## 3 The Microwave Wireless Power Transfer System  
The simulation model of the MWPT system can be built by using the simulation software HFSS. The model of the proposed MWPT system is shown in Figure 9a. The frequency reconfigurable antenna array is used as the transmitter of the MWPT system to transmit energy. The antenna is also used as the receiver of the MWPT system to receive energy. The capacitance value of the varactor diode changes with different voltage, which has been shown in Figure 9a. This suggests that the frequency reconfigurable antenna array can work at the continuous switchable resonant frequency within a certain range. The energy is transmitted from the transmitter to the receiver through the electromagnetic  
Figure 8: (**a**). Simulated and measured gains of the antenna (four smaller side patches are all connected to the larger main patch). (**b**). Simulated and measured gains (one smaller side patch is connected to the larger main patch).  
Figure 7: The gains of the single patch antenna and the patch antenna array.  
field at the different working state, as shown in Figure 9a. The variable symbol \(d\) is the distance between the transmitter and the receiver.  
The experimental platform for the MWPT system is illustrated in Figure 9b. The transmitter and the receiver are connected to port 1 and port 2 of the vector network analyzer (Agilent Technologies N5230A, which is manufactured by Agilent in Palo Alto, USA.), respectively. The adjustable DC voltage source (KEYSIGHT E3633A, which is manufactured by KEYSIGHT in Shenzhen, China.) is used to provide the variable DC bias voltage for the varactor diode. The transmitter is fixed in a certain position, and the receiver is placed in a coaxial position of the transmitter. PTE of the frequency reconfigurable MWPT system is calculated by the equation in [21], which is:  
\[PTE=10^{|S_{21}|/10}\times 100\%. \tag{5}\]  
The \(S_{21}\) of the MWPT system is measured by the vector network analyzer. Simulation and measurement results of PTE of the MWPT system at different frequencies between S-band and C-band are illustrated in Figure 10a,b, respectively. The measured results have shown that the PTE of the MWPT system stays at around 20% at different frequencies. The measured results agree with the simulated results, but there is an error rate of about 10% between the simulation results and the measurement results. Also, the measured results are lower than the simulated results due to the fabricated tolerance and measurement errors. The MWPT system based on the frequency reconfigurable antenna array can be used to power the receiver at different frequencies, and the PTE of the system does not decrease as the resonant  
As we know, the energy is transmitted from the transmitter to the receiver, while the antenna is operated as the transmitter to transmit energy, as well as being operated as the receiver to receive energy. The research based on the transmitter and the receiver is very important. In this paper, we proposed the idea that the frequency reconfigurable microstrip patch antenna array can be used for a microwave wireless power transfer system. This would allow the energy to be transmitted to the receiver at different frequencies. Also, when the energy is transmitted to the load from the receiver in the wireless power transfer system, there should be a rectifier circuit which converts alternating current to direct current. In this paper, we only verify the efficiency of the power transmitted to the receiver from the transmitter. Notably, the rectifier circuit is not involved in power transfer from the transmitter to the receiver. As a result, the rectifier circuit is not in our present work. The systematic efficiency involving the rectifier circuit will be focused on in future design research.