# Analysis of 3D Printed Dielectric Resonator Antenna Arrays for Millimeter-Wave 5G Applications
## 3 Millimeter-Wave DRA Array for 5G Systems
### Parametric Analysis for 3D Printing Process  
In the 3D printing process for millimeter-wave applications, dimensional changes are expected during fabrication. The effects of these changes on various parameters of a standalone DRA are well documented. However, their impact when placed in an array has not been reported, particularly when taking into consideration the anticipated 3D-printing errors. It is important to note that we only consider uniform changes across all printed elements, assuming that the 3D printer will consistently produce deviations from the initial dimensions.  
A parametric study was conducted in this section to investigate the impact of potential dimensional changes and errors when printing the DRA array on its electrical performance. The efficiency and realized gain instead of \(S\)-parameters were considered for this kind of multi-port array. The results for varied radius, height, permittivity (\(\epsilon_{r}\)) and loss tangent (\(\tan\delta\)) of the DRA element are shown in Figures 10 and 11. The values used in the proposed mmWave DRA array are highlighted in bold. In FDM printing processes, the maximum expected fabrication error is approximately 0.2 mm, which corresponds to about 12.5% of the radius and 10.5% of the height for the mmWave DRA elements. Such errors can lead to an increase in resonant frequency of about 7.5% when increasing the radius and a 2.5% decrease when increasing the height. Additionally, as shown in Figure 10a,b, increasing the size of the DRAs results in lower realized gain. A reduction of 0.45 dB, from 12.7 dB to 12.45 dB, in maximum realized gain was observed when reducing the radius of the DRA element, whereas changes in the height had minimal effect, keeping the maximum realized gain nearly unchanged.  
Figure 10: Gain at broadside direction with different (**a**) radius, (**b**) height, (**c**) \(\epsilon_{r}\), (**d**) \(\tan\delta\) of DRA element.  
Unwanted air gaps introduced during the printing process can cause variations in the equivalent permittivity and loss tangent of the material. To assess the impact of these electrical properties, simulations were conducted. As depicted in Figures 10 and 11, the permittivity of the DRAs influences both the resonant frequency and the realized gain of the overall array, while the loss tangent primarily affects the realized gain. In the case of mmWave printed DRA antennas, the relative permittivity is likely to decrease due to gaps formed during fabrication, as observed in the previous section. A 10% decrease in relative permittivity leads to a 5% increase in resonant frequency. Additionally, this decrease in permittivity can increase the gain by about 0.3 dB. The loss tangent is also a crucial factor in determining antenna performance. Typically, PREPERM material maintains a consistent and relatively low loss tangent of 0.003. Air gaps introduced during fabrication can further reduce the loss tangent, resulting in slight improvements in gain and efficiency. However, any contamination of the filament or the use of more lossy materials can increase the loss tangent, significantly reducing both gain and efficiency. As illustrated in Figures 10 and 11, an increase in the loss tangent to 0.1 causes the efficiency to drop from nearly 100% to 45%.  
These results provide valuable insights into the effects and underlying causes of dimensional and material parameter variations on the array's radiation and impedance matching performance. Proper control of fabrication processes and material selection is critical for optimizing the performance of DRAs, especially at mmWave frequencies.