## 2 The Normal-Mode Helical Antenna Design Considerations  
A normal-mode helical antenna (NMHA) was selected due to the fact that it functions as a circularly polarized omnidirectional antenna at a minimum size compared to any alternative at HF [10]. The helical antenna polarization sense is based on its dimensions according to Equation (1) below [11]:  
\[\mathrm{C}_{\lambda}=\sqrt{\mathrm{S}_{\lambda}} \tag{1}\]  
where  
\(\mathrm{C}_{\lambda}\): the circumference of the helix in terms of wavelengths. \(\mathrm{S}_{\lambda}\): the spacing between turns in terms of wavelengths. In particular, the axial ratio (AR) of the helical antenna depends solely on the dimensions of its circumference and on the distance between the turns of the coil, i.e., the pitch angle as given by [PERSON] in Equation (2) below:  
\[\frac{\left|\mathrm{E}_{\Theta}\right|}{\left|\mathrm{E}_{\Phi}\right|}=\frac {\mathrm{S}\lambda}{2\pi\mathrm{A}}=\frac{2\mathrm{S}\lambda}{\pi^{2}\mathrm{ D}^{2}}=\frac{2\mathrm{S}_{\lambda}}{\mathrm{C}_{\lambda}^{2}} \tag{2}\]where  
A: circle area;  
D: circle diameter;  
S: spacing between the turns of the helix;  
\(\lambda\): wavelength. The current distribution of the normal-mode helical antenna along the helix generates two orthogonal components of the electric field: one parallel and another perpendicular to the axis of the helix. This is demonstrated by Equation (2), which expresses the far-field components E\({}_{\Phi}\) and E\({}_{\Theta}\) of the helix, which are in phase quadrature. Therefore, the three special cases pertaining to the NMHA polarization sense are given as follows [11]:  
E\({}_{\Phi}\) = 0 \(\rightarrow\) linear vertical polarization. E\({}_{\Theta}\) = 0 \(\rightarrow\) linear horizontal polarization. E\({}_{\Phi}\) = E\({}_{\Theta}\)\(\rightarrow\) circular polarization. The helical antenna operates according to the principles of a coil antenna. This implies that its design incorporates a coiled structure, which affects its impedance [12; 13]. The coil structure introduces reactance into the antenna system, resulting in a reactive radiator behavior. In this respect, the NMHA typically exhibits a narrow bandwidth due to its reactive nature. To extend the narrow bandwidth of the helical antenna further, additional enhancements may be required. Various techniques and design optimizations can be employed for this purpose, as discussed in Section 2.1. Furthermore, the gain of the helical antenna compared to that of a half-wave dipole (commonly used as a reference) remains unknown. To address these considerations, the dimensions of the two helical antennas of the array were calculated using Equations (1) and (2). Employing Wheeler's equation, the circumference of the helical antennas required to achieve a circular polarization radiation pattern was calculated as 15 cm. Both helices consist of 5.5 turns made of a 2.5 mm diameter copper wire, standing at a total height of 6 cm (0.05 \(\lambda\)) at 25 MHz. Figure 1 illustrates the helical antenna under test when operating as a standalone antenna. The circular polarization (C.P.) radiation pattern of the helical antenna operating in normal mode was simulated using EZNEC Pro2v.6.0 modeling software, as depicted in Figure 2 [14]. Figure 1: The normal-mode helical antenna under test. During the initial phase of the normal-mode helical antenna (NMHA) design, the focus was on evaluating its bandwidth as a passive radiator while considering the mismatch losses that reduce the gain of the antenna [15]. Measurements in a non-reflective environment were conducted at each desired frequency within the range 20-30 MHz using the Nano VNA-FV2 network analyzer [16]. Subsequently, the resulting impedance values were utilized in Equations (3) and (4) to calculate the reflection coefficient (\(\Gamma\)) and the load mismatch attenuation of the helical antennas, as illustrated in Figures 3 and 4 [17].