## 3 Design Method of MCRWPT System Based on Simulation
### Design Circuit and Excitation Frequency
#### 3.2.2 Design Excitation Frequency  
By analyzing Equations (6) and (8), the voltage gain and PTE of the MCRWPT system are affected by the coil winding, mutual inductance, equivalent load resistance, and excitation frequency. Changing the excitation frequency is a relatively simple way to adjust the output voltage and PTE, given the shape of the coil windings and the distance between the two coil windings. The TTE decreases due to the application of the DC-DC converter, so it is necessary to study the influence of excitation frequency on TTE and further optimize the TTE of the system. Designing the excitation frequency is divided into three steps: (1) Determine the excitation frequency range. (2) Excitation frequency for maximum TTE obtained without considering output power. (3) The PTE is optimized by changing the excitation frequency under the same output power condition. The first step is to determine the excitation frequency range and ensure that the output voltage of the MCRWPT system is within the input voltage range of the DC-DC converter. Based on the model of Case4, the influence of excitation frequency on the output voltage  
Figure 8: Block diagram of the MCRWPT system. of the MCRWPT system is analyzed. The equivalent load resistance is assumed to vary from 10 \(\Omega\) to 1 M\(\Omega\). Figure 9 shows the output voltage variation with excitation frequency for different \(R_{L}\). The orange curve shows that the equivalent load resistance is 1 M\(\Omega\), and the output voltage increases first and then decreases with the increase of the excitation frequency. The maximum output voltage occurs at the resonant frequency of 100 kHz. Assuming that the input voltage is 19 V and the maximum input voltage of the DC-DC converter is 40 V, the output voltage should be less than 40 V. Therefore, the design range of excitation frequency is less than 83 kHz, or more than 135 kHz. The output voltage should be more than 5 V, and the corresponding excitation frequency should be greater than 47 kHz, considering the limits of the minimum input voltage of the DC-DC converter. Because the inverter excitation frequency is limited, the maximum excitation frequency should be less than 300 kHz. The output voltage with \(R_{L}\) of 10 \(\Omega\) is shown in the blue curve, and the maximum value of the output voltage is less than 40 V, so the output voltage is too high to damage the DC-DC converter is not considered. Therefore, the design range of excitation frequency is from 47 kHz to 83 kHz, and from 135 kHz to 300 kHz. The second step is to determine the excitation frequency corresponding to the maximum TTE by analyzing the influence of excitation frequency on the TTE based on the Case4 model. The resonance frequency of the MCRWPT system is 100 kHz, and the equivalent load resistance is fixed at 50 \(\Omega\). For the same output voltage, the higher the excitation frequency, the higher the PTE, as shown in Figure 10. Therefore, the case where the excitation frequency is greater than the resonant frequency is analyzed below. As shown in the dash-dot line PTE\({}_{WPT}\) in Figure 11a, the variation of PTE\({}_{WPT}\) with output voltage is obtained through the joint simulation of ANSYS Maxwell and ANSYS Simplorer. When the output voltage of the DC-DC converter is fixed, the efficiency of the DC-DC converter decreases with the increase of input voltage, as shown in the dotted  
Figure 10: The output voltage and PTE vary with the excitation frequency. Figure 9: With different \(R_{L}\), output voltage changes with excitation frequency. line PTE\({}_{DC}\) in Figure 11a. As the output voltage increases, the TTE of the system first decreases and then increases, as shown by the solid line in Figure 11a. The minimum value of TTE is 74.54%, which corresponds to an output voltage of 27.17 V and an excitation frequency of 140 kHz as shown in Figure 11a,b. The TTE can be optimized by adjusting the excitation frequency.