## 3 Design and Analysis of the Whole Structure  
By integrating the three parts presented above, the whole structure of the presented dielectric rod antenna is shown in Figure 8a. As the primary feeding, the tapered helix of wire 0.7 mm diameter is left-hand circularly polarized (LHCP) and is designed to operate at 8-9.7 GHz. The helix is planted on a circular bottom reflector and embedded inside the dielectric hollow covered by a cylindrical metal waveguide. The reflector dimension parameters are shown in Figure 8b.  
In the presented antenna, the printed loops are designed on the substrate with a thickness of 2 mm and a relative dielectric constant of 2.65. The dielectric structure is designed with Teflon material. All the design parameters are given in Table 1.  
\begin{table}
\begin{tabular}{c c c c} \hline \hline
**Symbol** & **Value (mm)** & **Symbol** & **Value (mm)** \\ \hline
**L\({}_{0}\)** & 2 & D\({}_{3}\) & 22 \\ \hline
**L\({}_{1}\)** & 30 & D\({}_{2}\) & 24 \\ \hline
**L\({}_{2}\)** & 57.48 & D\({}_{1}\) & 26 \\ \hline
**L\  
According to Table 2, the antenna developed in [11] has good circular polarization performance, but the gain is only 9 dBi within the 4.2 \(\lambda\times 0.5\,\lambda\) aperture. According to [12], the gain is 17.5 dB can be achieved with a length of 11.9 \(\lambda\) and side lobe level are on \(-10\) dB. The side lobe levels are better in [13; 14], but the gain is low as compared to the proposed antenna. In [16], a Compact High Gain Dielectric Rod Antenna Array is designed to get high gain with low side lobe levels, but the gain for a single element is only 9 dB which is very low. It is concluded that the performance of the proposed antenna is better than all conventional dielectric rod antennas.  
Figure 9a shows a comparison of the simulated return loss between the helix alone and the whole structure. It can be seen that the return losses are better than \(-15\) dB in the working band of 8-9.7 GHz. Additionally, these two return losses are almost the same, which means that the operating band of the presented antenna is mainly determined by the primary feeding. Figure 9b provides the radiation patterns at 9.5 GHz, where it is found that the gain of the embedded structure is 7.43 dB more than the gain of a single helix and the side lobe level is also very low for the proposed design.  
Figure 10a,b shows the radiation patterns and axial ratio at the zenith of the presented antenna for the whole working band. It can be found that the gain of the antenna is higher than 15 dB in the whole band, and a maximum gain of 18.9 dB is achieved at 9.7 GHz. The side lobe levels are below \(-20\) dB in the whole band. Additionally, good polarization purity can be found; in Figure 10b, the axial ratio is below 1.14 dB in the whole band. The mathematical description of the amplitude of the field along the surface wave antenna is described in [12], and the electric field distribution of the proposed structure is shown in Figure 10c.  
\begin{table}
\begin{tabular}{c c c c c c c} \hline \hline
**Reference** & [11] & [12] & [13] & [14] & [16] & **This Work** \\ \hline
**Frequency** & & & & & & \\
**(GHz)** & & & & & & \\ \hline
**Gain** & & & & & & \\
**(dB)** & & & & & & \\ \hline
**SLL (dB)** & \(-10\) & \(-10\) & \(-20\) & \(-15\) & \(-7\) & \(-20\) \\ \hline
**Dimension** & \(10\,\lambda\times 0.75\,\lambda\) & \(11.9\,\lambda\times 0.6\,\lambda\) & \(6\,\lambda\times 0.8\,\lambda\) & \(3.2\,\lambda\times 12\,\lambda\) & \(1\,\lambda\times 0.5\,\lambda\) & \(7.7\,\lambda\times 0.74\,\lambda\) \\ \hline
**Polarization** & Circular & Linear & Linear & Linear & Linear & Circular \\ \hline \hline \end{tabular}
\end{table}
Table 2: Comparison Table.  
Figure 9: (a) The return loss of Tapered helix with metal reflector and whole structure (b) the gain comparison of Helix and whole structure.