## 2 Designing the \(4\times 1\) Microstrip Square Patch Array Antenna
### The Single Microstrip Square Patch Antenna
#### 2.2.2 Tapered Power Distribution  
To reduce sidelobe levels in the radiation patterns of the 4 \(\times\) 1 array antenna, a 4 \(\times\) 1 shunt-connected series feed network using a tapered power distribution ratio of 1:5:5:1 was designed, and the geometry and scattering parameter characteristics are shown in Figure 3. In this case, the characteristic impedance, length, and width of the microstrip line connected to port 1 are \(Z_{\rm c1}=50\)\(\Omega\), \(l_{1}=1.87\) mm, and \(w_{1}=0.54\) mm, respectively. Similarly, the input impedance of ports 2 to 5 was set to 100 \(\Omega\) with the characteristic impedance and width of the microstrip line connected to ports 2 to 5 at \(Z_{\rm c2}=100\)\(\Omega\) and \(w_{2}=0.125\) mm, respectively. For a tapered power distribution with a power ratio of 1:5:5:1, the power delivered to the two center ports (3 and 4) is five times that delivered to edge ports (2 and 5). Therefore, the power delivered to center ports 3 and 4 is \(P_{3}=P_{4}=(5/12\times P_{1})\), whereas the power delivered to edge ports 2 and 5 is \(P_{2}=P_{5}=(1/12\times P_{1})\). Two QWTs were used for impedance matching: one at the input microstrip line of the T-junction structure, and the other in the middle of the microstrip line of edge ports 2 and 5. For QWT 1 at the input microstrip line of the T-junction structure, different power distributions connected to the input microstrip line need to be considered. For instance, since the power delivered to port 4 (\(P_{4}\)) is five times the power delivered to port 5 (\(P_{5}\)), and the power ratio of the microstrip line is inversely proportional to the impedance ratio, the impedance of port 5 (\(Z_{\rm p5}\)) should be five times the impedance of port 4 (\(Z_{\rm p4}\)). If we  
Figure 3: Design and scattering parameter characteristics of the 4 \(\times\) 1 shunt-connected series feed network using tapered power distribution: (**a**) the geometry and (**b**) scattering parameters. assume the impedance of port 4 as \(Z_{\text{c2}}=100\)\(\Omega\), the impedance toward port 5 should \(Z_{\text{p5}}=5\times Z_{\text{c2}}=500\)\(\Omega\). The input impedance at the junction of the microstrip lines toward ports 4 and 5 was \(Z_{\text{i1}}=Z_{\text{c2}}/Z_{\text{p5}}=83.33\)\(\Omega\). Therefore, the characteristic impedance of the QWT 1 can be calculated as follows:  
\[Z_{\text{c3}}=\sqrt{Z_{\text{c2}}\times Z_{\text{i1}}}=\sqrt{100\times 83.33}=91.29\)\(\Omega \tag{7}\]  
The length and width of QWT 1 are \(l_{1}=1.87\) mm and \(w_{3}=0.16\) mm, respectively. For QWT 2 in the middle of the microstrip line of edge ports 2 and 5, impedance transformation of \(Z_{\text{p5}}\) (=500 \(\Omega\)) to \(Z_{\text{c2}}\) (=100 \(\Omega\)) needs to be considered. For example, if a QWT is directly used to transform \(Z_{\text{p5}}=500\)\(\Omega\) to \(Z_{\text{c2}}=100\)\(\Omega\), the impedance of the QWT became 223.61 \(\Omega\), where the corresponding microstrip line width is extremely small and hard to implement. To avoid this problem, a 100 \(\Omega\) microstrip line with a quarter-wavelength was located first, followed by the QWT. In this case, the impedance seen at the input of the QWT 2 becomes:  
\[Z_{\text{i2}}=\frac{Z_{\text{c2}}^{2}}{Z_{\text{p5}}}=\frac{100^{2}}{500}=20\ \Omega \tag{8}\]  
Therefore, the impedance of QWT 2 can be calculated as follows:  
\[Z_{\text{c4}}=\sqrt{Z_{\text{c2}}\times Z_{\text{i2}}}=\sqrt{100\times 20}=44.72\ \Omega \tag{9}\]  
The corresponding length and width of QWT 2 are \(l_{1}=1.87\) mm and \(w_{4}=0.65\) mm, respectively. For tapered power distribution with a power ratio of 1:5:5:1, the scattering parameter between port 1 (input) and ports 2 and 5 (output) is theoretically \(S_{\text{21}}=S_{\text{S1}}=\sqrt{1/12}=-10.79\) dB, whereas the scattering parameter between port 1 (input) and ports 3 and 4 (output) is \(S_{\text{31}}=S_{\text{41}}=\sqrt{5/12}=-3.8\) dB. The 4 \(\times\) 1 shunt-connected series feed network with a tapered power distribution of 1:5:5:1 in Figure 3a was simulated using CST Studio Suite.