## 3 Antenna Structure  
Figure 1 shows an integrated 3D layout of the proposed antenna. It consists of two orthogonal printed dipole antennas (Dipole \(A\) and Dipole \(B\)) fed by a broadband quadrature hybrid coupler (QHC) printed on the backside of the ground plane circuit board. To obtain circularly polarized radiation, it is necessary to excite two orthogonal current vectors in phase quadrature. The electric field at the far zone can be expressed in the spherical coordinates as follows [31]. \[\mathbf{E}=E_{\theta}\hat{\mathbf{\theta}}+E_{\varphi}\hat{\mathbf{\varphi}}=E _{R}\mathbf{a}_{R}+E_{L}\mathbf{a}_{L} \tag{1}\]  
where \(E_{\theta}\) and \(E_{\varphi}\) are the phasor of the theta and phi components of the electric field, and \(\mathbf{a}_{R}\) and \(\mathbf{a}_{L}\) are base vectors for the RHCP and LHCP, respectively, that are given by the following:  
\[\mathbf{a}_{R}=\frac{1}{\sqrt{2}}(\hat{\mathbf{\theta}}-j\hat{\mathbf{\varphi} })\;,\;\mathbf{a}_{L}=\frac{1}{\sqrt{2}}(\hat{\mathbf{\theta}}+j\hat{\mathbf{ \varphi}}) \tag{2}\]  
\(E_{R}\) and \(E_{L}\) are the RHCP and LHCP components of the electric field given by the following:  
\[E_{R}=\mathbf{E}\cdot\mathbf{a}_{R}^{*}=\frac{1}{\sqrt{2}}(E_{\theta}+jE_{ \varphi})\;,\;E_{L}=\mathbf{E}\cdot\mathbf{a}_{L}^{*}=\frac{1}{\sqrt{2}}(E_{ \theta}-jE_{\varphi}) \tag{3}\]  
The maximum electric field or the semi-major axis of the polarization ellipse is given by the following:  
\[|E|_{\text{max}}=\frac{1}{\sqrt{2}}(|E_{R}|+|E_{L}|) \tag{4}\]  
While the minimum electric field or the semi-minor axis is given by the following:  
\[|E|_{\text{min}}=\left\{ \begin{array}{ll}\frac{1}{\sqrt{2}}(|E_{R}|-|E_{L}|) \;\text{if}\;|E_{R}|\;>\;|E_{L}|&(\text{RHCP})\\ \frac{1}{\sqrt{2}}(|E_{L}|-|E_{R}|)\;\text{if}\;|E_{L}|\;>\;|E_{R}|&(\text{ LHCP})\end{array} \right. \tag{5}\]  
Figure 1: A 3D representation of the proposed antenna. The axial ratio (AR) is now given by the following:  
\[\text{AR}=20\log_{10}\frac{|E|_{\text{max}}}{|E|_{\text{min}}} \tag{6}\]  
For an ideal axial ratio of 0 dB, one needs two orthogonal electric field vectors of the same magnitude and of \(\pm 90^{\circ}\) phase difference, where the plus or minus sign determines the sense of polarization, i.e., RHCP or LHCP. Two symmetric crossed dipoles fed in 90-degree phase difference in the absence of a conducting ground plane offer 0 dB axial ratio in the direction normal to the plane of the dipoles and infinite axial ratio in the plane of the dipoles. One method of obtaining a wide axial ratio and gain beamwidths is to place the crossed dipoles at a suitable distance from a ground plane of optimum diameter and to add parasitic monopoles excited by the dipoles as shown in Figure 1. The monopoles generate an electric field vector normal to the ground plane, which widens the axial ratio and gain beamwidths. The size of the ground plane is important since a large ground plane will short-circuit the electric field vector tangential to the ground plane, leaving out only the normal component of the electric field. This in turn makes the axial ratio approach infinity. For wide beamwidth over a large frequency range, the dimensions of the dipoles, monopoles, and ground plane are optimized along with the dipole feed network using an electromagnetic simulation tool. For a good axial ratio, the balancing of the dipole current and the monopole current is important as well as the size of the ground plane. For broadband performance, the width of the dipole strip and the shape of the monopole are key parameters, as well as the wideband feed network. Table 2 shows the axial ratio versus the amplitude ratio and phase difference in two vector components, \(E_{\theta}\) and \(E_{\varphi}\). The axial ratio is calculated and tabulated using Equation (6) for the phase difference (Arg (\(E_{\theta}\))-Arg (\(E_{\varphi}\))) from 50 to 90 degrees and the magnitude ratio (\(\left\lvert\,E_{\theta}\,\right\rvert/\left\lvert\,E_{\varphi}\,\right\rvert\)) of 0, 1, 2, and 3 dB.