## 2 Structure of the Tri-Band Antenna  
This section describes the structure of the developed antenna and the rationale behind using a single arm inverted L-shaped strip (ILSS) in the design. The structure of the proposed antenna is shown in Figure 1. It consisted of a rectangular monopole printed on an FR4 substrate and fed by a 50-\(\Omega\) coplanar waveguide (CPW), resonating at 5.5 GHz. The thickness of the substrate was 1.6 mm. The basic configuration was an omnidirectional pattern and dual bands. To make it a bidirectional pattern, a wide circular slot (WCS) connecting to the ground plane was constructed to encircle the monopole. An unintended benefit of this WCS was that it also expanded the impedance bandwidth. That basic structure still did not provide a tri-band capability. To make the antenna tri-band, an inverted L-shaped strip was welded to the inner surface of WCS at the location shown in the figure. This strip induced the resonance at a center frequency of 2.45 GHz [18]. Figure 1: Structure of the proposed antenna: (**a**) schematic model (**b**) prototype. The design parameters of this antenna were based on the following mathematical equations of the radiating antenna [32]. \[w_{r}=\frac{c}{2f}\sqrt{\frac{2}{\varepsilon_{r}+1}} \tag{1}\]  
where \(w_{r}\) was the width of the rectangular patch; \(c\) was the speed of light in free space; \(f\) was a resonant frequency at 5.5 GHz; and \(\varepsilon_{r}\) was the relative permittivity of the FR4 substrate (a value of 4.3). \[l_{r}=\frac{c}{2f\sqrt{\varepsilon_{rff}}}-0.824h\left[\frac{\left(\varepsilon _{rff}+0.3\right)\left(w_{r}+0.264h\right)}{\left(\varepsilon_{rff}-0.258 \right)\left(w_{r}+0.8h\right)}\right] \tag{2}\]  
where \(l_{r}\) was the length of the rectangular patch; \(\varepsilon_{rff}\) was the effective dielectric constant of the substrate; and \(h\) was the thickness of the substrate base. \[\varepsilon_{rff}=\frac{\varepsilon_{r}+1}{2}+\frac{\varepsilon_{r}-1}{2} \sqrt{1+\frac{12h}{w_{r}}} \tag{3}\]  
From these three equations, which already took into account the fringing effect, the initial \(w_{r}\) and \(l_{r}\) of 17 mm and 12 mm were obtained, respectively. To achieve 50-\(\Omega\) impedance matching, the width \(w_{f}\) and length \(l_{f}\) of fed line were calculated by Equations (4) and (5) [26],  
\[w_{f}=\frac{2h}{\pi}\bigg{\{}B-1-\ln(2B-1)+\frac{\varepsilon_{r}-1}{2 \varepsilon_{r}}\bigg{(}\ln(B-1)+0.39-\frac{0.61}{\varepsilon_{r}}\bigg{)} \bigg{\}} \tag{4}\]  
where \(B=\frac{60\pi^{2}}{Z_{o}\sqrt{\varepsilon_{r}}}\), and \(Z_{o}\) was the characteristic impedance of 50 \(\Omega\). \[l_{f}=\frac{\lambda}{4\sqrt{\varepsilon_{rff}}} \tag{5}\]  
Feeding strip widths, \(w_{f}\), of 3 mm and a feeding strip length, \(l_{f}\), of 8 mm were selected and used. A gap \(g\) of 0.4 mm between the feed line and the ground plane was selected to support 50-\(\Omega\) impedance. For compactness, the width \(w\) and length \(l\) of the substrate material were chosen to be 40, i.e., \(w\times l\) = 40 \(\times\) 40 mm\({}^{2}\). This rectangular patch was encircled by a WCS of radius \(r\) connected to the ground plane, designed according to Equation (6) to provide the dominant mode propagation of TE\({}_{11}\) at 2.45 GHz, where \(f_{r}\) is the resonance frequency [26]. Consequently, \(r\) = 17 mm was selected and used throughout the study. In addition, a single-arm ILSS of width \(l_{1}\), thickness \(l_{2}\) and length \(l_{3}\) was welded to the inner wall of the WCS at the position \(p\) in Figure 1 to induce resonance at 2.45 GHz. The total length (\(l_{1}+l_{3}\)) of the ILSS was about a quarter wavelength of 2.45 GHz [1]. \[r=\frac{18,412}{f_{r}2\pi\sqrt{\mu_{0}\varepsilon_{0}}} \tag{6}\]  
where \(\mu_{0}\) was the permeability in free space, and \(\varepsilon_{0}\) was the permittivity in free space. The rationale for the single-arm ILSS design of the developed antenna in contrast to the double-arm design of one of our previous works [18] is described below.