# Helmholtz Coils Based WPT Coupling Analysis of Temporal Interference Electrical Stimulation System
## 3 Analysis of Calculation and Experimental Results
### Experimental Study of the Current at the Receiving Coil  
In order to verify whether the proposed WPT system can apply electrical stimulation of a sufficient intensity and suitable frequency to the target through TI, a real experimental platform with the same parameters as in the calculation was built for this paper, as shown in Figure 9. The corresponding schematic block diagram of the experimental prototype is shown in Figure 10. In the experiment, the energy input of the whole system was provided by a high-precision dual-channel signal generator. Since the power of the signal generator cannot reach the power requirement needed by the load, its output signal needed to be processed by a high-frequency power amplifier before it could be used as the excitation of the WPT system. The transmitting and receiving coils shown in the diagram were placed in air and fixed, and the three axes were kept aligned. Due to the hand winding, the actual inductance of transmitting coil 1 was 19 \(\upmu\)H and the actual inductance of transmitting coil 2 was 18.94 \(\upmu\)H. The resonance compensation capacitors were 5553 pF and 5570 pF, respectively. The parameters of the experimental test platform were set up as shown in Table 4, under the condition that the current amplitude applied to the two transmitting  
Figure 8: Magnetic field distribution in the _xoy_ plane in a multi–layered human tissue model. Figure 7: Magnetic field distribution after the addition of multi–layer human tissue. coils was guaranteed to be equal. Then, the oscilloscope's reference side was connected to the signal generator's ground side to measure and observe the current on the receiving coil. The current waveform at the receiving coil displayed in the oscilloscope is shown in Figure 11. It can be seen that when the two transmitting coils are passed through to the differential frequency excitation, an envelope modulated current of 42.4 mA in amplitude and 10 Hz in frequency appears on the receiver side. The current range used for sciatic nerve stimulation is generally 0.2-0.8 mA [44]. The amplitude of the envelope modulated \begin{table}
\begin{tabular}{c c c} \hline
**Experimental Equipment** & **Parameters** & **Value** \\ \hline \multirow{4}{*}{Transmitting Coil 1} & Current Frequency & 490 kHz \\  & Current Amplitude & 0.2 A \\ \multirow{4}{*}{Transmitting Coil 1} & Resistances & 10 \\  & Inductance & 19 \\  & Capacitances & 5553 pF \\ \hline \multirow{4}{*}{Transmitting Coil 2} & Current Frequency & 490 kHz + 10 Hz \\  & Current Amplitude & 0.2 A \\ \multirow{4}{*}{Transmitting Coil 2} & Resistances & 10 \\  & Inductance & 18.94 uH \\ \multirow{4}{*}{Receiving Coil} & Capacitances & 5570 pF \\ \hline \multirow{4}{*}{Receiving Coil} & Resistances & 1.09 \(\Omega\) \\  & Current Frequency & 10 Hz \\ \cline{1-1}  & Current Amplitude & 42.4 mA \\ \hline \end{tabular}
\end{table} 
Table 4: The equipment parameters in experimental tests. Figure 10: Block diagram of the experimental prototype. Figure 9: Experimental platform and receiving coil for Helmholtz coils wireless power transfer system. current in the receiving coil far exceeds the current density threshold for causing excitation of the sciatic nerve, which can meet the stimulation intensity of the sciatic nerve. At the same time, the frequency of the envelope modulated current is the frequency difference of the added excitation. Its value falls within the low-frequency range of the excitation of the sciatic nerve, which can induce the expected response of the sciatic nerve. Considering that this system has two transmitting coils, it can be calculated from Equation (12) that the transmitting power of the system is 400.98 mW for an excitation current amplitude of 0.2 A. As the resistance of the receiving coil is 1.09 \(\Omega\), the received power of the load resistor can be calculated to be approximately 0.98 mW at this point. Dividing the two powers calculates an efficiency of 0.244% for the load resistance at the system's receiving end.