# Quasi-Isotropic Hybrid Dielectric Resonator Antenna--Bow-Tie Patch with Harmonic Suppression
## 1 Introduction
### Simulated Result Analysis of the Proposed Antenna  
Figure 6 shows the comparison of S11 and the maximum gain of the proposed antenna with harmonic suppression and the antenna without harmonic suppression. The simulated S11 (\(\leq\)\(-\)10 dB) bands of the antenna without a filter and the proposed antenna are 3.06-3.33 GHz (8.45%) and 3.09-3.3 GHz (6.25%), respectively. The gain in the operating band of the proposed antenna is the same as that of the antenna without a filter, and the maximum gain difference is prominent in the harmonic region, confirming that the filter effectively suppresses harmonics. In addition, it can be confirmed that the harmonics outside the operating band are sufficiently suppressed in the proposed antenna. Table 4 shows the gain concerning the operating band and harmonics of the antenna without a filter and the proposed antenna. The gain of the proposed antenna in the operating band is approaching that equal to the antenna's gain without a filter. Compared with the antenna without a filter, the operating band and isolation from harmonics were 9.781 and 13.272 dB, respectively. In addition, the gain of the second and third harmonics of the proposed antenna decreased by 10.847 and 15.774 dB, respectively, compared with the antenna without a filter. Therefore, it can be confirmed that the filter sufficiently suppresses harmonics. Figure 5: S-parameters of simulated fifth- and seventh-order Chebyshev low-pass filters. Figure 6: Comparative analysis with and without filter: (**a**) simulated S11 and (**b**) simulated maximum gain. Figure 7 is an analysis of the effect of the integrated filter on realizing the quasi-isotropic pattern. After the filter was integrated, the band realizing the quasi-isotropic pattern was reduced. The reason is that the minimum gain from 3.2 to 3.3 GHz is reduced while the filter's cutoff frequency is reduced to suppress harmonics adjacent to the operating band. The gain difference of the proposed antenna is increased in the 3.2-3.3 GHz band compared with the antenna without a filter. When the cutoff frequency of the filter is set to high, the band of the quasi-isotropic pattern increases; however, the suppression of adjacent harmonics is weakened, so an appropriate tradeoff is required in designing the antenna with a filter. In this paper, the proposed antenna was designed so that the gain difference from 3.1 to 3.18 GHz had a value less than 10 dB. The simulated gain difference (\(0^{\circ}\leq\varphi\leq 360^{\circ}\) and \(0^{\circ}\leq\theta\leq 180^{\circ}\)) at 3.1, 3.13, and 3.15 GHz of the proposed antenna is 7.211, 7.422, and 8.24 dB, respectively. The radiation pattern of the antenna without a filter and the proposed antenna were compared to analyze whether the integrated filter affects the radiation pattern. Figure 8 displays the radiation patterns of the proposed antenna at 3.1, 3.13, and 3.15 GHz. Since the two antennas implemented a quasi-isotropic radiation pattern covering all areas, it was confirmed that the filter's effect on implementing the quasi-isotropic pattern was minimal. Figure 9 shows the electric field distribution of the proposed antenna. The electric field is radiated in all areas, and it can be seen that the electric field is particularly concentrated in the +y-axis direction. This is because the electric field is scattered by the SMA port of the conductor component located in the +y-axis direction. On the other hand, it can be seen that the magnitude of the electric field in the \(-\)y-axis direction without the SMA port is relatively low. In addition, it can be seen that the magnitude of the electric field in the \(-\)z axis direction is relatively low. This is because some electric fields are reflected by the ground of the proposed antenna. \begin{table}
\begin{tabular}{c c c} \hline  & **Without a Filter** & **With the Seventh-Order Filter** \\ \hline
3.1 GHz & 1.854 dBi & 2.092 dBi \\
6 GHz (second harmonic) & 3.158 dBi & \(-\)7.689 dBi \\
9 GHz (third harmonic) & 4.594 dBi & \(-\)11.18 dBi \\ \hline \end{tabular}
\end{table}