## 2 Proposed Antenna with SIW Feeding Network
The detailed design parameters are listed in Table 1.  
Figure 1: Design approach and geometry of the proposed antenna: (**a**) isometric view of the proposed antenna; (**b**) bottom view of the patch antenna; (**c**) side view of the proposed antenna; (**d**) top and bottom views of the substrate integrated waveguide (SIW) feeder for TE\({}_{10}\) mode; (**e**) top and bottom views of the SIW feeder for TE\({}_{20}\) mode. Figure 2: Design methodology of the proposed antenna. Figure 3 presents photographs of the fabricated antenna, in which all three parts are combined. Each part is designed to be assembled like a separate block so that they can generate each sum and difference pattern through the single rectangular radiator simultaneously. The microstrip lines, baluns, and patch radiator of the proposed antenna are fabricated by etching the metallic surface on the FR4-substrate, while the SIW is implemented by drilling a number of holes in the substrate and applying metal paint on the perforated surface. Figure 4 presents a comparison of the measured and simulated reflection coefficients of the SIW for both the TE\({}_{10}\) and TE\({}_{20}\) modes. For the TE\({}_{10}\) mode, the measurement of \(-18.8\) dB agrees well with the simulation of \(-15.8\) dB at 4.85 GHz, as shown in Figure 4a. Figure 4b again shows the reflection coefficients of the SIW for the TE\({}_{20}\) mode, where the measurement and simulation are \(-11.5\) dB and \(-16.6\) dB, respectively, at the same frequency of 4.85 GHz. Figure 5 shows the measured mutual coupling in comparison with the simulated data as a function of frequency. Measured and simulated mutual couplings are \(-37.8\) dB and \(-34.9\) dB at 4.85 GHz, respectively, and they are maintained below \(-30\) dB from 4.5 GHz to 5.5 GHz. From these results, it can be seen that even with a single radiator, the patterns of each mode are well generated without significantly affecting each other. Figure 6 shows measured and simulated radiation efficiencies of the proposed antenna. The measured efficiencies of TE\({}_{10}\) and TE\({}_{20}\) modes were 38% and 29% at the target frequency of 4.85 GHz. There is an efficiency reduction due to conduction and dielectric losses. For example, when the TE\({}_{10}\) mode is excited by the total available power of 1 W, the resulting total power loss is 0.62 W (efficiency = 38%). Over this total loss, the dielectric and conduction losses are 0.59 W and 0.03 W, where the dielectric loss is dominant. The detailed values of the losses and the efficiencies for each SIW mode are listed in Table 2. \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Parameters** & **Values** & **Parameters** & **Values** \\ \hline \(p_{1}\) & 44.5 mm & \(s_{1}\) & 1 mm \\ \(P_{2}\) & 12.6 mm & \(s_{2}\) & 2 mm \\ \(h_{1}\) & 6.4 mm & \(l_{1}\) & 28 mm \\ \(h_{2}\) & 1.6 mm & \(l_{2}\) & 28 mm \\ \(g\) & 4.1 mm & \(l_{u1}\) & 8 mm \\ \(w_{1}\) & 18.7 mm & \(l_{u2}\) & 21.8 mm \\ \(w_{2}\) & 44.5 mm & \(w_{b}\) & 6.3 mm \\ \(l_{1}\) & 43 mm & \(l_{b}\) & 4.2 mm \\ \(l_{2}\) & 43 mm & \(m_{11}\) & 4.55 mm \\ \(w_{u1}\) & 4.4 mm & \(m_{2}\) & 20.75 mm \\ \(w_{u2}\) & 3.2 mm & \(l_{s1}\) & 15.3 mm \\ \(d_{1}\) & 1 mm & \(l_{s2}\) & 3 mm \\ \(d_{2}\) & 2 mm & \(w_{s1}\) & 0.5 mm \\ \(b_{1}\) & 3 mm & \(b_{2}\) & 2 mm \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Design parameters of the proposed antenna. Figure 3: Photographs of the fabricated antenna: (**a**) isometric view; (**b**) side view. To improve the antenna radiation efficiency, we designed another model using a Duroid 5880 (\(\varepsilon_{r}\) = 2.2, tan \(\delta\) = 0.0009) substrate for a low loss material. The detailed parameters of the efficiency improved model are listed in Table 3. Figure 7 shows the simulated efficiency results for the Duroid and FR-4 designs, and the antenna efficiency can be increased up to 82% at 4.85 GHz using the Duroid substrate compared to that of 38% for the FR-4 substrate in the TE\({}_{10}\) mode.