \\ \hline \hline \end{tabular}
\end{table}
Table 1: Measured parameters of the proposed IPT system.  
Figure 3: Conventional resonance design in the SS topology: (**a**) voltage gain for different load resistances; (**b**) phase angle for different load resistances.