# Low Cost Circularly Polarized Antenna for IoT Space Applications
## 2 Antenna Design and Simulations  
### Radiating Elements  
The 3-element configuration will require to split the power into three equi-amplitude signals with \(0^{\circ},120^{\circ}\), and \(240^{\circ}\) phase shifts. The proposed structure is composed of three identical elements that are symmetrically placed around a central axis. A ground plane with a disk or triangular shape is by nature more suitable for this solution. The disk form is preferred in order to maximize the antenna frequency bandwidth. Then, the antennas are built on a top PCB, as shown in Figure 1. By using a vertical Inverted F antenna structure, these radiating elements are placed on the edges of the disc with the feeding lines coming from the disk center. The top layer is connected to the ground plane at the bottom layer by 1 mm diameter metal wires. The antenna is simulated and optimized with a 3D EM solver. S-parameters are plotted on Figure 2. For clarity and considering the structure symmetry, only \(S_{1}1\) and \(S_{2}1\) are presented. A maximum coupling between the feeding ports of \(-8\) dB is simulated. Considering that the three feeding ports are fed with a \(120^{\circ}\) phase shift, power will be dissipated, due to the coupling. Nevertheless, the loss will depend on the way the two coupled signals will be recomb In order to generate three RF signals with a 120\({}^{\circ}\) phase shift, a compact circuit based on a hybrid coupler is proposed (Figure 3). One-third of the signal will be reflected from the direct and coupled port of the coupler by using a simple reactive load, and the reflected signal will recombine constructively in the coupler isolated port, thus providing three equal amplitude outputs. In order to get the required phase shift, additional delay lines are needed on each port access. Figure 1: Top, side, and 3D view of the radiating structure. Figure 2: Simulated S-parameters of the proposed radiating elements. The hybrid coupler circuit is based on a quasi-lumped quadrature coupler (QLQC), which is composed of two \(45^{\circ}\) transmission lines (\(\theta_{2}\)) and two capacitors \(C_{1}\), which enable strong miniaturization and lower loss compared with a classical branch-line coupler [17]. For a QLQC, the phase of the direct port and coupled port are respectively \(-90^{\circ}\) and \(0^{\circ}\). On the direct and coupled port of the QLQC, shunt capacitors \(C_{2}\) are connected to reflect a part of the signals. The reflected signals combine constructively on Port 1. The reflection on the shunt capacitor is given by Equation (1)  
\[ \begin{split} S_{aa}&=-2\Pi\dot{J}\omega C_{2}Z_{0} /(2+2\Pi\dot{J}\omega C_{2}Z_{0})\\ S_{ba}&=(2-\Pi\dot{J}\omega C_{2}Z_{0})/(2+2\Pi \dot{J}\omega C_{2}Z_{0})\end{split}  \tag{1}\]  
The value of capacitor \(C_{2}\) is chosen to reflect one-third of the signal at 868 MHz; thus a capacitance of 5.1 pF is required and it provides a reflection phase of \(124^{\circ}\). Transmission of the QLQC is extracted from [18]. Phase \(S_{ba}\) at 868 MHz is \(-34^{\circ}\). Phase \(S_{aa}\) at 868 MHz is \(-124^{\circ}\). \(\theta_{3}\) is tuned to provide a \(-30^{\circ}\) phase shift at 868 MHz. From Equation (2), \(\theta_{1}\) must provide a phase shift of \(-57^{\circ}\). A feeding line (\(\theta_{4}=-30^{\circ}\)) is also added on port 4 to access to the coupler  
\[ \begin{split} phase(S_{24})&=\theta_{4}+0^{\circ} +phase(S_{ba})=-64^{\circ}\\ phase(S_{34})&=\theta_{4}-90^{\circ}+phase(S_{ba})+ \theta_{2}=176^{\circ}\\ phase(S_{14})&=\theta_{4}+0^{\circ}+phase(S_{aa})-90^ {\circ}+\theta_{4}=56^{\circ}\end{split}  \tag{2}\]  
The circuit is designed in a very compact way with meandered lines on a 1.6 mm-thick FR4 substrate (\(\epsilon_{r}=4.4\) and \(tan\delta=0.02\)) as shown in Figure 4. S-parameters results are presented in Figure 5. A perfect circuit would provide an equal amplitude of \(-4.7\) dB on each port and a \(120^{\circ}\) phase shifts at 868 MHz. A level of \(-5.3\) dB is obtained at 870 MHz, corresponding to a 0.6 dB insertion loss.