## 2 Frequency Reconfigurable Microstrip Patch Antenna Array
### Simulation and Measurement Results  
Simulation results are obtained in the simulation software HFSS, and the return losses are measured by the vector network analyzer (Agilent Technologies N5230A, which is manufactured by Agilent in Palo Alto, USA.) to verify the accuracy of the frequency reconfigurable antenna array. When four smaller side patches are all connected to the larger main patch, the simulated and measured return losses at different frequencies for the reconfigurable antenna array are illustrated in Figure 5a. The resonant frequency of the antenna array changes significantly from 3.41 GHz to 3.96 GHz by varying the DC bias voltage from 0 to 20 V. The working frequency from 3.41 GHz to 3.96 GHz belongs to the S-band (2-4 GHz). The simulated and measured return losses at different frequencies that are obtained when just one smaller side patch is connected to the larger main patch are illustrated in Figure 5b. The working frequency changes significantly from 5.7 GHz to 6.3 GHz by varying the DC bias voltage from 3 to 11 V. The working frequency in this case belongs to the C-band (4-8 GHz). The frequency which belongs to the S-band and the C-band have been widely used in the fields of radar, satellite communication and so on. Now other widely used forms of technology such as Bluetooth, ZIGBEE, wireless routing, wireless mouse device and a wide range of electronic products also use this frequency, which belongs to the S-band and C-band. The resonant frequency of the antenna array shifts toward higher values with an increase in DC bias voltages and a decrease in capacitance values of the varactor diodes. For the adjustable range of frequencies, the return loss of the antenna array is less than \(-15\) dB at the resonant frequency. There is a slight difference between simulation results and measurement results because of the fabrication tolerance and small measurement errors. Also, the ohmic loss of the varactor diodes cannot be precisely modeled in the simulation software HFSS. Also, there are a number of modulations that are needed because lots of varactor diodes are welded between the larger main patches and the smaller side patches, and lots of wires are used. The frequency reconfigurable antenna array is affected by interference caused by using lots of wires. The antenna pattern refers to the pattern in which the relative field intensity of radiation field changes with the direction at a certain distance from the antenna. The antenna pattern is an important pattern to measure the antenna performance. The antenna pattern is a diagram used to show the directivity of the antenna. The parameters of the antenna can be observed from the antenna pattern. The frequency reconfigurable antenna is continuously adjusted at the working frequency within a certain frequency range. A good frequency reconfigurable antenna should have a relatively stable antenna pattern. We show the antenna pattern of the frequency reconfigurable antenna array at different  
Figure 5: (**a**). Simulated and measured return losses for the antenna (four smaller side patches are all connected to the larger main patch). (**b**). Simulated and measured return losses (one smaller side patch is connected to the larger main patch). frequencies. This pattern indicates that the frequency reconfigurable antenna array works normally at different working frequencies. As a result, the antenna is very important for the wireless power transfer system. The radiation gain patterns of the antenna array in the xz plane and yz plane at different frequencies are shown in Figure 6. The xz plane means that Phi is 0 deg, and the yz plane means phi is 90 deg. Radiation gain patterns maintain similar shapes at different states. In summary, with 16 varactors, this array can operate with the maximum gain varying from 7.87 to 7 dBi when the operating frequency is tuned from 3.96 to 6.21 GHz. The gain of the single patch antenna and the gain of the patch antenna array without any smaller side patches are simulated.