## 5 Design of a Crossed-Dipole Antenna  
With the design of a single dipole antenna completed, Dipole \(B\) is constructed, whose dimensions are the same as those of Dipole \(A\) except for the microstrip-slotline coupling  
Figure 8: Co-polarized gain patterns of a single dipole antenna at (**a**) 1.16 GHz, (**b**) 1.30 GHz, and (**c**) 1.61 GHz. point position C\({}_{1B}\). Dipole \(A\) and Dipole \(B\) are arranged in orthogonal directions as shown in Figure 9 to form a crossed-dipole antenna. Rectangular coordinate axes are shown in Figure 9 for far-field angle identification in spherical coordinates. Dipoles \(A\) and \(B\) are placed in \(\varphi\) = 45\({}^{\circ}\) and \(\varphi\) = 135\({}^{\circ}\) planes, respectively. Dimensions of Dipole \(A\) and Dipole \(B\) are slightly readjusted for good impedance matching and high isolation between the two dipoles. The ground plane diameter is finely tuned for wide gain and axial ratio beamwidths. Dipole \(A\) and Dipole \(B\) are excited with equal magnitude and with a 90\({}^{\circ}\) phase difference using delta-gap sources. This is equivalent to feeding the dipoles with a perfect quadrature hybrid coupler. Dimensions of the designed crossed-dipole antenna are given in Table 3. Figure 10 shows the reflection coefficient of Dipole \(A\) (S1,1) and Dipole \(B\) (S2,2) and the transmission coefficient (S2,1) from Dipole \(A\) to Dipole \(B\). The transmission coefficient S1,2 from Dipole \(B\) to Dipole \(A\) is not drawn in Figure 10 since it is the same as S2,1. The reflection coefficient of Dipole \(B\) is similar to that of Dipole \(A\) and less than \(-\)10 dB above 1.10 GHz. The transmission coefficient, or negative of isolation, is less than \(-\)24 dB above 1.10 GHz. Figure 11 shows 2D RHCP gain patterns of the crossed-dipole antenna at 1.16, 1.30, and 1.61 GHz. In the spherical coordinate system, the range of angles \(\theta\) and \(\varphi\) can be defined in various ways. In Figure 11, the elevation angle \(\theta\) (Theta) ranges from \(-\)180\({}^{\circ}\) to +180\({}^{\circ}\), while the azimuth angle \(\varphi\) (Phi) ranges from \(-\)90\({}^{\circ}\) to +90\({}^{\circ}\), covering the entire angle range in the spherical coordinate. Angular symmetry of gain patterns in the \(\varphi\) direction is excellent. Figure 10: Reflection and transmission coefficients of the crossed-dipole antenna. Figure 9: Crossed-dipole antenna with delta-gap sources. From 1D gain patterns (not shown), we find that the maximum gain \(G_{\rm max}\) and the minimum gain \(G_{\rm min}\) in the horizontal plane are as follows:  
\[ \begin{array}{l}\mbox{At 1.16 GHz, }G_{\rm max}=-2.65\mbox{ dBic at }\varphi/\theta=62^{\circ}/90^{\circ}\mbox{ and }G_{\rm min}=-3.06\mbox{ dBic at }\varphi/\theta=-48^{\circ}/-90^{\circ};\\ \mbox{At 1.30 GHz, }G_{\rm max}=-1.42\mbox{ dBic at }\varphi/\theta=36^{\circ}/-90^{\circ} \mbox{ and }G_{\rm min}=-2.61\mbox{ dBic at }\varphi/\theta=-73^{\circ}/90^{\circ};\\ \mbox{At 1.61 GHz, }G_{\rm max}=-0.55\mbox{ dBic at }\varphi/\theta=34^{\circ}/-90^{\circ} \mbox{ and }G_{\rm min}=-1.22\mbox{ dBic at }\varphi/\theta=78^{\circ}/90^{\circ}.\\ \end{array} \]  
The horizontal gain is increased with frequency, as can be seen from the above numerical values and Figure 11.  
Figure 12 shows the 2D axial ratio (AR) patterns of the crossed-dipole antenna at 1.16, 1.30, and 1.61 GHz. Axial ratio is less than 6 dB in the upper hemisphere (\(-90^{\circ}\leq\theta\leq+90^{\circ}\) and \(-90^{\circ}\leq\varphi\leq+90^{\circ}\)). In the 1D gain patterns of a single dipole antenna shown in Figure 8, one can see that the gain symmetry versus the \(\varphi\) angle is better at 1.16 GHz than at 1.30 GHz, suggesting a better AR performance at 1.16 GHz. This can be seen by comparing Figure 12a with Figure 12c. The AR is largest at the horizon (\(\theta=90^{\circ}\)) in the  
Figure 11: RHCP gain patterns at (a) 1.16 GHz, (b) 1.30 GHz, and (c) 1.61 GHz. upper hemisphere (\(-90^{\circ}\leq\theta\leq+90^{\circ}\)).