## 2 Designing the \(4\times 1\) Microstrip Square Patch Array Antenna
### The Single Microstrip Square Patch Antenna
#### 2.2.2 Tapered Power Distribution
The simulated scattering parameters between port 1 (input) and ports 2 and 5 (output) at 24.125 GHz were \(S_{\text{21}}=S_{\text{51}}=-10.79\) dB, whereas the simulated scattering parameters between port 1 (input) and ports 3 and 4 (output) at 24.125 GHz were \(S_{\text{31}}=S_{\text{41}}=-3.88\) dB. The simulated scattering parameters at 24.125 GHz are close to the theoretical scattering parameters, and this validates the tapered power delivery from port 1 to ports 2 to 5. Performance of the 4 \(\times\) 1 Microstrip Square Patch Array Antenna Combined with Shunt-Connected Series Feed Networks Using Uniform and Tapered Power Distributions  
This subsection compares the performance of the 4 \(\times\) 1 microstrip square patch array antenna when combined with shunt-connected series feed networks using uniform and tapered power distributions. First, the 4 \(\times\) 1 microstrip square patch array antenna combined with a shunt-connected series feed network using a uniform power distribution was designed by adding four square patches at ports 2 to 5 from Figure 2a, as shown in Figure 4a. Note that the location of port 1 is between ports 3 and 4 to reduce the size of the array antenna, compared to Figure 2a, and a circular disk was appended to port 1 for impedance matching with a coaxial feed to the SMA connector. The final radius of the circular disk was \(r_{1}=0.45\) mm. The width and length of the inset in the patch are \(w_{\text{i8}}\) = 0.25 mm and \(l_{\text{i8}}\) = 1.1 mm, respectively. The width and length of the ground plane were set at \(W_{\text{g2}}\) = 30 mm and \(L_{\text{g2}}\) = 12 mm, respectively. The values of other parameters were the same as those in Figure 2a. Figure 4b shows the electric field distribution of the 4 \(\times\) 1 microstrip square patch array antenna combined with the shunt-connected series feed network using uniform power distribution at 24.125 GHz. We observed that the electric fields were almost equally distributed on the four patches corresponding to the uniform power distribution. Next, the 4 \(\times\) 1 microstrip square patch array antenna combined with a shunt-connected series feed network using a tapered power distribution ratio of 1:5:5:1 was designed by adding four square patches at ports 2 to 5 from Figure 3a, as shown in Figure 5a. The parameter values are the same as those in Figures 3a and 4a. Figure 5b shows the electric field distribution of the 4 \(\times\) 1 microstrip square patch array antenna combined with the shunt-connected series feed network using tapered power distribution at 24.125 GHz. The electric fields on the two center patches were much higher than those on the two edge patches, which confirmed the tapered power distribution. Figure 6 compares performance characteristics such as input reflection coefficient, realized gain in the +\(z\)-axis main lobe direction, and the radiation patterns of the 4 \(\times\) 1 microstrip square patch array antennas combined with the shunt-connected series feed networks using uniform and tapered power distributions. For the 4 \(\times\) 1 patch array antenna using uniform power distribution, the simulated frequency bandwidth for a VSWR less than 2 in the input reflection coefficient was 23.805 to 24.429 GHz (2.59%), which is slightly larger than that of the single patch antenna. The frequency bandwidth for a VSWR less than 2 in the 4 \(\times\) 1 patch array antenna using the tapered power distribution was 23.836 to 24.402 GHz (2.35%), which is slightly less than the uniform power distribution. Realized gain in the +\(z\)-axis direction of the antenna using uniform power distribution ranged from 11.44 dBi to 11.64 dBi in the 24.0 to 24.25 GHz band with maximum gain at 24.125 GHz, whereas it ranged from 10.94 dBi to 11.11 dBi in the 24.0 to 24.25 GHz band with maximum gain at 24.125 GHz in the 4 \(\times\) 1 patch array antenna using the tapered power distribution. Therefore, maximum gain at 24.125 GHz was decreased by 0.53 dB when the tapered power distribution was employed instead of the uniform power distribution.