# High-Gain Multi-Band Koch Fractal FSS Antenna for Sub-6 GHz Applications
## 3 Results and Discussion
### Parametric Investigations
#### 3.1.4 FSS Loading for Frequency Tunability and Gain Enhancement  
In the previous section, it is found that a miniaturized antenna results in a resonant frequency at 3.44 GHz, a reduction in the gain, and a \(-10\) dB fractional bandwidth for the sub-6 GHz band. To achieve an appropriate resonant frequency at 3.5 GHz, an improvement in gain, and an enhancement in the first band \(-10\) dB bandwidth, the miniaturized antenna is further loaded with an FSS structure, as discussed in Section 2.3. The distance between the two substrates (H) is varied at a step size of 0.8 mm below the antenna substrate. All of the reflection coefficients of the FSS loading and gain enhancement processes are shown in \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline \multirow{2}{*}{**Miniaturization**} & **Antenna** & \multirow{2}{*}{\(\mathbf{f_{r}}\)} & \multirow{2}{*}{\(\mathbf{S_{11}}\)} & & **Gain** & **Gain** & **Gain** \\  & **Size (mm\({}^{2}\))** & & **(GHz)** & **(dB)** & **(dB)** & **(dBi)** & **3.5 GHz** \\  & \(\mathbf{W_{S}\times L_{S}}\) & & & & **at \(\mathbf{f_{r}}\)** & **(dBi)** \\ \hline Primary antenna & & 3.26, 4.58 & \(-14.34\), \(-17.66\) & 1.87 (2.89\(-\)4.76) & 16.66, 9.06 & \\ \(\mathrm{W_{S}=4a_{e}=47.92\;mm}\) & 47.92 \(\times\) 46.15 & 6.50, 7.52 & \(-27.98\), \(-29.50\) & 3.55 (5.65\(-\)9.20) & 12.67, 5.84 & 15.11 \\ \(\mathrm{L_{S}=L_{F}+3a_{e}=46.15\;mm}\) & & 12.32 & \(-14.74\) & 2.53 (10.47\(-\)13.0) & 8.55 & \\ \hline Reduced width & & 3.44 & \(-37.92\) & 1.68 (2.90\(-\)4.58) & 12.92 & \\ \(\mathrm{W_{S}=3a_{e}=35.94\;mm}\) & 35.94 \(\times\) 46.15 & 7.82 & \(-14.08\) & 1.66 (6.89\(-\)8.55) & 6.25 & 11.96 \\ \(\mathrm{L_{S}=L_{F}+3a_{e}=46.15\;mm}\) & & 10.16 & \(-12.63\) & 1.88 (9.43\(-\)11.31) & 8.05 & \\ \hline Reduced width & & 3.44 & \(-13.02\) & 0.84 (3.08\(-\)3.92) & 10.97 & \\ \(\mathrm{W_{S}=2a_{e}=23.96\;mm}\) & 23.96 \(\times\) 46.15 & 7.70 & \(-26.61\) & 3.23 (5.16\(-\)8.39) & 5.99 & \\ \(\mathrm{L_{S}=L_{F}+3a_{e}=46.15\;mm}\) & & 10.88 & \(-10.74\) & 0.85 (10.44\(-\)11.29) & 7.83 & 11.02 \\ \(\mathrm{L_{S}=L_{F}+3a_{e}=46.15\;mm}\) & & 13.64 & \(-34.64\) & 1.58 (12.52\(-\)14.10) & 9.85 & \\ \hline Miniaturized antenna & & 3.44 & \(-42.37\) & 1.71 (2.90\(-\)4.61) & 9.52 & \\ \(\mathrm{W_{S}=3a_{e}=35.94\;mm}\) & 35.94 \(\times\) 38.97 & 7.70 & \(-13.96\) & 1.59 (6.86\(-\)8.45) & 6.15 & 9.37 \\ \(\mathrm{L_{S}=L_{F}+2a_{e}+3h=38.97\;mm}\) & & 10.16 & \(-13.21\) & 1.33 (9.47\(-\)10.80) & 7.41 & \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Antenna miniaturization. Figure 10: Miniaturization process. Figure 11a, and their performance parameters are given in Table 5. It is noticed from the table and figure that the exact resonance at 3.50 GHz occurs for an FSS gap 3.8 mm below the radiating patch antenna. It improves the tri-band bandwidth while reducing the gain to 7.14 dBi, and the first band bandwidth reduces from (2.90-4.61 GHz) to (2.86-4.53 GHz). As the air gap between the substrates increases, the lower band becomes stronger, with a right shift in the resonating frequency noticed, and the reflection coefficient values in the mid- and upper frequency bands become inferior. Since the first band bandwidth is almost the same in all cases, an excellent gain enhancement from 9.37 dBi (without FSS) to 14.02 dBi (with FSS) is achieved when the FSS is arranged at 7.0 mm beneath the ground of the antenna. Therefore, a 7.0 mm air gap below the FSS surface is considered the final case for the proposed design. The effect of the air gap will change the cumulative effective permittivity of the FSS antenna as given in Equation (4). The linear effect of the change in the resonating frequency and the cumulative effective permittivity of the FSS with the air gap is shown in Figure 11b. It is noticed that a 3.8 mm air gap is suitable for fine tuning, while an air gap from 4.6 to 6.4 mm does not change the resonating frequency, and an excellent gain enhancement in the miniaturized antenna is achieved with a 7.0 mm gap between the substrates.