# Analytical Solution and Experimental Validation of the Electromagnetic Field in an IPT System
## 6 Experimental Verification  
The electric field intensity cannot be measured directly. According to Equation (42), the electric field generated by the coil is along the \(\phi\) direction, but the electric field intensity is independent of \(\phi\). For a single-turn measurement coil, when its plane is oriented parallel to the plane of the current-carrying coil, the electric field intensity can be measured using the relationship \(U=\oint_{I}|E|\,dl\). When current flows in the source coil and the measurement coil is opened, the relationship between the open-circuit voltage and the circular electric-field strength at the measurement coil can be expressed as \(|E|=U/(2\pi a)\), in which \(a\) is the radius of the measurement coil. The experimental configuration is shown in Figure 11.  
By changing the position and size of the measurement coil, the variation of the electric-field strength at different positions can be measured, where \(Q\) is an arbitrary point on the measurement coil. To facilitate the experiment, the radius of the measurement coil was set equal to the radius of the primary and secondary coils. Figure 10: Analytical and simulated synthesized electric-field intensity with different \(N\) values. (**a**) is the electric field curve when the number of coil turns on both sides is 4, (**b**) is the electric field curve when the number of coil turns on both sides is 8. Figure 9: The three points are located in the \(z\)-axis. When the secondary side is at resonant state, the reflected impedance from the secondary side to the primary side is purely resistive, while the resonant frequency of the primary side is independent of the secondary side. The experimental steps were as follows [18]:  
Firstly, a compensation capacitor with \(C_{S}\) = 1000 pF, a load with \(R_{L}\) = 20 \(\Omega\) and an adjustable current source were connected in series with the primary coil. The current source frequency was adjusted to a specific value so that the load current and voltage were in the same phase, which is the resonant frequency. In the experiment, the measured resonant frequency was set at \(f_{0}\) = 486.7 kHz. Then, the current source was removed and the secondary side of the circuit was connected as shown in Figure 11.  
Secondly, to achieve full resonance (i.e., the primary side and secondary side are both resonant), a compensation capacitor must be connected in series with the primary coil. The experimental circuit configuration is shown in Figure 11. The experimental set up is shown in Figure 12, and the frequency of the power amplifier shown in Figure 12 was maintained at \(f_{0}\) = 486.7 kHz, and the compensation capacitance \(C_{P}\) was adjusted until the voltage and current of the power source were in the same phase, at which point the circuit achieves full resonance. The relevant parameters are listed in Table 1.  
Finally, different values of \(h_{1}\) in Figure 11 were chosen, and the output current of the power amplifier was changed. The corresponding induced voltages of the measurement coil at different positions were measured. The voltage was divided by the perimeter of the measurement coil to obtain the electric field intensity at that point. Figure 13 shows waveforms of the experiment result, measured by Tektromix DPO4104B when the effective current on the primary side was 0.499 A and \(h_{1}\) = 52 mm. The purple line is the primary side current \(i_{p}\), the dark blue line is the output voltage of the power amplifier \(u_{p}\), the green line is the induced current in the secondary side coil \(i_{s}\) and the light blue line is the induced voltage of the measurement coil \(u_{m}\). Figure 11: Experimental configuration. Figure 12: Experimental set-up. The experimental results of electric field intensity at different h values are shown in Figure 14. H\({}_{1}\), H\({}_{2}\) and H\({}_{3}\) represent values of \(h_{1}\) at 27 mm, 52 mm and 80 mm, respectively.