# A Fundamental Study on Circularly Polarized Double-Loop Antennas with Quasi-Two Sources
## 3 Antennas with an Outer Parasitic Loop  
Figure 1 shows the antenna configuration. Two concentric square loops with a spacing \(S\) are located at height \(h\) above the ground plane. The outer and inner loops are parasitic and driven, respectively, and the driven loop's perimeter is designated as \(P\).  
The driven loop has adjacent corners \(F_{\mathrm{n}}\), which are excited by a branched feedline \(F_{\mathrm{n}}\)-\(B\)-\(F_{2}\)\({}^{\prime}\) that is vertical to the ground plane, where the branch point \(B\) is at height \(h_{\mathrm{B}}\), as shown in Figure 1c. The driven loop corners \(F_{\mathrm{n}}\) are connected to the parasitic loop corners \(C_{\mathrm{n}}\) by lines \(F_{\mathrm{n}}\)-\(C_{\mathrm{n}}\), as shown in Figure 1b. The antenna is made of wires with a radius \(\rho\)[9].  
We analyzed the antenna using the moment method [10]. The ground plane size was assumed to be infinite, and image theory was applied to the analysis. The antenna was designed to radiate a CP beam in a direction that was normal to the antenna plane in the \(z\)-axis direction. For this, the loop perimeter was initially set to be \(P=1\lambda_{0}\) (\(\lambda_{0}\): the free-space wavelength at \(f_{0}\)), so that the traveling wave-type current distributes along the loop arm, which is necessary for the CP beam. Taking this into consideration, we selected the loop  
Figure 2: Axial ratios versus frequency for three square-loop antennas with a single feed above the ground plane [7]. (**a**) Single-loop antenna. (**b**) Discrete double-loop antenna. (**c**) Connected double-loop antenna.  
perimeter and feedline branch height (\(P\), \(h_{\text{B}}\)) as a function of loop spacing \(S\). The other configurations are the same as those in [9]: (\(h\), \(\rho\)) = (\(\lambda_{0}/4\), \(\lambda_{0}/200\)).  
The lower part of Figure 3 shows the simulated 3 dB axial ratio bandwidth versus loop spacing \(S\). At each value of \(S\), the parameters (\(P\), \(h_{\text{B}}\)) were selected to maximize the bandwidth. The selected loop perimeter \(P\) versus \(S\) is shown in the upper part of the figure. It was found that as \(S\) increases, the bandwidth increases and reaches a maximum value. This maximum value is 23% at \(S\) = 0.02\(\lambda_{0}\) with (\(P\), \(h_{\text{B}}\)) = (0.96\(\lambda_{0}\), 0.06\(\lambda_{0}\)).  
The simulated gain and axial ratio versus frequency for \(S\) = 0.02\(\lambda_{0}\) are shown with solid lines in Figure 4. The gain was found to be more than 5.1 dB in the abovementioned CP wave bandwidth. For reference, the dotted lines show the results of a single-loop antenna [9]. The single-loop antenna has an axial ratio bandwidth of 12%. It can be said that the present antenna's bandwidth is two times as wide as that of the single-loop antenna. The wider bandwidth is because the parasitic loop corners \(C_{\text{n}}\) are connected to the driven loop corners \(F_{\text{n}}\), which are excited by the same amplitudes with a phase difference of 90\({}^{\circ}\)[9]. In other words, a double-loop antenna without an \(F_{\text{n}}\)-\(C_{\text{n}}\) connection does not show an increased axial ratio bandwidth.  
The radiation patterns for \(S\) = 0.02\(\lambda_{0}\) are shown in Figure 5. The radiation is decomposed into right- and left-hand CP wave components. It can be seen that the antenna radiates a CP beam that is normal to the antenna plane. The half-power beam widths (HPBWs) are 85\({}^{\circ}\) and 81\({}^{\circ}\) in the \(\phi\) = 0\({}^{\circ}\) and 90\({}^{\circ}\) planes, respectively. The gain is 7.2 dBi. The corresponding HPBWs and gain for the single-loop antenna are 89\({}^{\circ}\), 81\({}^{\circ}\), and 7.4 dBi [9].  
Figure 4: Simulated frequency responses of axial ratio and gain for an outer parasitic loop with \(S\) = 0.02\(\lambda_{0}\).  
Figure 3: Simulated axial ratio bandwidth and the selected loop perimeter \(P\) versus loop spacing \(S\) for an outer parasitic loop.