## 2 Case of Study: Effect of T-Shaped Stub-Loading
The monopole width and its gap from the GND were determined based on a 50 Ohm coplanar line design, resulting in a width of 0.5 mm and a gap of 1 mm. By adjusting the distance, \(d\), between the thinner arm of the stub and the GND from 9 mm to 13 mm, the simulated frequency responses are presented in Figure 2. It is observed that the best performance, in terms of \(-10\) dB bandwidth and port matching magnitude, was achieved with \(d=11\) mm. Figure 2: (**a**) S11 parameter, d in mm; (**b**) real part of the input impedance, d in mm; and (**c**) imaginary part of the input impedance; (**d**) variations of the \(S_{11}\) parameter for different stub length and positions. As shown in Figure 2a, the frequency response of the monopole is modified as expected due to the interaction with the loading by the T-shaped stub, resulting in a broadened operating bandwidth. While the conventional monopole operates from 4.5 GHz to 5.9 GHz (black line) with a resonance frequency of 5.2 GHz, the monopole with the T-shaped stub exhibits an operating range of 2.7 GHz to 7.3 GHz when \(d\) is set to 11 mm. Analysis of the results depicted in Figure 2b,c, for the case where \(d\) = 11 mm, reveals that the real and imaginary components of the conventional monopole's impedance can be stabilized through the use of the T-shaped stub. For the conventional strip-monopole, the real component of its impedance varies from approximately 90 Ohms to nearly 200 Ohms within the \(-\)10 dB impedance bandwidth. In contrast, the configuration with the stub exhibits variations from 65 Ohms to a maximum of 105 Ohms over a broader bandwidth. Regarding the imaginary component of the input impedance, the reactance of the conventional monopole varies from 40 Ohms to a value of \(-\)100 Ohms. However, for the stub-loaded monopole, the reactive component maintains a capacitive behavior with values close to zero Ohms, with a threshold from \(-\)10 Ohms to 0 Ohms within the operating bandwidth. A similar effect was demonstrated in [11], where the imaginary part of the mutual impedance of two dipoles approached zero according to their position and separation. As a complementary analysis, variations of the position of the stub from the monopole, as well as its length, are presented in Figure 2d, in which it is observed that the port matching and bandwidth are also dependent on these dimensions. Observing that for a stub length of 14 and 15 mm, a good match and bandwidth are also obtained. As a result of the presence of the stub, hither can be concluded that the monopole impedance is stabilized over a wider bandwidth, exhibiting minimal variations and compensating for the reactive component, bringing it closer to zero Ohms. On the other hand, considering the \(-\)10 dB reflection coefficient, the unloaded monopole presents a 1.4 GHz bandwidth, while the loaded monopole shows a 4.9 GHz bandwidth; besides, the lower cutoff frequency for the latter was shifted from 4.5 GHz to 2.7 GHz. Therefore, it can be assured that the use of the proposed technique elongates the antenna's electric length. The mutual coupling and modification of the antenna input impedance of the loaded monopole can be modeled with an equivalent electric circuit response. To model the antenna through the electrical circuit shown in Figure 3a, the theoretical current distribution of a quarter-wavelength monopole is considered [10]. For this reason, the circuit represents the antenna's behavior in three sections: the feed section near the ground plane, where the current intensity is the highest; the central part of the monopole, where the current intensity possesses a medium value; and the end of the radiator near the thin part of the stub, where theoretically, the current intensity should be zero. However, due to the stub loading, these characteristics change. The first section is composed of C1, L1, C2, and L2. The second section is determined by L3, C3, L4, and C4, while the third section is modeled by L5 and C5.