## 2 Proposed Antenna Design  
### Design and Configuration of Antenna  
Figure 2 shows the configuration and realization of the proposed antenna. The K-band two-port array consists of a modified diamond-shaped microstrip feedline with tapered terminals and four circular patch elements on the top layer and a ground plane on the bottom layer. A 0.25 mm thick Rogers RT/Duroid 5880 NS substrate with a relative permittivity (\(\varepsilon_{r}\)) of 2.2 and loss tangent (tan\(\delta\)) of 0.009 is chosen as the dielectric material of the antenna. All simulations are performed using CST Microwave Studio Suite 2021. Each patch couples and radiates a fraction of energy from the guided waves traveling on the feedline from one port to the other. The gap between the traveling feedline and the element is constant with the parameter \(G\) to provide the same coupling strength. Figure 3 illustrates the current distribution of the proposed antenna at two different phases, namely 0\({}^{\circ}\) and 90\({}^{\circ}\) at a frequency of 24 GHz. This visual representation effectively depicts the resonance of the antenna when the traveling wave propagates from port 1 to port 2, resulting in RHCP. On the other hand, the excitation from port 2 to port 1 will yield LHCP. To ensure minimum signal leakage from one port to the other, it is necessary to obtain at least 15 dB of isolation between the ports. Any leakage between the ports can cause signal coupling interference, leading to signal degradation and reduced system performance. Therefore, in this paper, the operational bandwidth of the antenna is defined as the band where the reflection coefficients at each port are below \(-10\) dB, and the transmission coefficients between the ports are below \(-15\) dB. Maintaining in-phase alignment among the patches is crucial for achieving broadside radiation. Furthermore, the patches are positioned along the feedline with 90\({}^{\circ}\) angular rotation, determined by the number of elements. To ensure the desired in-phase condition, adjacent patches are separated by a microstrip line, and the length of this line is determined by the following Equation (1)  
\[\lambda_{g}-\frac{\lambda_{g}}{4} \tag{1}\]  
where \(\lambda_{g}\) is the guided wavelength on the feedline. The term \(\lambda_{g}/4\) provides a relative orientation between adjacent patches, providing a phase difference of 90\({}^{\circ}\). The modified diamond-shaped feedline not only satisfies the desired in-phase condition between the patches but also maintains the spacing between the patches close to \(\lambda_{0}/2\), where \(\lambda_{0}\) is the wavelength in free space. This design enables the proposed antenna to achieve compact size and high gain through the array. The radiated energy through the patch is determined by the small gap between each patch and the feedline through proximity coupling. That is, the smaller the gap, the larger the radiated energy through each patch. However, the gap size is limited by the available PCB fabrication process. Narrowing down the feedline width (\(W_{4}\)) can increase the coupling strength, resulting in a more pronounced fringing field. However, 0.25 mm was chosen here, considering fabrication constraints and ensuring impedance matching. The circular patch resonates at the fundamental mode and generates  
Figure 1: Conceptual diagram of non-linear tag system with body attachment. CP through uniform current rotation. However, a single conventional circular patch does not provide a sufficient coupling rate due to its inherent structure. Therefore, in a previous study [26], a configuration with seven elements was used. In this study, we propose a modified circular patch to enhance the coupling rate and achieve a compact array structure. By utilizing only four elements, we ensure the desired operational bandwidth.