## 3 Design and Geometry of the Proposed Antenna
### S-Band Antenna Design
This aspect, therefore, represents the primary strength of the antenna [26]. Firstly, the 8% impedance bandwidth has been achieved by placing a parasitic patch in a stacked patch configuration. In this setup, the lower patch is fed through a co-axial pin, while the upper patch is electromagnetically coupled to the lower patch. This configuration enables the lower frequency to be determined by the lower patch while the upper patch sets the upper frequency, thereby increasing the bandwidth [19; 20; 21]. Additionally, to generate circular polarization, the coaxial pin is rotated by an angle of 45\({}^{\circ}\) with respect to the center line, thereby establishing the orthogonal components of the field with equal magnitude and a 90\({}^{\circ}\) phase shift, resulting in circular polarization but with a narrow bandwidth [27]. By incorporating sufficiently large slots or notches in both patches, the axial ratio (AR) bandwidth is enhanced without compromising the radiation characteristics. Consequently, the antenna achieves a bandwidth of 8%, encompassing both uplink (2.03 GHz) and downlink (2.205 GHz) frequencies, thereby ensuring robustness in gain and polarization vs. frequency. This guarantees the link's viability under any conditions that may cause a deviation in the antenna's operating frequency. In consideration of the aforementioned factors, the proposed circularly polarized antenna is to be constructed from a multilayer stack-up. In order to minimize manufacturing costs and in accordance with the principles of CubeSat development, a low-cost substrate will be utilized HF Rohacell [28] and Rogers 4360 [29] (Figure 3). The layers of this multi-layer stack-up are divided into three RO4360 dielectric boards separated by two Rohacell spacers, which provide structural integrity while behaving almost like air: a lower board formed by two layers consisting of a RO4360 dielectric layer (H2) covered with a copper layer on one of its sides (H1). The copper layer H1 functions as a ground plane, upon which the SMP connector is soldered, while the primary function of the RO4360 is to provide rigidity while reducing weight compared to a metallic board. The central board comprises an additional layer of RO4360 dielectric featuring copper metallization on one side, which is partially removed to create the lower patch. The pins of the SMP connectors are soldered to this patch. Finally, a third board is constructed using an additional layer of RO4360 with copper metallization on the top side, which is partially removed to create the parasitic patch. The excitation of this parasitic patch is facilitated through electromagnetic coupling from the lower patch, with the coupling strength being determined by the thickness of the Rohacell spacers. Additionally, two miniature coaxial 50 ohm SMP connectors (right and left polarizations) are employed to feed the lower patch, ensuring the integration of the antenna without interfering with other functional units inside the satellite (see Figure 4). The subsequent investigation in Section 4 will entail a parametric analysis of the parasitic element and the presence of notches, with the objective of achieving circular polarization across a broad frequency range. Additionally, the gain bandwidth performance will be assessed and contrasted with the impedance bandwidth of the proposed antenna.