## 2 Design and Analysis
### Stub-Notch Configuration Analysis  
Open-circuit stubs are loaded with the radiating edge of the antenna. A dual-band frequency response is achieved with this configuration. Without loading the stubs, the inset-fed antenna gives only one \(-\)10 dB resonance and two band notches in the higher bands. According to [21; 22; 23], placing an open circuit stub with a length nearly equal to a quarter of the wavelength on the radiating \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Parameters** & **Value (mm)** & **Parameters** & **Value (mm)** \\ \hline l\({}_{1}\) & 33.5 & w\({}_{5}\) & 1.9 \\ \hline l\({}_{2}\) & 19.17 & w\({}_{6}\) & 0.5 \\ \hline l\({}_{3}\) & 7.38 & w\({}_{7}\) & 2.1 \\ \hline l\({}_{4}\) & 6 & g\({}_{1}\) & 11.91 \\ \hline w\({}_{1}\) & 33.5 & g\({}_{2}\) & 5.58 \\ \hline w\({}_{2}\) & 9.1 & g\({}_{3}\) & 10.09 \\ \hline w\({}_{3}\) & 12.91 & g\({}_{4}\) & 5.81 \\ \hline w\({}_{4}\) & 3.68 & g\({}_{5}\) & 1 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Detailed Dimensions of the proposed antenna. Figure 1: Schematic of the microstrip line edge-fed rectangular patch. (**a**) Top view with the stub loaded and slot etched rectangular patch; (**b**) Back view of the defected ground structure (DGS)-integrated ground plane. edge, can offer a capacitive impedance for the frequencies lower than the patch resonant frequency, and inductive impedance for the frequencies higher than the patch resonant frequency which leads to a dual frequency response. But for different stub lengths, this quarter wavelength approximation does not give exact results for the given resonant frequency [23]. Moreover, the position of the stub on the radiating edge changes the impedance variation along the edge. So, to have appropriate impedance matching, the feed position should be near the area of the opposite edge of the stub, and for further improvement, the feed position can be displaced from the y-axis position where the stub is present [24]. In the present work, a stub of length not equal to quarter the wavelength has been loaded on the radiating edge which gives two \(-10\) dB resonance but does not affect the middle-band notch. Though its length is not equal to a quarter of the wavelength, it still offers capacitive impedance to the lower resonance frequency and inductive impedance to the higher resonance frequency. For this reason, both \(-10\) dB resonance positions shift to the lower frequency regions, but the lower passband frequency (\(3.96\) GHz) is not the desired frequency for this application. So, we need to further shift the passband frequencies to lower frequency regions. Loading of additional stubs whose lengths are not equal to a quarter of the wavelength and symmetric to the middle stub has the same effect of loading a single stub, i.e., offering more capacitive and inductive impedance to the lower and higher resonant frequencies, respectively. But loading of these stubs forms a coupling capacitance between each of them and the center stub. So, they are responsible for another resonant frequency, and a spike is observed between the two resonant frequencies achieved earlier. In addition, the impedance matching of the previous passband frequencies degrade. To solve this problem, instead of changing the position of the feed line, a pair of rectangular slots are cut in between these three stubs and from the same radiating edge. These rectangular slots can be referred to as notches. The loading of these notches increases the current path at the radiating edges where the stubs are located, which further increases the inductive impedance offered by the stubs. At the same time, the notches will slightly increase the value of the coupling capacitance. For the negligible value of coupling capacitance with respect to the inductive impedance, the resonance behavior of the side stubs diminishes. On the other hand, the widths of these notches have little effect on the position of the resonance frequencies [24] as depicted in Figure 2a.