# Bio-Inspired Dielectric Resonator Antenna for Wideband Sub-6 GHz Range
## 2 Bio-Inspired Spiral Shell DRA
### Evaluation of SsDRA Design Based on the Fabrication Feasibility  
The proposed SsDRA has a typical 2.5D geometry, since it develops as a straight protrusion of a thin planar section. The main fabrication issue displayed along the z-axis direction concerns the aspect ratio (AR) of the geometry, defined as h\({}_{\text{DRA}}\)/t. In order to guarantee the successful fabrication of a stiff structure, the AR should be higher than a critical threshold, which depends on the mechanical  
\begin{table}
\begin{tabular}{c c c c c c c c c c} \hline \hline
**f(\(\theta\))** & **K** & **c\({}_{\text{theta}}\)** & **a** & **b** & **m\({}_{1}\)** & **m\({}_{2}\)** & **n\({}_{1}\)** & **n\({}_{2}\)** & **n\({}_{3}\)** \\ \hline
[-] & [-] & [-] & [-] & [-] & [-] & [-] & [-] & [-] & [-] \\ \hline e\({}^{\text{C}_{\text{theta}}\ast\theta}\) & 6 & 0.2 & 1 & 1 & 10 & 10 & 5 & 5 & 5 \\ \hline \hline \end{tabular}
\end{table}
Table 1: Gielis’ parameters used in Equation (1) to generate the Spiral shell DRA.  
Figure 1: (**a**) Picture of a Button snail Modulus modulus (spiral seashell). (**b**) 3D sketch of the Spiral shell Dielectric Resonator Antenna (DRA).  
properties of the material and the chosen fabrication technology. Therefore, in the antenna optimization, the values of t and h\({}_{\text{DRA}}\) were set by taking into account this limitation.  
The spiral section evolving along the X-Y plane represents the main challenge for the fabrication of the proposed geometry, and, as such, it dictates the actual selection of the most suitable Additive Manufacturing process. In order to come up with feasible solutions for the further SsDRA fabrication, preliminary considerations were made, basing on the SsDRA prototype drawings reported in Figure 2, as follows:  
1. By fixing the parameter \"m\" equal to 10, the geometry has 10 peaks and valleys and the step-angle between them is kept constant and equal to 36 degrees (360/m), independently of the position along the spiral curve. Ridges and valleys are rounded, but the lower the cylindrical coordinate \(\theta\) (and distance from the origin GT(\(\theta\))) is, the lower the radius of the circle which approximates locally the curve on ridges or valleys. In addition, the amplitude of the oscillation along the spiral is proportional to the values of parameters n\({}_{1}\), n\({}_{2}\) and n\({}_{3}\) of the Gielis formulation (1): in this case, they are all equal to 5. This setting allows us to have smaller amplitude close to the origin, i.e., micro-features which requires an accurate fabrication assessment.
2. Since the radius of the spiral increases monotonically from the origin to the end of the spiral, the smaller features of the geometry are in close proximity to the origin, thus generating micro-scale features.  
The measurement of circle approximations of the curve is important to evaluate the feasibility of 3 Dprinting technologies in the SsDRA fabrication. Indeed, the majority of the Additive Manufacturing technologies build the objects using a layer-by-layer strategy, accomplished by moving a circular end-effector: in particular, the end-effector is an extrusion nozzle in the Fused Deposition Modelling (FDM), and a laser spot in the stereolithography (SLA) [39; 40]. Therefore, the previous considerations lead to select an AM process that should be capable of reproducing accurately the micro-features and ensuring the target value of roundness for the ridges and valleys. Detailed discussions about the evaluation of the best candidate among AM processes along with fabrication challenges and solutions about the optimized SsDRA fabrication are reported in Section 4.  
Figure 2: (**a**) Side view and (**b**) top view with main dimensions and rounds radii R (inset) related to the spiral shell DRA (SsDRA).