# Wideband Millimeter-Wave Perforated Hemispherical Dielectric Resonator Antenna
## 2 Antenna Configuration
### Layered HDRA Using Alumina with a Perforated Coat  
An equivalent configuration to the presented layered HDRA has been created, which consists of a physically single alumina layer with a top perforated section extending to a depth equal to the thickness of the polyimide coat presented in the previous section. This approach makes it easier to fabricate the proposed mmWave hemispherical DRA in accordance with the FDM 3D-printing technology. Therefore, no physical assembly of the two layers is needed, and there are no potential air gaps since alumina was used for the DRA and coat. Moreover, it is possible to realize the different dielectric constants of the dielectric coat by using different hole sizes, as per the filling-ratio theory [24]. The proposed 3D-printable HDRA is illustrated in Figure 8, which reveals that the DRA comprises two concentric alumina sections. Specifically, the outer section is characterized by different air-filling ratios designed to deliver diverse effective dielectric constants of the coating layer [25]. It should be noted that the DRA and coat dimensions, as well as the feed  
Figure 5: Simulated axial ratio with various radii of the outer layer. Figure 6: Simulated gain with various radii of the outer layer. network of the previous section, have been utilized in the proposed configuration. Figure 9 demonstrates the overall 3D-printing compatible antenna. A cubic unit cell with a dielectric constant of \(\varepsilon_{r1}\), i.e., the same as that of the DRA, was introduced to create the perforated coat. The unit cell is intended to secure an effective dielectric constant of \(\varepsilon_{r2\mathit{eff}}\) for the perforated coat that can be calculated using [17]. \[\varepsilon_{r2\mathit{eff}}=0.55t_{c}\varepsilon_{r1}-0.04\varepsilon_{r1}+1.3 \tag{4}\]  
The unit cell has a side length of 2.73 mm, or 0.254\(\lambda_{0}\), where \(\lambda_{0}\) denotes the free space wavelength at 28 GHz and a wall thickness of \(t_{c}\). The unit cells possess the intrinsic capacity to provide mutual structural support, eliminating the necessity for supplementary support materials during the 3D printing process. As a direct outcome, there is a substantial diminution in both printing duration and material expenditure. The control over the effective permittivity of a perforated dielectric coat can be exercised by modulating the wall thickness as stipulated in Equation (4). The influence of the unit cells' thickness was explored over a \(t_{c}\) range of 0.59 to 0.79 mm, progressing in increments of 0.1 mm, in a hemispherical DRA design adorned with a perforated dielectric coat. Figure 8: Hemispherical alumina DRA with a perforated alumina dielectric coat. Figure 7: Maximum bandwidth as a function of the outer layer thickness. As illustrated in Figure 10, approximately the same S\({}_{11}\) bandwidths were achieved using wall thicknesses of 0.59 and 0.69 mm, which are wider than that achieved using a thickness of 0.79 mm. Figure 11 corroborates these findings in the context of AR bandwidth (AR BW), revealing the maximum AR BW is achieved using a \(t_{c}\) = 0.69 mm, whilst the most restricted AR BW was associated with \(t_{c}\) = 0.59 mm. The impact of the wall thickness on the gain is distinctly depicted in Figure 12 with the highest gain achieved using \(t_{c}\) = 0.69 mm. According to Equation (4), this is expected since a wall thickness of 0.69 mm provides the required effective permittivity of 3.5 for the perforated coat. It should be noted that the 3D printable antenna offers a maximum broadside gain of 9.5 dBic compared to 8.5 dBic achieved with an equivalent HDRA configuration of physically two dielectric layers. This demonstrates that the perforated coat has helped focus the main beam. Figure 13 compares the return losses of the original structure of two solid layers and that of the 3D-printed HDRA version, underlining the close congruity between the two configurations.