## 3 Design of Triple-Band Antenna  
Firstly, a rectangular microstrip patch antenna operating in 2.4 GHz of WLAN was designed by using formulations given in the literature [51]. The patch width (\(W\)) is computed by (20) for a rectangular microstrip patch antenna whose resonance frequency and relative permittivity of the substrate are \(f_{r}\) and \(\varepsilon_{r}\), respectively [51]:  
\[W=\frac{c}{2f_{r}}\sqrt{\frac{2}{\varepsilon_{r}+1}} \tag{20}\]  
where \(c\) denotes the velocity of light in free space. The length of the antenna patch (\(L\)) can be calculated by [51]:  
\[L=\left[\frac{c}{2f_{r}\sqrt{\varepsilon_{reff}}}\right]-2\Delta L \tag{21}\]  
Here, \(\Delta L\) is the extension of the length due to the effect of fringing fields and is given as [51]:  
\[\Delta L=0.412\hbar\frac{\left(\varepsilon_{reff}+0.3\right)\left(\frac{W}{ \hbar}+0.264\right)}{\left(\varepsilon_{reff}-0.258\right)\left(\frac{W}{ \hbar}+0.8\right)} \tag{22}\]  
Effective permittivity \(\varepsilon_{reff}\) is given by [51]:  
\[\varepsilon_{reff}=\left[\frac{\varepsilon_{r}+1}{2}\right]+\left[\frac{ \varepsilon_{r}-1}{2}\right]\left[1+\frac{12\hbar}{W}\right]^{-1/2} \tag{23}\]  
The desired resonance frequency of the rectangular microstrip patch antenna is selected as 2.4 GHz, WLAN base frequency. The antenna substrate is selected as Rogers RT/duroid 5870 with relative permittivity of 2.33, thickness of 0.787 mm, and loss tangent of 0.0012. By using (20-23), antenna patch dimensions \(L\) and \(W\) are computed as 38.6 mm and 47.5 mm, respectively. Then, parametric analysis in a High-Frequency Structural Simulator (HFSS) [37] is carried out to find the best reflection coefficient and input impedance and tune the resonance frequency to be close to 2.4 GHz for obtaining the feed location of the microstrip patch antenna without slots. A parametric analysis method is used to simulate multiple variations for a design model [37]. A parametric analysis begins with the description of a series of variable values (variations) with chosen step sizes within a range. HFSS carries out an analysis of the design for each variation. Then, the results can be compared to see how each variation affects the performance of the design. Parametric analysis is frequently employed before the optimization process since it provides a reasonable range of variable values [37]. As a result of this process, the feed location of the antenna is computed as \(\chi_{f}\) = 7.0 mm and \(y_{f}\) = 0 mm. The same location is preserved for the microstrip patch antenna with triple slots and arc truncation. After that, multiple slots were added to the conventional microstrip antenna that had the same patch dimensions and substrate to obtain multiband property. Then, the arc-truncation technique [40; 41; 52; 53] was applied to the four edges of the antenna to improve gain performance. It is shown that there is an inverse relationship between the length of truncation and the \(Q\) factor of a truncated microstrip patch antenna [52; 53]. Low radiation \(Q\) factor causes high antenna efficiency [52] value, which means high gain. In this study, it has also been observed that the reflection coefficient value decreases by introducing arc truncations to the antenna. This leads to an increase in the realized gain. The effect of the arc-truncation on the gain performance is ~1 dB increase. Center points for the two large slots are selected such that the slots are far away from the feed point and not so near to the edge of the antenna patch. The center point for the small slot is located at the upper half of the antenna patch. Thus, it is ensured that slots would not coincide with each other, feed point, and edges of the antenna. The initial positions of the slots were selected randomly. Then, parametric analysis via HFSS was carried out with a few steps to determine the positions of the slots, which provide frequency values close to the desired frequency bands.