## 2 Antenna Configuration and Design Strategy
### Systematic Design Process
#### 2.2.1 Multiband Antenna  
Antenna design passes through various consecutive iterations to achieve the multiband operation. For the said purpose, a truncated printed structure is selected as the base of the design, as depicted in Figure 3a. Truncated structures are well known for their broadband behavior, and the smooth transition of the shape from the rectangular feed toward the radiator allows more current to flow, which consequently improves the overall bandwidth of the antenna. The resultant antenna in stage 1 possesses the wideband ranges from 3.85 GHz to 7.37 GHz, as depicted in Figure 3a. Hereafter, the stubs are loaded to achieve multiband behavior, and efforts are made to achieve lower bands across 1.8 GHz. For this objective, initially an inverted L-shaped stub is loaded at the top-left side of the radiator, as shown in the inset of Figure 3b. The stage-2 antenna offers the dual-band response while covering the lower band ranges from 3.27 GHz to 4.02 GHz, while the upper band ranges from 4.72 to 7.29 GHz, as depicted in Figure 3b. The lower band is the result of loading the stub, whereas the effective length of the stub to achieve the lower band is calculated by using the following expression provided in [35; 36]:  
\[f_{\rm L}=\frac{c}{xL_{e}\sqrt{\epsilon_{eff}}} \tag{1}\]  
Here, the f\({}_{\rm L}\) shows the resonating frequency due to addition of the stub, which is the ratio of the speed of light in a vacuum (c) to the product of the effective length of the stub (I\({}_{\rm e}\)), the square root of the effective permittivity (\(\epsilon_{\rm eff}\)) of the substrate, and variable x, which correspond to the fraction of the wavelength at the desired frequency f\({}_{\rm L}\). Rearranging the  
Figure 2: Proposed multi-mode frequency-reconfigurable antenna: (**a**) top view, (**b**) side view.  
Equation (1) results in the following expression, which is utilized to estimate the length of the stub for the desired frequency of 3.5 GHz:  
\[L_{e}=\frac{c}{xf_{L}\sqrt{e_{eff}}} \tag{2}\]  
By inputting the value, the effective length is mm with x corresponding to 4.  
Following the same aforementioned methodology, a meandered line stub is loaded to the top of the radiator in stage 3, as depicted in the inset of Figure 3c. The stub consequently achieves resonance at 2.45 GHz with an impedance bandwidth of 2.1 GHz-2.6 GHz while the upper band remains unvaried, offering wideband behavior from 4.72 GHz to 7.29 GHz, as shown in Figure 3c. In the last stage, a combination of the stub designed earlier is utilized, where the inverted L-shaped structure is connected to the one end of the meandered line stub. This stage 4 effectively results in achieving the targeted band spectrum of 1.8 GHz ranging from 1.76 to 1.85 GHz, that covers the globally allocated band spectrum for GSM 1800 MHz applications. It is worth mentioning that the proposed antenna achieved the lower band of 1.8 GHz with physical size of 15 \(\times\) 20 mm\({}^{2}\) that corresponds to 0.09 \(\lambda_{\mathrm{fl}}\times\) 0.12 \(\lambda_{\mathrm{fl}}\), where \(\lambda_{\mathrm{fl}}\) is the wavelength at the lowest resonance.