# Ferrite-Loaded Spidron Fractal Loop VHF Antenna for UAV Applications
## 2 Antenna Design  
Figure 1a presents a the 3-D view of the Spidron fractal loop antenna with cuboid ferrite. The top of the loop antenna is designed with two symmetrical Spidron fractal structures which are connected to each other. A Spidron fractal is a structure in which the base of a scaled down triangle \(S_{n}\left(n\right.=2,3,\ldots,10\)) is continuously connected to the hypotenuse of triangle \(S_{n-1}\)[15]. In order to form a symmetric shape of the ferrite structure, the Spidron fractal consists of isosceles right triangles, with a down scaling factor of \(\sqrt{2}/2\). The Spidron fractal structure is attached to a shorting patch and a feeding patch. The ground plane is connected to the shorting patch and a coaxial cable is connected at the center of the feeding patch. The shorting and feeding patches are \(h\,\times\,L_{1}\) and \((h-1\text{ mm})\times L_{1}\) in size, respectively. Table 1 shows the theoretical maximum gain of the electrically small loop antenna at 30 MHz. The gain is calculated according to \(ka\) (the size of the antenna) [16]. The values of \(h\) and \(L_{1}\) are the height of the loop antenna and the length of the base of the first triangle, respectively. To ensure low-profile characteristics, the height is set to 51 mm. The length of \(L_{1}\) is set to 121 mm to achieve a theoretical maximum gain identical to the gain of a commercial antenna at 30 MHz (MT-2040/E/D, MTI Wireless Edge LTD [17]). Because the fuselage length and wingspan of a medium-altitude long-endurance UAV are longer than 10 m on average, the size of the antenna ground plane is determined to be 10 m \(\times\) 10 m. The conductor of the loop antenna structure and ground consists of copper on a Taconic RF-35 dielectric substrate with a relative dielectric constant of 3.5, a loss tangent of 0.0018, and a thickness of 1.52 mm. Figure 1b shows the side view of the Spidron fractal loop antenna with cuboid ferrite. To increase the gain of the antenna, the ferrite structure is located inside the loop structure and attached onto the ground plane. The size of the cuboid ferrite is 240 \(\times\) 240 \(\times\) 13.4 mm\({}^{3}\). The complex permeability and magnetic loss tangent properties of the ferrite (SN-20, Samwha Electronics [18]) are shown in Figure 2. Here, \(\mu^{\prime}\) and \(\mu^{\prime\prime}\) are respectively real and imaginary parts of the complex permeability, and the magnetic loss tangent of the ferrite is calculated by \(\mu^{\prime\prime}/\mu^{\prime}\). The permittivity value of the ferrite is 12 in the operating frequency band (from 30 MHz to 300 MHz). SN-20 with a high \(\mu^{\prime}\) in the HF/VHF band is very useful to improve the gain of a loop type ESA. However, the value of \(\mu^{\prime}\) gradually decreases to 1 as the frequency is increased. The magnetic loss tangent of the ferrite increases sharply as the frequency is increased because the decreasing rate of \(\mu^{\prime}\) is higher than that of \(\mu^{\prime\prime}\). Figure 3 plots the simulated realized peak gains of the Spidron fractal loop antenna with and without cuboid ferrite. The gains of the antenna with and without ferrite range from \(-\)27.4 to \(-\)2.2 dBi and from \(-\)35.1 to 4.5 dBi, respectively, in the operating band. When the ferrite is loaded into the antenna, the radiation \(Q\) of the antenna is reduced due to the high \(\mu^{\prime}\) of SN-20. As the result, the gain of the Spidron fractal loop antenna with the ferrite is considerably improved than that without the ferrite in the low frequency band. On the other hand, a gain reduction was noted in the high frequency band due to the high magnetic loss tangent of the ferrite. Figure 1: Geometry of the Spidron fractal loop antenna with cuboid ferrite: (**a**) 3-D view; (**b**) Side view. Figure 2: Complex permeability and magnetic loss tangent properties of the SN-20 ferrite. To maintain the gain improvement in the low frequency band and to solve the gain reduction problem in the high frequency band, the amount and configuration of the ferrite are optimized.