## 5 Measured and Experimental Results
The slight deviations in the theoretical, experimental, and fabricated results are due to inevitable human errors in measurement, losses in SMA connectors and substrate material, and the effect of soldering. Figure 14: Validation of second band control w.r.t \(L_{4}\). Figure 15: Validation of third band control w.r.t \(L_{5}\). Figure 16: Validation of third band control w.r.t \(L_{6}\). \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Serial No.** & **Theoretical Results** & **Simulated Results** & **Measured Results** \\ \hline
1 ststopband & 5.5 GHz & 4.9 GHz & 4.83 GHz \\
2 ndstopband & 8.1 GHz & 8.3 GHz & 8.51 GHz \\
3 rdstopband & 10.8 GHz & 11.5 GHz & 11.69 GHz \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Results variation of the stopbands. Figure 17: Validation of all bands w.r.t \(L_{8}\). Another important parameter is the coupling coefficient discussed by the authors [25; 26]. As shown in Figure 12, the space S is responsible for the generation of coupling phenomena in the filter, and by increasing the space S from 0.08 mm to 0.2 mm, the coupling coefficient decreases, or vice versa, as shown in Figure 18, and is obtained due to Equation (21) by considering the values of Table 5.  
\[K_{e}=\frac{f_{2}{}^{2}-f_{1}{}^{2}}{f_{2}{}^{2}+f_{1}{}^{2}} \tag{21}\]  
In above equation,\(f_{2}\) and \(f_{1}\) represents the upper and lower frequency of each stopband. Figure 19 shows the simulated current distribution at the stopbands for validation of the resonance frequencies produced by the corresponding stubs. As discussed above, a novel T-shaped shorted stub-loaded resonator with a central square ring is utilized for the formation of notches in the ultra-passband response; therefore, most of the energy is absorbed by this resonator, as shown below. Figure 19: Current distribution graph of the triple-notched filter. \begin{table}
\begin{tabular}{c c c c} \hline \hline
**S\({}_{1}\) (mm)** & **1 st Band (GHz)** & **2 nd Band (GHz)** & **3 rd Band (GHz)** \\ \hline
0.08 & 0.08 & 0.06 & 0.04 \\
0.09 & 0.065 & 0.058 & 0.038 \\
0.1 & 0.055 & 0.048 & 0.031 \\
0.2 & 0.03 & 0.01 & 0.021 \\ \hline \hline \end{tabular}
\end{table} 
Table 5: Simulated result of “K” for different values of S.  
Figure 18: Coupling phenomena with respect to the parameter S.  
Equations (22) and (23) described another important parameter in the design of UWB filters and antennas called the group delay (\(\tau_{d}\)) [27; 28]. It is expressed as:  
\[\tau_{d}=d\varphi_{21}(\omega)/-d\omega \tag{22}\]  
\[\varphi_{21}(\omega)=\arg S_{21}(\omega) \tag{23}\]  
In above equations, \(\varphi_{21}\) and \(\tau_{d}\) denote the parameter phase and group delay, respectively. As seen in Figure 20, the group delay is almost flat over the passband except at the notches, which guarantees that all the frequencies have the same group velocity and phase. This leads to a minimum frequency dispersion in the passband and a maximum at the stopbands [29; 30]. The phase response of the proposed filter is illustrated in Figure 21.  
The superiority of this research work is a simple topology to reduce the cost, which is then compared with the most recent published articles in reputed journals in terms of good FBW or wide absolute bandwidth, central frequency (CF), low  
Figure 21: Phase response of the proposed triple-notched filter. Figure 20: Group delay response of the proposed notched filter. high returns loss (RL), and independently controlled notch bands, which are listed in Table 6, respectively. Moreover, the final S\({}_{11}\) and S\({}_{21}\) frequency plots of the measured and simulated results with the fabricated prototype are shown in Figure 22. This verifies that the proposed architecture eliminates the potential interference in the ultra-wideband microwave applications and has the advantage of stopping and controlling the unwanted wireless bands according to the user's needs.