# Analysis of 3D Printed Dielectric Resonator Antenna Arrays for Millimeter-Wave 5G Applications
## 2 3D Printed DRA at Microwave Frequency  
A DRA operating within the microwave frequency band at 13.2 GHz was designed to initially test the FDM feasibility. The DRA design is depicted in Figure 1. The radius (\(r_{d}\)) and height (\(h_{d}\)) of the DRA are 3.075 and 2.625 mm, respectively. The resonant frequency of the \(TE_{01,6}\) mode of a cylindrical DRA can be calculated by [40],  
\[f=\frac{2.921c\epsilon_{r}^{-0.465}}{2\pi r}\Big{[}0.691+0.319x-0.035x^{2} \Big{]} \tag{1}\]  
where \(c\) is the speed of light, \(x=r/2h\), \(\epsilon_{r}\), \(r\), and \(h\) are the relative permittivity, radius, and height of the DRA, respectively. The substrate used is the RT Duroid 5880 (\(\epsilon_{r}=2.2\)) with a thickness of 0.51 mm and a dimension of 20 mm \(\times\) 20 mm. The DRA has a relative permittivity \(\epsilon_{r}=10\). It is slot-fed by a microstrip line with an impedance of 50 ohms to ensure better matching with the SMA connector. The slot has a length (\(l_{s}\)) of 3.2 mm and a width (\(w_{s}\)) of 0.5 mm, and the feeding line measures 13 mm in length (\(l_{ms}\)) and 1.6 mm in width (\(w_{ms}\)). A set of such DRAs were manufactured using the widely available FDM Raise E2 3D printer (Shanghai, China) and a low-loss dielectric thermoplastic filament. A 0.4 mm nozzle was used with an extrusion temperature of 250 \({}^{\circ}\)C and a heated bed at 80 \({}^{\circ}\)C during the printing process. The filament diameter was 1.75 mm, and the layer thickness was set to 0.2 mm. Four DRAs with 100% infill were printed in parallel orientation to the bed during each batch, with a printing speed of 60 mm/s. The PREPERM (catalog ABS1000 filament, manufactured by Avient Corp. (Liverpool, UK), was used in this work. This filament provides a stable dielectric constant, \(\varepsilon_{r}\), of 10 \(\pm\) 0.35 across a wide range of frequencies and temperatures, with a loss tangent, tan \(\delta\), of about 0.003. The standard resolution provided by the manufacturer of this machine exceeds 0.2 mm along the z-axis and 0.4 mm along the xy-axis. Figure 2 displays the photo of the printed DRA element. Surface profiles and photos were taken using a KEYENCE VHX-7000 series portable microscope (KEYENCE (UK) Ltd., Milton Keynes, UK), which offers a large depth of field, high resolution, and up to 6000\(\times\) magnification. The results are shown in Figures 2-4. Thirteen uniform layers of about 0.2 mm height were required and observed to achieve the total height of 2.6 mm of the microwave DRA. Reasonably smooth surfaces were observed, considering the expected resolution of about 0.2 mm for FDM printing. As seen in Figure 3, the DRA is relatively consistent with the simulation model in overall shape. Protuberances with a maximum height of the profile (\(R_{2}\)) of 112.01 \(\upmu\)m and an arithmetic average roughness (\(R_{a}\)) of 28.38 \(\upmu\)m can be observed in the 3D side view and 2D cut surface profile shown in Figure 4. \(R_{z}\) and \(R_{a}\) are commonly used to evaluate surface profile, as defined by the ISO 4287 standard [41]. These values reflect the protuberances and uneven surface along the sides of the DRA. Some air gaps could also be observed. These errors and residuals may lead to a lower equivalent relative permittivity of the overall structure and thus a frequency shift to a higher band. Figure 1: Configuration of the FDM printed microwave DRA: (**a**) DRA on top of a metallic ground plane, (**b**) substrate and DRA made transparent to show the microstrip transmission line on the back of the substrate and the slot on the top ground plane. Figure 2: Zoom-in view of the top and bottom surfaces of the FDM-printed microwave DRA. (**a**) top view, (**b**) bottom view. The design simulation was performed using the EM simulator Ansys HFSS (Ansys, Inc., Canonsburg, PA, USA). All the dimensional parameters of the DRA mentioned above are consistent with those used in the simulation model.