# Electrically Small Water-Based Hemispherical Dielectric Resonator Antenna
## 3 Results and Discussion  
We designed the antenna to operate at 300 MHz and 20 \({}^{\circ}\)C, where the relative permittivity of water was \(80.2-j1.34\). However, to study the influence of the dispersion of water, we compared it with an antenna designed for 1000 MHz, where the relative permittivity of water was \(79.9-j4.46\), clearly showing higher losses. We used two designs exciting different resonances in the hemisphere. With the PEC plane imaging the induced volume currents inside the hemisphere, the resonances will effectively be similar to the ones in the full sphere (the resonant properties of spherical configurations are known [29] also when water is used as the dielectric [30] and were utilized presently for the design of water-based DRAs. See also Appendix B.1 for more details). After a systematic parametric study of the two parameters \(l_{\mathrm{m}}\) and \(x_{\mathrm{m}}\), the most efficient designs were found, and the final results are summarized in Table 1 for both frequencies. The total efficiency (\(\eta_{\mathrm{eff}}\)) is shown as a function of frequency in Figure 2a for both designs. At 300 MHz, a magnetic (electric) dipole resonance could be excited in a sphere with the radius 55.18 mm (78.53 mm) equal to \(\lambda_{0}\)/18 (\(\lambda_{0}\)/14). The maximum total efficiency for the magnetic (electric) dipole antenna was 29.5% (15.6%). For comparison, the total efficiency without water was only 0.037% (0.0013%), with almost total reflection of the input power. Thus, introducing water not only matched the antenna to the transmission line but also to the ambient free space, as also confirmed by the reflection coefficient (S\({}_{11}\)) and radiation efficiency (\(\eta_{\mathrm{rad}}\)) in Figure 2b. The magnetic dipole resonance in a water sphere is the most pronounced [30]. This was also the case here, as illustrated in Figure 2. However, due to the losses in water, both antennas absorbed (i.e., dissipated) more power than they radiated: the magnetic (electric) dipole antenna absorbed 70.1% (76.3%). Compared to the antennas at 1000 MHz, where the losses of water were even greater, we found that the total efficiency dropped by approximately a factor of 3 (see Table 1). As both resonances could be excited in a single hemisphere but at different frequencies, we fabricated one antenna, where the position and the length of the monopole could be adjusted for each resonance type. The antenna was fabricated by hollowing out a hemisphere with the radius 55.18 mm in a Rohacell 51 HF block. The permittivity of Rohacell 51 HF was measured to be 1.075 [26]. The Rohacell block was then glued to an aluminum plate in which holes were drilled for insertion of the monopole antennas and water. Photographs of the antenna are shown in Figure 3a. Two holes (\(x_{\mathrm{m}}=7\) mm and \(x_{\mathrm{m}}=0\) mm) and two monopole antennas (\(l_{\mathrm{m}}=43.6\) mm and \(l_{\mathrm{m}}=15.3\) mm) were made so that both dipole DRA resonances could be excited. The ground plane was realized by attaching a circular aluminum plate with a diameter of 1 m to the antenna. The antenna was mounted on a tripod with a rotating joint, and the reflection coefficient was measured with an Anritsu MS2024B vector network analyzer calibrated for 50 Ohm matching. Figure 1: A sketch of the water-based dielectric resonator antenna (DRA). The water inlet made it easy to insert and extract water from the antenna. With no water, we measured a reflection coefficient of 0 dB with both monopole antennas. The measured reflection coefficients for the antenna filled with water are shown in Figure 3b. Clearly, the reflected power was reduced at the resonance frequencies for specific combinations of \(x_{\mathrm{m}}\) and \(l_{\mathrm{m}}\). When the monopole antenna was positioned in the center of the hemisphere, the magnetic dipole resonance was not excited, and thus most of the power was reflected at 300 MHz. The electric dipole was optimally excited around 420 MHz with \(x_{\mathrm{m}}=0\) and \(l_{\mathrm{m}}=43.6\) mm.