## 2 Materials and Methods  
The proposed antenna is designed for established 1U, 2U and other nanosatellite structures, and addresses the problems associated with the limited volume and surface area for solar panel and antenna placement. First, the resonant condition for the nanosatellite structure was examined. Then an inverted-F antenna was designed, considering one face of the nanosatellite body as the ground plane that functions as an infinite ground plane to achieve lower UHF frequency. Sufficient space for placing the solar panel between the radiating element and ground plane was given priority in the initial design. The resonant frequency of the inverted-F antenna was initially estimated by the Equation (1) [17], where, \(c\) is the light velocity, and \(L\) and \(W\) are the length and width of the radiator, respectively. \[f=\frac{c}{4(L+W)} \tag{1}\]  
The design was optimized with the nanosatellite structure maintaining both electromagnetic and structural constraints. Estimation of the antenna performance was carried out with the commercially available numerical simulator Computer Simulation Technology (CST). The proposed lower UHF antenna is illustrated in Figure 1. The antenna consists of a rectangular radiating patch with a shorting wall, two linear slots on the patch, and a 50 \(\Omega\) radio frequency (RF) coaxial feed. Two rectangular slots were etched out such that the equivalent inductance caused by the shorting pins and feeding probe were reduced, and more than fifty percent of the surface area of the radiating element remained uncovered to ensure proper solar penetration on the solar panel. The design parameters are distinctively studied to investigate their influences on the resonant frequency, and the other parameters remained unchanged. The effect of the rectangular slot width \(a\) on the antenna reflection coefficient, efficiency, and realized gain was studied, and is shown in Figure 2. The figure shows that decreasing the slot width causes the resonant frequency to shift upwards, i.e., an inverse relation is formed between the resonant frequency and slot width due to the change in effecting the electrical area. The total efficiency and realized gain were observed to have shifted in accordance with the resonant frequency. The dimension of the parameters \(e\) and \(f\) have an influence on the antenna reflection coefficient, total efficiency, and realized gain, as shown in Figure 3. It is observed from Figure 3 that, the radiating element \(e\) had a strong influence on the resonant frequency rather than \(f\). Thus, it was easier to tune the resonant frequency by varying the length of \(e\). It is seen from Figure 1 that variation of the slots dimension had a direct effect on the open space for solar penetration. Therefore, these parameters were numerically investigated. Figure 1: (**a**) Design layout of the proposed antenna; yellow radiating patch and gray ground plane, (**b**) antenna integrated with 1U nanosatellite structure, solar panel placed in between the radiating patch and the ground plane. Figure 2: Parametric study on slot length \(a\); (**a**) reflection coefficient, (**b**) total efficiency and, (**c**) realized gain: decreasing the slot length causes the resonant frequency to shift upwards. The effect of antenna performance on the gap between the radiating element and ground plane was investigated and is plotted in Figure 4. The resonating frequency remained almost unchanged as the gap height increased, but the gain and total efficiency increased. Despite the relation between the gap and antenna radiation performance, the gap between the radiating element and ground plane could not be increased randomly because of the constraint introduced by the satellite structure. On the other hand, when the gap was decreased to below 4 mm, the resonant frequency was shifted as well, thereby decreasing the gain and efficiency. This occurs because of the close interaction of the antenna radiator with the lossy solar panel [8].