## 3 Results and Discussion
### Design of Unit Cell and Cascade Connection Analysis of Corrugated PPW Structures
However, it is evident that the design specifications have not yet reached their target. Selecting unit cell parameters with a broader stopband would prove beneficial in terms of both size and design goals. Figure 12b unequivocally illustrates that a periodic arrangement with \(N=10\) adequately fulfills the design specifications, and the passband ripple levels are considerable. The specified design requirements primarily provide the starting stopband frequency for the suppression level but do not determine the required stop bandwidth in Figure 13b. Figures 11 and 12b illustrate that the results of the full-wave electromagnetic simulation and the EC model converge with an increasing number of unit cells. In Figure 13b, although an EC simulation result that aligned with the required stopband was achieved, it was noted that the full-wave electromagnetic simulation results yielded a smaller and less deep stopband region. The discrepancies occur due to the placement of the anticipated stopband region in the upper modes of the dispersion diagram, the prominence of discontinuity regions inside the structure, and the resultant increase in higher-order mode interactions. The single-corrugated and glide-symmetric double-corrugated PPW designed bandstop filters for two examples exhibit ripples outside the band. Figures 10b-13b indicate that these ripples are at lower levels in the substantially single-corrugated PPW filter. In the X-band filter designs, significant ripples have been observed, particularly in the low passbands. The characteristics of the periodic arrangement anticipate these ripples. Furthermore, Figures 11-13 clearly demonstrate that the use of glide symmetry enhances the ripples generated by the periodic design. In this situation, passband ripples can be managed using a different design method that employs the AFGSM algorithm, either by adjusting the unit cell parameters of the broken glide symmetry [15; 27; 37; 42; 51; 52; 53] or by examining each unit cell parameter with tapering technology [15; 54]. These solutions are not investigated here due to the stopband characteristics of the periodic arrangements of the GS-DCPPW unit cell only being taken into account for testing purposes. The frequency characteristics of \(|S_{21}|\), with a constant unit cell count of \(N=10\) for all selected scenarios, are presented in Figure 14.  
Table 3 presents the design unit cell parameter values for all scenarios and the overall filter dimensions achieved for \(N=10\). Currently, there are trade-offs regarding filter performance and dimensions for the scenarios given in Figure 14 and Table 3. Initially, fulfilling the design specifications of Scenario 1 will evidently necessitate an increased number of unit cells. This circumstance will lead to a substantial increase in passband ripple levels. Consequently, Scenario 1 fails to satisfy the design specifications. Scenario 2 satisfies the design specifications with an identical quantity of unit cells, in contrast to the other two scenarios, which utilize varying sizes yet yield the same stopband width. Furthermore, the overall filter length of Scenario 2 is shorter than that of Scenario 3, presenting a compact design possibility. Conversely, while Scenario 3 does not entirely fulfill the design specifications, its ripple levels in the passband surpass those of Scenario 2, thereby providing a design advantage to Scenario 3. Table 3 shows that Scenario 3 provides a compact design that is advantageous in terms of filter height. In glide-symmetrical double  
CPPWs, the frequency characteristics of \(|S_{21}|\), illustrated by the finite periodic combinations in Figures 11b, 12b, and 13b, indicate that frequency behaviors of the cascaded unit cell begin to approach the center frequency of the stopband depicted in Table 2 as the number of unit cells increases. The situation is important to consider in ascertaining the designer's requirements.