# FPGA-Based Frequency Tracking Strategy with High-Accuracy for Wireless Power Transmission Systems
## 4 Experimental Verification
### Frequency-Tracking Experiment  
Keeping the experimental conditions consistent with Section 4.2, the frequency-tracking method based on the FPGA tracking input phase difference proposed in this paper is used for the experiments. Figure 15 shows the experimental waveforms. Figure 14: \(R_{\mathrm{L}}\) = 7 \(\Omega\), voltage and current phase diagram of transmitter: (**a**) coil distance of 18 cm; (**b**) coil distance of 28 cm. Figure 13: The coil distance is 24 cm, the voltage and current phase diagram of the transmitter: (**a**) \(R_{\mathrm{L}}\) = 5 \(\Omega\); (**b**) \(R_{\mathrm{L}}\) = 15 \(\Omega\). In order to prevent the switch tube from being damaged due to the bridge arm conduction, the drive signal should have a certain dead time. Considering the characteristics of the selected MOSFET, the dead time design is 600 ns, and the corresponding angle is \(\varphi\geq 360^{\circ}\times f\times t_{\text{d}}=10.37^{\circ}\), where \(f\) is the drive signal frequency, and \(t_{\text{d}}\) is the dead time selected by the system. In order to ensure that the system can work to maintain ZVS while preventing the inverter output voltage from generating large spikes and polarity reversal phenomena that can lead to damage to the switching tubes, the voltage and current phase difference should be greater than the dead time and leave a certain margin. This paper selects the phase difference between \(10.5^{\circ}\) and \(13^{\circ}\). Figure 15a shows that the voltage leads the current by \(11.51^{\circ}\) after phase locking when \(R_{\text{L}}=5~{}\Omega\). The system changes from capacitive to inductive at a fixed frequency. With output power from a fixed frequency of \(116.34\) W to \(305.55\) W, the power has a relatively apparent increase. Figure 15b shows that the voltage leads the current by \(11.94^{\circ}\) after phase locking when \(R_{\text{L}}=15~{}\Omega\). The output power is increased from \(273.13\) W at a fixed frequency to \(301.52\) W. Figure 15c shows that the voltage leads the current by \(11.20^{\circ}\) after phase locking. The output power is increased from \(53.6\) W at a fixed frequency to \(229.13\) W. Figure 15d shows that the voltage leads the current by \(12^{\circ}\) after phase locking. The output power is increased from \(311.33\) W to \(328.24\) W at a fixed frequency. The phase difference of the emitter current and voltage after phase locking all meet within the set range. The transmitting and receiving coils are placed parallelly and symmetrically on the same axis, keeping the distance between the two coils at \(24\) cm. The resistance value of the load at the receiver side is changed, and the transmission efficiency and output power of  
Figure 15: Voltage and current phase diagram based on frequency-tracking method: (**a**) \(R_{\text{L}}=5~{}\Omega\), coil distance of \(24\) cm; (**b**) \(R_{\text{L}}=15~{}\Omega\), coil distance of \(24\) cm; (**c**) \(R_{\text{L}}=7~{}\Omega\), coil distance of \(18\) cm; (**d**) \(R_{\text{L}}=7~{}\Omega\), coil distance of \(28\) cm. fixed frequency and frequency-tracking modes are compared. Figure 16 shows a graph of the comparison results. It can be observed from Figure 16 that as the load resistance gradually increases, the output power and transmission efficiency of the WPT system in the fixed frequency mode gradually increase. The frequency-splitting phenomenon occurs when the load is less than 9 \(\Omega\). The output power in frequency-tracking mode is much larger than that in fixed-frequency mode, and the transmission efficiency is lower than that of the fixed-frequency mode. After the load is greater than 9 \(\Omega\), the system frequency does not split. The output power is still higher than in the fixed-frequency mode, and the transmission efficiency is also higher than in the fixed-frequency mode. With a fixed load of 7 \(\Omega\) at the receiver side of the system, the distance between the transmit and receive coils varies.