# Electrically Small Water-Based Hemispherical Dielectric Resonator Antenna
## 3 Results and Discussion
The numerical results are included in Figure 3b, showing full agreement with the measurements. The small mismatch of 0.4 MHz in frequency between experimental and numerical reflection minimum can be explained by a small difference in temperature and/or water filling in the hemisphere. The water was removed from the hemisphere and then filled in to check the reproducibility of the measurements. This was done five times, and only a slight difference was observed between the measurements, with the values of the mean and maximum deviation being 299.725 MHz and 0.375 MHz, respectively. We found some differences in the magnitude of the reflection coefficient too (between -23 and -35 dB), but because its absolute value was very low, these differences could have come from small changes in the experimental conditions. \begin{table}
\begin{tabular}{c c c c c} \hline \multirow{2}{*}{**Parameter**} & \multicolumn{2}{c}{**300 MHz**} & \multicolumn{2}{c}{**1000 MHz**} \\ \cline{2-5}  & **Magnetic Dipole** & **Electric Dipole** & **Magnetic Dipole** & **Electric Dipole** \\ \hline \(r_{\mathrm{w}}\) (mm) & 55.18 & 78.53 & 16.56 & 22.5 \\ \(l_{\mathrm{m}}\) (mm) & 43.6 & 16 & 15.4 & 7.9 \\ \(x_{\mathrm{m}}\) (mm) & 7 & 0 & 2.4 & 0 \\ \(f\) (MHz) & 300 & 298 & 1000 & 1010 \\ \(G_{\mathrm{real}}\) (dBi) & 0.16 & –3.1 & –4.3 & –8.2 \\ \(\eta_{\mathrm{eff}}\) & 29.5\% & 15.6\% & 9.1\% & 4.8\% \\ \(\eta_{\mathrm{rad}}\) & 29.6\% & 17\% & 9.5\% & 4.8\% \\ \(|\mathrm{S}_{11}|\) (dB) & –24.1 & –10.9 & –13.7 & –19.1 \\ \(Z_{\mathrm{A}}\) (\(\Omega\)) & \(43-j0.7\) & \(28-j6.7\) & \(32.1-j0.9\) & 40 + /3.5 \\ \(k_{0}a\) (rad) & 0.35 & 0.46 & 0.35 & 0.48 \\ FBW\({}_{\mathrm{3 dB}}\) & 7.81\% & 2.85\% & 24\% & 11.4\% \\ \(Q_{\mathrm{ratio}}\) & 1.06 & 22.4 & 1.10 & 21.5 \\ \hline \end{tabular}
\end{table} 
Table 1: Geometrical and important antenna parameters for magnetic and electric dipole antennas designed for 300 and 1000 MHz. Figure 2: The numerical results for (**a**) total efficiency and (**b**) reflection coefficient and radiation efficiency as functions of frequency. Water temperature was 20 \({}^{\circ}\)C.  
In Figure 4a, the electric field distribution in the \(xz\)-plane of the magnetic dipole antenna is shown at 300 MHz. From the direction of the electric field (shown by the arrows), it is clear why the monopole cannot be positioned in the center of the hemisphere (\(x_{\mathrm{m}}\
eq 0\)) if the magnetic resonance is to be excited. In order to excite a circulating electric displacement current, the monopole has to be displaced from the center of the hemisphere. The calculated radiation pattern for the magnetic dipole antenna is shown in Figure 4b by the normalized radiation intensity in the \(xz\)- and \(xy\)-planes. It can be seen that there was no radiation in the negative \(z\) direction because of the ground plane. The radiation pattern was similar to that of a half-loop antenna, while the radiation pattern of the electric dipole antenna was similar to that of the monopole antenna (see Appendix B.2). The magnetic (electric) dipole antenna had isotropic radiation in the \(xz\)-plane (\(xy\)-plane) with the maximum realized gain (\(G_{\mathrm{real}}\)) of 0.16 dBi (-3.1 dBi). The radiation pattern was also measured with a simple dipole antenna designed for 300 MHz. By rotating the antenna under test, the transmission coefficient was measured at different angles in the \(xz\)-plane of the antenna. The normalized transmission coefficient is included in Figure 4b. From 0\({}^{\circ}\) to \(\pm\)90\({}^{\circ}\), the measurements were similar to the numerical results. However, at higher angles, they started to deviate. This was expected because the simulated ground plane was infinite, whereas a ground plane of 1 m diameter was used in the measurements. The 3 dB fractional bandwidth, FBW3 dB, of the magnetic (electric) dipole antenna was 7.81% (2.85%).