## 4 Design of a Single Dipole Antenna
With the other dipole's PCB inserted in the slot, the characteristic impedance will be decreased due to dielectric loading. The heights \(H_{A}\) (for Dipole \(A\)) and \(H_{B}\) (for Dipole \(B\)) determine the short-circuited line length of the slotline together with the slot-strip coupling point \(C_{1A}\) (for Dipole \(A\)) and \(C_{1B}\) (for Dipole \(B\)). The position \(C_{1A}\) of the microstrip-slotline coupling point relative to the arm of Dipole \(A\) is crucial in the impedance matching, and it is adjusted by parameter sweep. When crossed dipoles are formed in a later stage, the corresponding value \(C_{1B}\) in Dipole \(B\) is set as close to \(C_{1A}\) as possible to excite the two dipoles with almost the same phase and to obtain the same impedance matching. The gap between the half-width microstrip line crossing the slotline is set to 0.5 mm. The coupling position \(C_{1A}\), position \(H_{A}\) of the slotline short circuit, and length \(C_{5}\) of the microstrip open circuit are all interrelated and thus changed simultaneously. The dipole design is the most laborious step in the development of the proposed antenna, requiring extensive simulations as well as intuition and experience. The results of the design of Dipole \(A\) are presented in Table 3 for dimensions, in Figure 7 for reflection coefficient, and in Figure 8 for gain patterns. Dimensions in Table 3 are values slightly readjusted with the addition of Dipole \(B\) and the quadrature hybrid coupler as described in the later sections. Figure 7 shows the reflection coefficient of the designed Dipole \(A\) and Dipole \(B\) when they are alone on a ground plane as shown in Figure 5. The reflection coefficient of Dipole \(A\) is less than \(-10\) dB from 1.10 GHz to 1.74 GHz with resonances at 1.20 GHz and 1.56 GHz. The resonance at 1.20 GHz is due to the dipole, while the one at 1.56 GHz is due to the monopole. The resonance frequency is determined by the combined effects of the dipole, monopole, dipole-monopole coupling, ground plane diameter, and dipole feed line. From Table 3, the lengths of the dipole and the monopole in terms of the resonant wavelength at 1.20 GHz and 1.56 GHz are found to be 0.424 \(\lambda\) and 0.179 \(\lambda\), respectively. The reflection coefficient of Dipole \(B\) shows a frequency response similar to Dipole \(A\). Figure 8 shows the co-polarized gain patterns of the design Dipole \(A\) at 1.16, 1.30, and 1.61 GHz for \(\varphi\) = 0\({}^{\circ}\), 45\({}^{\circ}\), 90\({}^{\circ}\), and 135\({}^{\circ}\) with Dipole \(A\) in the \(\varphi\) = 135\({}^{\circ}\) plane as shown in Figure 6a. First, it is noted that the \(E\)-plane (\(\varphi\) = 135\({}^{\circ}\)) pattern is still narrower than the \(H\)-plane (\(\varphi\) = 45\({}^{\circ}\)) pattern. The two diagonal plane (\(\varphi\) = 0\({}^{\circ}\), 90\({}^{\circ}\)) patterns are the same. The beamwidth is increased as the frequency increases. This is due to the fact that the dipole resonates at 1.20 GHz while the monopole resonates at 1.56 GHz. At lower frequencies, the dipole current is stronger, resulting in decreased gain in the horizontal angle (\(\theta\) = 90\({}^{\circ}\)) and increased gain at zenith (\(\theta\) = 0\({}^{\circ}\)). At higher frequencies, the monopole is more strongly excited, yielding reduced zenith gain and increased horizontal gain. With the use of parasitic monopoles, the angular symmetry of the gain pattern in the \(\varphi\) direction is much improved from that of a dipole alone. The front-to-back ratio ranges from 10 dB to 15 dB.