# A Novel Approach to Reach Impedance Matching in Wireless Power Transfer Systems
## 4 Experimental Results  
In order to prove the feasibility of the above method, the four-coil system was established as shown in Figure 9. The structure parameters of the coils were the same as those of the simulation module in Table 2. The electrical parameters were measured by high-quality impedance analysis \begin{table}
\begin{tabular}{c c c c c c} \hline
**Name** & **Turns** & \(L\) **(mm)** & **\(t\) (mm)** & \(w\) (mm)** & \(s\) (mm) \\ \hline Drive loop & 1 & 204 & 0.035 & 4 & \(\backslash\) \\ \(Tx/Rx\) coils & 7 & 204 & 0.035 & 4 & 8 \\ Load loop & 2 & 104 & 0.035 & 4 & 8 \\ \hline \end{tabular}
\end{table} 
Table 2: Coil structure parameters. Figure 8: Comparison of the mutual inductance calculations based on this paper and the mutual inductance simulation using Ansys Maxwell 16.0. (**a**) Mutual inductance of \(Tx\) coil and \(Rx\) coil, (**b**) mutual inductance of \(Tx\) coil and drive loop, (**c**) mutual inductance of \(Rx\) coil and load loop. (MICROTEST 6379), as listed in Table 3. The operating frequency of the resonant coils can reach 3 MHz by adjusting the series capacitance of the resonant coils. Firstly, all coils were aligned in the coaxial direction and \(d_{23}\) was the distance between the \(Tx\) coil and the \(Rx\) coil, which was fixed at 40 cm. Two ports of the network analyzer were connected to the load coil and the drive coil, respectively. The load and internal resistance of the source were both 50 \(\Omega\), accordingly. During the experiment, changing either \(d_{12}\) or \(\varphi\), caused the transfer efficiency to vary accordingly, as shown in Figure 10. Figure 10a shows the variation of \(\,1\,S_{21}\,1^{2}\) along with \(d_{12}\) when \(\varphi\) was fixed at 45 degrees. Obviously, there was an optimal \(d_{12}\) to maximize \(\,1\,S_{21}\,1^{2}\). At this time, the measured value of \(Z_{\text{in}}\) was approximately 50 \(\Omega\). Similarly, Figure 10b shows the variation of \(\,1\,S_{21}\,1^{2}\) with \(\varphi\) when \(d_{12}\) was fixed at 7 cm. There was also an optimal \(\varphi\) that maximized the \(\,1\,S_{21}\,1^{2}\). The experimental results were basically consistent with the simulation results based on the electrical parameters in Table 3, which showed that the circuit analysis, mutual inductance analysis and calculation in this paper were accurate. The trend of the curve showed that the transfer efficiency can be maximized by adjusting \(d_{12}\) and \(\varphi\) when the transmission distance is fixed. Figure 10: The transfer efficiency at a fixed transmission distance, (**a**) changes to the \(d_{12}\) at fixed \(\varphi\), (**b**) changes to the \(\varphi\) at fixed \(d_{12}\). \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Name** & **Internal Resistance (ohm)** & **Self-Inductance (\(\mu\)H)** & **Resonant Frequency (MHz)** \\ \hline Drive loop & 0.16 & 0.75 & \(\backslash\) \\ \(Tx\) coil & 1.3 & 14.1 & 3 \\ \(Rx\) coil & 1.2 & 13.8 & 3 \\ Load & 0.12 & 0.86 & \(\backslash\) \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Coil electrical parameters. Figure 9: Experimental setup of the four-coil WPT system. In Figure 10, the \(\left\lvert\,S_{21}\,\right\rvert^{2}\) cannot represent the transfer efficiency because the magnitude of \(Z_{in}\) is not equal to the internal resistance of the source. Figure 11a shows the trend of transfer efficiency and transmission distance. \(d_{23}\) was changed from 25 cm to 80 cm with a step length of 5 cm. In an experiment that did not reach optimal load, \(\varphi\) was fixed at 0 degrees. Adjusting \(d_{12}\) caused the module of \(Z_{in}\) to be close to 50 \(\Omega\), the magnitude of \(S_{21}\) to be the maximum. The maximum transfer efficiency under each distance was then obtained, and the results were marked by circular spots. In contrast, the next experiment reached the optimal load by changing the \(\varphi\) and using \(d_{12}\) to match the source that makes \(Z_{in}\) equal to \(R_{S}\). The maximum transfer efficiency under each distance will then be attained; square spots indicate the results.