## 3 Results and Discussion
### Design of Unit Cell and Cascade Connection Analysis of Corrugated PPW Structures
Utilizing this knowledge, the designer begins the design by selecting a higher stopband center frequency, extracting the unit cell design parameters from the AFGSM functions and trying to ascertain the design requirements. The AFGSM method finds different solutions that meet the same design criteria. These solutions allow you to choose the unit cell with the smallest dimension possible, which makes it easier to create small designs. Figure 11: (**a**) Obtained passband–stopband characterization of designed glide-symmetric DCPPW with AFGSM functions and other computation methods for Scenario 1. (**b**) \(|S_{21}|\) frequency characterization of cascading different numbers of the designed GS-DCPPW unit cell of Scenario 1 via CST, HFSS, and equivalent circuit results. Figure 8:0 (**a**) Obtained passband–stopband characterization of designed glide-symmetric DCPPW with AFGSM functions and other computation methods for Scenario 2. (**b**) \(|S_{21}|\) frequency characterization of cascading different numbers of the designed GS-DCPPW unit cell of Scenario 2 via CST, HFSS, and EC results. Figure 8:1 Comparison of Scenario 1, Scenario 2, and Scenario 3 for obtaining design objectives. \begin{table}
\begin{tabular}{l c c c c c c c} \hline \hline \multirow{2}{*}{**Studies**} & \(a\) & \(b\) & \(h_{1}\) & \(h_{2}=h_{3}\) & \(p\) & \(h_{1}+h_{2}+h_{3}\) & **TFD** \\  & **[mm]** & **[mm]** & **[mm]** & **[mm]** & **[mm]** & **[mm]** & **[mm]** \\ \hline Scenario 1 & 1.5 & 13.2 & 0.5 & 1.2 & 27.9 & 2.9 & 279 \\ Scenario 2 & 1.5 & 12.5 & 0.5 & 2 & 26.5 & 4.5 & 265 \\ Scenario 3 & 2.3 & 13.1 & 0.5 & 1.1 & 28.5 & 2.7 & 285 \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Designed unit cell parameters for all scenarios and total filter dimensions (TFDs) for \(N=10\). Figure 13: (**a**) Obtained passband–stopband characterization of designed glide-symmetric DCPPW with AFGSM functions and other computation methods for Scenario 3. (**b**) \(|S_{21}|\) frequency characterization of cascading different numbers of the designed GS-DCPPW unit cell of Scenario 3 via CST, HFSS, and EC results. Table 4 compares the performance of designed periodic bandstop filters with similar performances reported in the open literature. The designed filter exhibits a broader suppression level bandwidth (SLBW) and achieves more compact design according to [5]. Bandstop filter designs based on microstrip technology given in [55; 56; 57] have notably compact configurations. Ref. [55] has a similar suppression level as Scenario 2, whereas the designed filter demonstrates a wider stopband bandwidth. However, Refs. [56; 57] show higher suppression characteristics and narrow bandwidths with respect to the developed filter. One clearly states that despite the conventional cavity BPF design given in [58] having small dimensions, the suppression level bandwidth could not be as wide as the designed filter. It can be revealed that although the BPF design based on hybrid (microstrip-stripline) technology [58] depicts compact dimensions, the developed filter has a wider suppression level. A major drawback of the developed filter is its very high fluctuation levels in the passband. Conversely, we note that the stopband slope is superior to other designs except [5; 58] for the upper transition band, respectively. However, regarding the normalized circuit size, the performance of the proposed filter is slightly lower compared to other designs. The AFGSM approach relies on the S-parameters of the unit cell, which emphasize the need to ascertain the S-parameters of the structure. One of the easiest ways to carry these calculations out is by utilizing the equivalent circuit model of the investigated periodic structure. Ref. [36] provides that the impact of glide symmetry is obviously identical to merely reducing the spatial period by half. This equivalent circuit model addresses the impact of the glide symmetry of the periodic structure within the AFGSM approach.