## 2 Antenna Design
### Patch Array Feed  
An array of microstrip patches is used to illuminate the offset reflector. The selected setup consists of a 2 \(\times\) 8 patch antenna array, illustrated in Figure 2. To prevent a grating lobe in the scanning plane of the reflector, an array spacing of d = 0.4\(\lambda\) (\(\lambda\) is the free space wavelength) is adopted. The substrate used is Rogers RT5880, featuring a dielectric constant of 2.2, a loss tangent of 0.0009, and a thickness of 0.508 mm. This substrate was selected for its low dielectric constant and minimal dielectric loss, offering an ideal balance between high performance (in terms of bandwidth and radiation characteristics) and the mission's size and mass constraints. Its low contribution to overall losses is primarily due to the minimal dielectric loss. The geometrical parameters of the antenna array are presented in Table 2. Rectangular patches receive power from microstrip power-dividing network on the same layer. The main line consists of a microstrip line width of W\({}_{1}\), with a characteristic \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Parameter** & **Value** & **Parameter** & **Value** \\ \hline Frequency & 17.2 GHz & Return loss & 20 dB \\ Polarization & Linear & Antenna gain & 25 dBi \\ Bandwidth & 200 MHz & Stowed & 10 \(\times\) 10 \(\times\) 10 cm\({}^{3}\) \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Reflector antenna specifications. Figure 1: 6U CubeSat employing the proposed deployable cylindrical reflector antenna. The antenna is designed to fit within 1U (10 \(\times\) 10 \(\times\) 10 cm\({}^{3}\)) [24]. impedance of 50 \(\Omega\). A 50 ohm coaxial connector mounted on the edge is utilized to excite the array feed. Designed with impedances of 70.7 \(\Omega\) and 100 \(\Omega\), the widths W\({}_{2}\) and W\({}_{3}\) support the necessary impedance transformation across the feed network. The lengths L\({}_{1}\) through L\({}_{5}\) along with other parameters, were optimized to achieve a reflection coefficient, S\({}_{11}\), of less than \(-\)20 dB at 17.2 GHz, ensuring the desired radiation characteristics for the array patch. It is important to mention that while the array could be further optimized, the primary aim here was to design a compact and lightweight array for testing the cylindrical reflector performance, as elaborated upon in Section 2.3. The simulation of the feed array was carried out using Computer Simulation Technology Microwave Studio (CST MWS). The patch array was manufactured using the MiniMill machine at the Machine Shop, Electrical Department, University of Manitoba, as depicted in Figure 3. The feed measurement was conducted at the antenna testing facilities at the University of Manitoba. The measured reflection coefficient, S\({}_{11}\), is shown in Figure 4 and closely aligns with the simulated result. The feed operates at 17.2 GHz with a bandwidth ranging from 17.02 GHz to 17.4 GHz. The measured bandwidth falls within the range of 17.08 GHz to 17.38 GHz. The slight discrepancy in bandwidth between the simulation and measurement could be attributed to fabrication tolerances and cable losses. The reflection coefficient is below \(-\)20 dB for both simulation and measurement data. Radiation pattern measurements were conducted in the anechoic chamber, as illustrated in Figure 5. The co- and cross-polarization radiation patterns of the feed, in the E- and H-planes, at 17.2 GHz are depicted in Figure 6a,b. There is excellent agreement between the simulation and measurement results for both polarizations. The addition of the second row of the array serves to narrow the beamwidth in the plane of the parabola and subsequently provides proper illumination of the reflector cut (along the \(y\)-axis, as shown in Figure 7). After a detailed analysis, a spacing of L\({}_{5}\) = 3.62 mm was found to be the optimal distance between the two patch rows, maintaining an operating frequency of 17.2 GHz and delivering the desired radiation characteristics.