# A 3D-Printed Enclosed Twist Dielectric Resonator Antenna with Circular Polarization
## 2 Dielectric Resonator Antenna Design and Parametric Studies
### Twist DRA Design  
The main object of the antenna corresponds to a twisted rectangular DRA to obtain CP. The twist consists of four stepped rectangular DRAs [21] that are rotated sequentially and then joined together to obtain the twist geometry. This structure will excite two orthogonal modes that will generate a CP on the desired operational frequency [22,23]. We proceed then to realize two parametric studies: one regarding the inner box dimensions and the other regarding the top rotation of the twist, as shown in Figure 1. For all the cases, the top box is rotated \(\theta\) degrees with respect to the bottom box, while the other boxes are rotated sequentially in an equally spaced degree increment. Finally, all boxes are connected through their vertices of the upper faces so as to obtain the twisted DRA. The relative permittivity used for this structure is \(\varepsilon_{r1}=13\).  
As this design has several variables that can affect the behavior of the antenna, most notably the inner box size and rotation between the structures, we proceed to conduct a parametric study of these variables using the software, ANSYS HFSS 2023 R1. The first parameter that was studied is the size of the inner rectangles in order to establish the lower dimensions suitable for exciting the required modes. Figure 2a shows the reflection coefficient \(|S_{11}|\) in dB as a function of the frequency while changing the size of the inner box. For this study, we keep a rotation of \(\theta=60\) degrees of the top box with respect  
Figure 1: Schematic of the proposed antenna. (**a**) Dimension of the rectangles. (**b**) Rotation of the rectangles.  
to the bottom box. Note that we kept the height of the box \(z_{rect}\) at a constant value, as this structure is intended for using as minimal a height space as possible in the target application. As expected, the inner dimensions of the boxes have a direct impact on the frequency behavior of the DRA by shifting the resonant frequencies of the generated modes. From these variations, even if for DRAs the resulting resonance can be achieved by a form factor, we can see that \(y_{rect}\) has the larger influence over the resonance frequency due to the nature of the excitation [10]. The resulting axial ratio, shown in Figure 3, follows the same tendency in terms of frequency shift.  
The second study is regarding the rotation of the top box in relation to the bottom of the antenna. The operation of the antenna is completely dependent on this rotation angle with respect to the x-y axis. Each rectangle is rotated by the same angle with respect to the previous one, so that the last rectangle will be rotated by \(3\theta\), as shown in Figure 1b. We will limit this rotation to a maximum of 30 degrees, meaning that the top rectangle would have a rotation of 90 degrees with respect to the x-y axis. For this parametric study, the chosen values for the rectangle are as follows: \(x_{rect}=17\) mm, \(y_{rect}=7\) mm and \(z_{rect}=6\) mm. In Figures 4 and 5, the sensitivity of the antenna for the reflection coefficient and axial ratio with respect to the rotation angle is shown. We can see that we must have a compromise between the axial ratio and matching the antenna for different angles of the structure.  
Figure 3: Axial ratio in dB as a function of the frequency and the inner box dimensions for the twist.  
Figure 2: Parametric study of the reflection coefficient \(|S_{11}|\) in dB as a function of the frequency and the inner box dimensions for the twist.