## 2 Frequency Reconfigurable Microstrip Patch Antenna Array
### The Configuration and Design of the Patch Antenna Array
The metal layer is copper and the effective dielectric constant \(\varepsilon_{\text{e}}\) can be derived as follows [29]:  
\[\varepsilon_{\text{e}}=\frac{\varepsilon_{r}+1}{2}+\frac{\varepsilon_{r}-1}{2 }(1+12\frac{h}{W})^{-\frac{1}{2}}. \tag{2}\]  
The length of the radiation gap is \(\Delta L\) and the length of the patch is \(L\)[30]. \[\Delta L=0.412h\frac{(\varepsilon_{\text{e}}+0.3)(W/h+0.264)}{(\varepsilon_{ \text{e}}-0.258)(W/h+0.8)} \tag{3}\]  
\[L=\frac{c}{2f\sqrt{\varepsilon_{\text{e}}}}-2\Delta L \tag{4}\]  
The simulation model of the frequency reconfigurable microstrip patch antenna array is shown in Figure 1. The patch antenna array mainly consists of 4 main patches, 16 side patches and the feed network. By placing the varactor diode (SMV1281) inside the larger main patch and the smaller side patch, the antenna can perform as a frequency reconfigurable antenna array. The SMV1281 varactor diode has an adequate range of capacitance values from 0.69 pF to 13.3 pF, and it has low series resistance. Adding 4 varactors on the side of the patch is used to changing the working frequency of the frequency reconfigurable antenna array. The feed network is used to feed the antenna array and the lumped port is used in the simulation software HFSS (High Frequency Structure Simulator) to excite the patch antenna array. The frequency reconfigurable antenna array has two working states. There are four smaller patches around the larger main patch, as shown in Figure 1. When four smaller patches are all connected to the larger main patch by using four varactors, the frequency reconfigurable patch antenna array works at frequencies from 3.41 GHz to 3.96 GHz. The details of simulation in this case are shown in Figure 2a. The varactor diode model in HFSS is replaced by the lumped RLC boundary. The return losses at different frequencies for the general reconfigurable antenna array are illustrated in Figure 2b. The working frequency belongs to S-band. In this case, the return losses are less than \(-15\) dB when the capacitance values are changed. Then, the working frequency of the patch antenna array are adjusted. When just one smaller patch is connected to the larger main patch, the frequency reconfigurable patch antenna array can work at frequencies from 5.7 GHz to 6.3 GHz. The details of simulation in this case are shown in Figure 3a. The varactor diode model in HFSS is also replaced by the lumped RLC boundary. The return losses at different frequencies in this case are illustrated in Figure 3b. The working frequency belongs to C-band, and the return losses are also less than \(-15\) dB at different working frequencies. The patch antenna array is designed on a double-sided substrate using the planar technology, while the feed network is designed on a single-sided substrate. In assembling the microstrip patch antenna array, the non-copper side of the feed network is placed in  
Figure 1: The general geometry of the patch antenna array (four smaller patches are all connected to the larger main patch). Figure 2: (**a**) Details of the simulation model (four smaller patches are all connected to the larger main patch). (**b**) The return losses at different frequencies for the reconfigurable antenna array. direct contact with the ground of the patch antenna array, as shown in Figure 4a. This leads to a low profile and compact structure. The dimensions of the frequency reconfigurable patch antenna array in Figures 1 and 4a are listed in Table 1. The fabricated patch antenna array is shown in Figure 4b,c for measurement. The SMA (SubMiniature Version A) connector is fed to the feed-line through the substrate material and the ground plane. The reconfigurable antenna array and the SMA connector are designed on the FR4 substrates, which have a dielectric constant of 4.4 and a loss tangent of 0.02.