## 5 Hardware and Software Simulation Implementation  
In this study, the SWB BPF with stopband characteristics was designed and implemented. The SUWB-BPF is made up of a UTL that has three-quarter-wavelength stubs loaded onto it; one of these stubs is placed on one upper side of the UTL and the other is positioned symmetrically on the other side to achieve high sharpness in the filter and a flat passband response. A Rogers RO-4350 dielectric substrate with a low tangent loss of 0.0003, h = 1.5 mm, and \(\epsilon_{r}\) = 3.6 was selected for the fabrication of the prototype to make the passband IL as low as possible, i.e., less than 0.4 dB, which leads to a flat group delay without ripples appearing in the passband. The structure was studied by considering a lossless transmission line and was investigated through the ABCD matrix. The replacement of conventional stubs with three new folded shunt stubs with pads enhances the filter's performance in terms of its wide bandwidth, high selectivity, and multiple TPs. In the second step, two notches were created using a shorted, T-shaped resonator, coupled with the initial wideband filter, and analysed using a method called even-odd mode analysis. Two controllable stopbands were achieved for the application of long-distance wireless ISPs (WISPs), centred at 4.4 GHz, and X-band communication centred at 7.5 GHz. The first 4.4 GHz stopband was created due to the equivalent circuit shown in Figure 6b, while the second 7.5 GHz stopband was achieved due to the equivalent circuit shown in Figure 6c. The simulated response of the dual stopband filter is depicted in Figure 8.  
It has the advantage that both stopbands can be controlled by the users, according to their application, based on the stubs' length. For example, as shown in Figure 9a, the first stopband can be controlled using the central shorted stub with dimensions of \(L_{6}\) = 3 mm, and by changing the dimension, only the first stopband moves down, while the second band is stable. Similarly, from Figure 9b, the second stopband can be controlled by the outer half-wavelength stubs with dimensions of \(L_{5}\) = 4.2 mm, and by changing the dimension, only the second stopband changes while the first band is stable. So, this makes the proposed filter capable of stopping any frequency, according to the user's applications. Figure 8: Simulated dual-stopband response. Another important phenomenon that needs to be discussed is the coupling coefficient (k) that appears when two or more resonators come in close contact [48]. As shown in Figure 7, the coupling phenomena originate based on the gap (G), which is given in Equation (22). As depicted in Figure 10, the \"K\" drops when the gap is increased from 0.08 mm to 0.2 mm, or vice versa. \[\mathrm{k}\ =\frac{\mathrm{f}_{2}{}^{2}\ -\mathrm{f}_{1}{}^{2}}{\mathrm{f}_{2}{}^{2 }+\mathrm{f}_{1}{}^{2}} \tag{22}\]  
where \(\mathrm{f}_{1}\) and \(\mathrm{f}_{2}\) represent the lower and upper stopband frequency. In the design of wideband filters or antennas, it is important to discuss the parameter group delay (\(\tau_{d}\)) and phase velocity (\(\varphi\)), which should be constant throughout the passband to avoid any frequency distortions, and can be expressed as [48]  
Figure 10: Coupling coefficient (k) plot with respect to the gap (G). Figure 9: Notch band control: (**a**) response of the first stopband with controllable features; (**b**) response of the second stopband with controllable features. \[\Gamma_{d}=\frac{d\varphi_{21}(\omega)}{-d\omega} \tag{23}\]  
\[\varphi_{21}(\omega)=\text{arg}S_{21}(\omega) \tag{24}\]  
The terms \(\varphi_{21}\) and \(\tau_{d}\) in the equations above stand for the parameter phase and group delay, relative to the magnitude (\(S_{21}\)). As shown in Figure 11a, the group delay is practically flat across the full passband, ensuring that all current flows with the same velocity and phase, resulting in the minimum amount of frequency dispersion possible. Also shown in Figure 11b is the suggested UWB filter's phase response.