# Electrically Small Water-Based Hemispherical Dielectric Resonator Antenna
## 1 Introduction  
Modern technology calls for increasingly smaller designs, which in turn ultimately requires increasingly smaller antennas. Even though electrically small antennas have been studied for decades [1; 2; 3; 4; 5; 6; 7; 8; 9], their inherently poor matching, low radiation efficiency, and narrow bandwidth pose a serious design obstacle. The matching issue is traditionally tackled with appropriate matching networks; however, such solutions suffer from narrow bandwidths, high tolerance requirements, and modest efficiencies [2]. While some recent approaches toward efficient small antennas have involved either specific shaping of the radiator or addition of conductors around it [3; 4; 5; 6], as well as exploiting artificial metamaterials (MMs) and MM-inspired structures [7; 8; 9], a more traditional approach to reduce the antenna size has been to load it with a high-permittivity material. Such antennas, known as dielectric resonator antennas (DRAs), rely on resonances supported in high-permittivity structures. A great variety of DRAs has been proposed and demonstrated [10], and, very often, expensive high-permittivity ceramics are used as the dielectric material. To this end, it is interesting to pay attention to water as an alternative material [11]. With its relatively high frequency and temperature-dependent permittivity in the microwave frequency range [12], water holds a great potential as an inexpensive, abundant, andbofriendly material for not only tunable antennas [11; 13; 14; 15; 16; 17; 18; 19; 20; 21; 22] but also more broadly as inclusions in MMs and metasurfaces (MSs) [22; 23; 24; 25; 26; 27] with tunable dynamic properties. These tunable properties can potentially be used for sensing as well. Indeed, several water-based DRAs have already been demonstrated [11; 13; 14; 15; 16; 17; 18], with effective excitation of resonances in water cavities. Cylindrical [13], rectangular [14], and bottle-shaped [18] cavities have been investigated. These antennas mainly operate in the very high frequency (VHF) and the low end of ultrahigh frequency (UHF) bands due to water losses at higher frequencies. Another type of water-based antenna that exploits conductive liquids (e.g., salt water) [19; 20; 21; 22] has also been reported. The operational frequency of these antennas can be tuned through a simple change of the conductive liquid volume. The electrical size of an antenna is defined as \(k_{0}a\), with \(a\) being the radius of the so-called Wheeler's radian sphere (the smallest possible sphere enclosing the antenna), \(k_{0}=2\pi/\lambda_{0}\) being the free-space wavenumber, and \(\lambda_{0}\) being the free-space wavelength. In the presence of a ground plane, \(k_{0}a\leq 0.5\) in order for the antenna to be qualified as electrically small [5]. Following this definition, we find that most of the water-based antennas demonstrated thus far are not electrically small. The purpose of the present work was to investigate an electrically small water-based DRA consisting of a short monopole antenna encapsulated by a hemispherical water cavity and fed against a large ground conducting plane. The working principle of the proposed DRA relies on the fundamental electric and magnetic dipole resonances (equivalent to the transverse magnetic (TM) and transverse electric (TE) modes, respectively), which can be excited in the high-permittivity water cavity. The spherical shape of the cavity maximizes the antenna volume, making it possible to obtain much smaller water-based antennas compared to any of those reported thus far. Specifically, the size of the smallest antenna proposed presently is \(\lambda_{0}/18\), representing the smallest water-based antenna to date. On the other hand, the dipole resonances in the water cavity are used to effectively match an otherwise inefficient short monopole antenna to its feed line as well as the surrounding free space. The length and the position (with respect to the water cavity) of the short monopole were determined for the optimal performance of the DRAs.