## 3 Results
In this work, we have set the current in the current source to 50 A and the resonance circuit to maintain operation in the linear section of the B-H curve. For simplicity, in this proof of concept study, the capacitors for each of the VC coils were selected at the zero position taking into account the current source. \begin{table}
\begin{tabular}{c c c c} \hline  & **DD** & **Q** & **Transmitter** \\ \hline DD & 328.870 & 0.057 & 21.017 \\ \hline Q & 0.057 & 222.470 & 0.001 \\ \hline Transmitter & 21.017 & 0.001 & 200.440 \\ \hline \end{tabular}
\end{table} 
Table 4: DDQ mutual-inductance [\(\mu\)H] matrix at 0 position (transmitter and receiver’s center overlap). \begin{table}
\begin{tabular}{c c c c c c c} \hline  & **VC 1** & **VC 2** & **VC 3** & **VC 4** & **VC 5** & **Transmitting** \\ \hline VC 1 & 1 & 0.393 & 0.258 & 0.174 & 0.1 & 0.03 \\ \hline VC 2 & 0.393 & 1 & 0.477 & 0.309 & 0.174 & 0.083 \\ \hline VC 3 & 0.258 & 0.477 & 1 & 0.477 & 0.258 & 0.105 \\ \hline VC 4 & 0.174 & 0.309 & 0.477 & 1 & 0.392 & 0.083 \\ \hline VC 5 & 0.1 & 0.174 & 0.258 & 0.392 & 1 & 0.03 \\ \hline Transmitting & 0.03 & 0.083 & 0.105 & 0.083 & 0.03 & 1 \\ \hline \end{tabular}
\end{table} 
Table 3: VC coupling matrix at 0 position (large model—transmitter and receiver’s center overlap). \begin{table}
\begin{tabular}{c c c c c c} \hline  & **VC 1** & **VC 2** & **VC 3** & **VC 4** & **VC 5** & **Transmitting** \\ \hline VC 1 & 178.74 & 82.07 & 55.91 & 36.47 & 17.91 & 5.66 \\ \hline VC 2 & 82.07 & 244.42 & 120.81 & 75.51 & 36.45 & 18.27 \\ \hline VC 3 & 55.91 & 120.81 & 261.95 & 120.81 & 55.88 & 24.14 \\ \hline VC 4 & 36.47 & 75.51 & 120.81 & 244.51 & 82.02 & 18.27 \\ \hline VC 5 & 17.91 & 36.45 & 55.88 & 82.02 & 178.71 & 5.66 \\ \hline transmitting & 5.66 & 18.27 & 24.14 & 18.27 & 5.66 & 5.66 \\ \hline \end{tabular}
\end{table} 
Table 2: VC mutual-inductance [\(\mu\)H] matrix at 0 position (large model—transmitter and receiver’s center overlap). \begin{table}
\begin{tabular}{c c c c} \hline  & **DD** & **Q** & **Transmitter** \\ \hline DD & 1 & \(21\times 10^{-5}\) & 0.081 \\ \hline Q & \(21\times 10^{-5}\) & 1 & \(5\times 10^{-6}\) \\ \hline Transmitter & 0.081 & \(5\times 10^{-6}\) & 1 \\ \hline \end{tabular}
\end{table} 
Table 5: DDQ coupling matrix at 0 position (transmitter and receiver’s center overlap). account the self-inductance values only. The calculated efficiency of both the DDQ and VC configurations is displayed in Figure 7. For the DDQ, the efficiency peaks at around 85% and remains relatively flat at approximately 80%, between positions of \(-\)50 cm and 50 cm. Beyond this range, efficiency drops sharply over the next 50 cm on either side, eventually reaching nearly 0%. This behavior indicates that the DDQ system charges the vehicle over about 200 cm. However, the most effective charging occurs within the central 100 cm. In the VC configuration, the maximum efficiency reaches approximately 93%. The graph reveals four distinct peaks: two central peaks reaching 93% efficiency, and two edge peaks reaching 66% efficiency. The most effective charging range spans between \(-\)40 cm and 40 cm. In addition, there are significant efficient regions from \(-\)110 cm to \(-\)70 cm and from 70 cm to 110 cm, although these are less efficient compared to the central region. Beyond these points, the efficiency declines, reaching nearly 0% at \(-\)150 cm and 150 cm. While the highest efficiency of the VC is still concentrated around the central region, it exhibits efficient energy transfer over a broader range than the DDQ configuration, with substantial but lower efficiency zones extending towards the edges. The reason why the VC configuration has a wider range of efficiency is due to the way the magnetic flux lines interact with the receiving coils. The presence of a ferromagnetic core alters the direction of the magnetic field lines. In the VC configuration, these lines run horizontally through the ferrite, meaning that receiving coils perpendicular to these lines pick up of more flux over a greater distance.