###### Abstract  
Glide-symmetric double-corrugated parallel-plate waveguides (GS-DCPPWs) have essential technical properties such as an electromagnetic bandgap, lower dispersion, and the ability to control the equivalent refractive index. For this reason, a fast and simple analysis and design of GS-DCPPW structures have great importance to improve related microwave systems. This paper introduces a novel design methodology based on the auxiliary functions of generalized scattering matrix (AFGSM) for the dimensional synthesis of GS-DCPPWs. We test the applicability of the AFGSM method on a variety of numerical examples to determine the passband/stopband regions of single and GS-DCPPWs before applying the design procedure. Certain design specifications are chosen, and unit cell dimensions are constructed in accordance with the proposed design technique. Three design scenarios are considered to assess the success of how well the design criteria can be met with the proposed method. The designed unit cells have been periodically connected in a various finite numbers to create periodic filters as a test application for adjusting the electromagnetic bandgap. The success of the periodic GS-DCPPW filters obtained with the proposed design strategy in meeting the specified design requirements has been tested using full-wave electromagnetic simulators (CST Microwave Studio and HFSS). The results indicate that the combined use of the equivalent transmission line circuit and the root-finding routine provided by the proposed method facilitates rapid, efficient, versatile, and approximate designs for corrugated parallel-plate waveguides. Moreover, the design methodology provides the viability of developing a minimal unit cell and a compact periodic filter performance with respect to the literature counterparts. c 2025 20  
filters, and metasurfaces [14; 15; 16; 17; 18; 19]. Essentially, periodic structures can be employed in filters to establish stopbands and attain multiple pass and stopband characteristics through the exploitation of degrees of freedom [14; 15; 16]; in antennas to facilitate wide-angle scanning and enhance radiation efficiency across an extensive frequency range [17]; in metasurfaces to direct electromagnetic waves and transform them into various wave configurations with specified attributes [18]; and in frequency-selective surfaces to generate passband and stopband regions, expand operational bandwidth, and improve polarization converter performance [19]. These components are indispensable to various devices utilized in microwave and millimeter-wave applications. In recent years, the analysis, design, and investigation of periodic structures with higher symmetries in microwave applications have gained prominence [20; 21; 22; 23; 24; 25]. The utilization of these symmetries in periodic structures began 50-60 years ago [1; 26; 27; 28]. Glide-symmetric periodic structures, applicable to various geometries [21; 26; 29; 30; 31; 32; 33; 34; 35; 36; 37], have been extensively studied by researchers due to their outstanding performance in reducing dispersion, controlling bandgaps and bandwidth, and adjusting the equivalent refractive index for particular applications [22; 27]. One of the geometries that implement glide symmetry comprise corrugated parallel-plate waveguides (CPPWs). These structures are frequently employed in the development of broadband microwave devices [17; 28; 38; 39]. When making microwave devices with CPPW periodic structures that have glide-symmetric corrugations, it is important to first figure out the structure's dispersion diagram. A dispersion diagram provides critical insights into the attenuation and phase connection of the structure [40]. Recent analyses of dispersion diagrams for these structures have been extensively performed through mode-matching techniques, method of moments, frequency domain, and eigenmode solvers of full-wave electromagnetic simulators, as well as their corresponding designs [29; 32; 36; 41; 42; 43; 44].