## 7 Design of a Crossed-Dipole Multi-GNSS Antenna  
The final design of the proposed antenna for multi-GNSS applications involves combining the designs of the crossed dipole and the QHC feed network and connecting coaxial cables to the QHC ports. The combined structure is finely tuned to compensate for the interaction between the crossed dipole and the feed network, and the dimensions of the proposed antenna are slightly different from the ones in Tables 3 and 4. Figure 15 shows a 3D view of the final design of the proposed antenna. Conducting materials are rendered in gray, while dielectric materials are in yellow. \begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Parameters** & **Value** & **Parameters** & **Value** & **Parameters** & **Value** \\ \hline \(L_{1}\) & 31.72 & \(L_{4}\) & 8.70 & \(W_{1}\) & 0.36 \\ \hline \(L_{2}\) & 4.35 & \(L_{5}\) & 4.80 & \(W_{2}\) & 3.10 \\ \hline \(L_{3}\) & 11.20 & \(W_{0}\) & 1.94 & \(W_{3}\) & 1.94 \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Dimensions of the designed QHC (mm). Figure 14: (**a**) Reflection and transmission coefficients and (**b**) the phase difference between two output ports of the designed QHC. Figure 16 shows the reflection coefficient (S1,1 for RHCP and S2,2 for LHCP) and transmission coefficient (S2,1 = S1,2) of the designed antenna. The reflection coefficient is less than -15 dB at 1.01-1.72 GHz. The transmission coefficient is less than \(-\)15 dB at 1.02-1.61 GHz, reflecting the performance of the QHC feed network. As can be seen in Figure 10, the isolation between the crossed dipoles without the feed network is greater than 24 dB at this frequency range. The limited isolation between the RHCP and LHCP ports needs to be improved if GNSS and satellite phones are to operate simultaneously using the designed antenna. The gain and axial ratio performance of the designed antenna are presented below in rectangular plots. Figure 17 shows the gain patterns in \(\varphi=0^{\circ}\), \(45^{\circ}\), \(90^{\circ}\), and \(135^{\circ}\) planes at 1.1, 1.3, and 1.6 GHz. The gain at zenith (\(\theta=0^{\circ}\)) is 5.8, 5.0, and 3.9 dBic at 1.1, 1.3, and 1.6 GHz, respectively. The front-to-back ratio is in excess of 30 dB at all frequencies. The designed antenna boasts wide-beamwidth symmetric gain patterns. Analysis of the gain patterns in the horizontal plane (\(\theta=90^{\circ}\) and \(-180^{\circ}\leq\varphi\leq 180^{\circ}\)) reveals the following values for the maximum and minimum gains:  
At 1.16 GHz, \(G_{\max}=-2.42\) dBic at \(\varphi=144^{\circ}\) and \(G_{\min}=-3.31\) dBic at \(\varphi=58^{\circ}\);  
At 1.30 GHz, \(G_{\max}=-1.19\) dBic at \(\varphi=123^{\circ}\) and \(G_{\min}=-3.17\) dBic at \(\varphi=-59^{\circ}\);  
At 1.61 GHz, \(G_{\max}=-0.23\) dBic at \(\varphi=-128^{\circ}\) and \(G_{\min}=-1.87\) dBic at \(\varphi=6^{\circ}\). Figure 16: Reflection coefficient and isolation characteristics of the designed antenna. Figure 15: A 3D view of the designed antenna. Figure 18 shows the axial ratio patterns of the designed antenna at 1.16, 1.30, and 1.61 GHz in \(\varphi=0^{\circ}\), \(45^{\circ}\), \(90^{\circ}\), and \(135^{\circ}\) planes. The axial ratio is smallest at zenith and 1.0, 0.6, and 0.6 dB at 1.16, 1.30, and 1.61 GHz. In the hemispherical space, the axial ratio is less than 6 dB for all \(\varphi\) angles. The axial ratio is greatest at \(\theta=\pm\)\(90^{\circ}\). Detailed analysis shows the following data for the axial ratio in the horizontal plane. Figure 17: Gain patterns of the designed antenna at (**a**) 1.16 GHz, (**b**) 1.30 GHz, and (**c**) 1.61 GHz. Figure 18: Axial ratio patterns of the designed antenna at (**a**) 1.1 GHz, (**b**) 1.3 GHz, and (**c**) 1.6 GHz.