## 1 Introduction  
A frequency selective surface (FSS) consists of an array of identical metallic structures arranged as a single or multi-dimensional periodic surface. The periodic structures have extensively been used in series of microwave, millimeter-wave (mm-wave) and terahertz (THz) applications such as band-stop filters, dichroic reflectors and circuit absorbers [1]. When excited by an incident plane wave, the FSS resonates at a particular frequency or multiple frequencies depending on the properties of the periodic array structure, dimensions and dielectric substrate. The conventional FSSs are interpreted as capacitive or inductive structures or sometimes a combination of both [2; 3; 4; 5; 6]. A plethora of FSS configurations have been actively investigated in wide application areas such as reflectors for satellite communications [7; 8], microwave radomes [9], waveguide filters [10], phase shifting surfaces [11], linear to circular polarization converts [12; 13] and various antennas [14]. In addition, the FSS has been used as metamaterials and metasurfaces in the mm-wave and THz technology for designing absorbers, sensors, spatial filters and imaging system components [15; 16; 17; 18; 19; 20; 21]. The FSS structures used in these studies include square structure, circular structure and the combination of square or circular with other structures. Recently, the FSSs were implemented as notch, band-stop and high-pass filters for mm-wave imaging diagnostic systems [22; 23; 24; 25; 26]. In the studies, the resonant frequencies of the FSS-based filterswere 105 GHz, 110 GHz, 140 GHz and 170 GHz for imaging diagnostic systems for tokamak plasmas ([PERSON] et al., 2016; [PERSON] et al., 2017). In these systems, the FSS-based protection was essential to protect the receiver electronics from unwanted stray signals by providing high rejection of, often, powerful unwanted signals. For example, in the ECEI (electron cyclotron emission imaging) system, which extracts images of plasma temperature fluctuations in tokamak plasmas by detecting weak plasma radiated signals in mm-wave band, protecting Schottky diode detector arrays from high-power stray ECRH (electron cyclotron resonance heating) signals was required. A large-sized thin planar FSS filter was required to be placed in front of the detector array box to reject or weaken the powerful stray signal ([PERSON] et al., 2017). For mm-wave applications, the performance of the reported mm-wave FSS structures was highly dependent on the fabrication accuracy due to the fine cell structure requirements. Therefore, for the implementation, high-precision and expensive fabrication techniques such as Electro-Fine Forming (EF2) technology ([PERSON] et al., 2017), thin-film technology ([PERSON] et al., 2017) and microfabrication ([PERSON] et al., 2017) were used to fabricate FSS filters. With small-sized FSS structures ([PERSON] et al., 2017; [PERSON] et al., 2017; [PERSON] et al., 2017), high-precision fabrication technique can be applied without difficulty, but, as the size of the FSS panel becomes bigger, significant increase in fabrication cost can occur. In this regard, recently, our group has developed and reported a low-cost fabrication technique for large-size FSSs (\(\sim\)19.7 \(\times\) 6.3 inches at 170 GHz) with high performance at mm-wave range to protect the mm-wave ECEI receiver ([PERSON] et al., 2016). In the study, an array of square loops on both sides of the substrate was used, but, with using the commercial PCB process, the resonant frequencies of the FSSs from multiple prototypes showed variations of around 3 GHz deviated from the designed values. In this paper, a comprehensive comparative parametric analysis including the effect of fabrication tolerances on the performance for square- and circular-loop FSS structures at the millimeter-wave frequency range is presented. It is shown that an array of circular loops is found to produce more predictable and accurate results as compared with the array of square loops under the same fabrication tolerance conditions.