## 2 Antenna Design  
An electrically small planar antenna having a quasi-isotropic radiation pattern was designed as shown in Figure 1a,b. The design parameters are also listed. The antenna is composed of a small meander dipole and arcs extended from each end of the dipole as in [18]. The arc at the top of the substrate rotates in a counterclockwise direction, while the arc at the bottom rotates in a clockwise direction, and they form a small loop together. Each meander arm is also placed at the top and bottom of the substrate, and the whole configuration is fed by a coaxial cable at the center. The signal line of the cable is connected at the arm on the top and the outer conductor is connected at the bottom. The material characteristic of a ferrite bead is characterized and implemented in a full-wave electromagnetic simulation to prevent current flowing over the outer layer of the feeding conductor. This helps to minimize the effect from the feed line such that the radiation pattern is not distorted. Ansys HFSS (High Frequency Structure Simulator) was used for the full-wave electromagnetic simulations. Rogers RT/duroid 5880(tm) with a thickness (h) of 0.72 mm (\(\epsilon_{\mathrm{r}}\) = 3 and tan\(\delta\) = 0.0009) was used for the substrate. Since the radius of the substrate r was 0.07 \(\mathrm{\SIUnitSymbolMicro g}\) at 2.45 GHz, the electrical length of the meander line and arc was also short. Therefore, the current distributions on each configuration of the meander part and arcs were nearly constant, as shown in Figure 2a, and are referred to as perpendicularly placed electrically small electric dipole (\(\overset{\rightarrow}{\mathrm{J}}\)) and magnetic dipole (\(\overset{\rightarrow}{\mathrm{M}}\)), having TM and TE mode radiation patterns, respectively. Consequently, their summed pattern was nearly isotropic, as shown by the simulated 3D radiation pattern in Figure 2b. The radiation pattern of the proposed antenna differs from the unidirectional radiation pattern of a Huygens source antenna that is also composed of the crossed electric and magnetic dipoles [29; 30; 31]. The main idea relies on the phase difference between the two dipole sources. When the phase difference is 180\({}^{\circ}\), a unidirectional radiation pattern can be created since the fields are constructively added at one direction whereas they are canceled at the opposite side (see Figure 1 of [29]). According to the theory, the total radiated electric fields from the two dipoles are summed to have the isotropic radiation pattern when the phase difference is 90\({}^{\circ}\)[14]. For this reason, the circular polarization is created at certain points of the radiation space. This will be discussed more with the axial ratio plot of the proposed antenna (See Figure 6). The radiation properties of the designed antenna are dependent on its profile. When carrying out the parameter study on h with all other design parameters being fixed, we observed that the resonant frequency of the antenna shifted down with a thinner height of the substrate, as seen in Figure 3a. Figure 1: The proposed antenna design with the design parameters: (**a**) 3D and (**b**) top views. Figure 2: Design concept: (**a**) current distribution and (**b**) 3D radiation pattern. This occurred because the capacitance of the structure increased as the metallic parts at the top and bottom of the substrate grew closer. Such phenomena can also be seen from the input reactance plotted in Figure 3b, where it decreased to negative values when h was smaller. The parameter study result is summarized in Table 1. The gain deviation worsened slightly when the height of the substrate h was thicker. This was due to the increased vertical current flowing through the substrate, which was not shielded by the ferrite bead.