## 3 Fabrication of the WG ZOR BPF and Test of the Prototype
It is inferred that the error in R (round) formed by the end-mill affects the inductive part which causes the frequency shift in the first place, and secondly, connected pieces in the longitudinal direction do not tightly contact each other, making a tiny gap between metal rims with rotational misalignment. This proposed geometry as a guided component is applied to an antenna system as the electromagnetic radiation problem. \begin{table}
\begin{tabular}{c c c c} \hline \hline  & \multicolumn{2}{c}{**Resonator\#1**} \\ \hline
**Variable** & **Value [mm]** & **Variable** & **Value [mm]** \\ \hline _L1_ & 12.77 & _W1_ & 1 \\ _L2_ & 4.7 & _W2_ & 1 \\ _L3_ & 1.74 & _W3_ & 1 \\ \hline \multicolumn{4}{c}{**Resonator\#2**} \\ \hline
**Variable** & **Value [mm]** & **Variable** & **Value [mm]** \\ \hline _L1_ & 9.8 & _W1_ & 1 \\ _L2_ & 4.7 & _W2_ & 1 \\ _L3_ & 3.48 & _W3_ & 1 \\ \hline \multicolumn{4}{c}{**Resonator\#3**} \\ \hline
**Variable** & **Value [mm]** & **Variable** & **Value [mm]** \\ \hline _L1_ & 9.15 & _W1_ & 1 \\ _L2_ & 4.7 & _W2_ & 1 \\ _L3_ & 3.84 & _W3_ & 1 \\ \hline \multicolumn{4}{c}{**Resonator\#4**} \\ \hline
**Variable** & **Value [mm]** & **Variable** & **Value [mm]** \\ \hline _L1_ & 9.1 & _W1_ & 1 \\ _L2_ & 4.7 & _W2_ & 1 \\ _L3_ & 3.86 & _W3_ & 1 \\ \hline \multicolumn{4}{c}{**Gap**} \\ \hline
**Variable** & **Value [mm]** & **Variable** & **Value [mm]** \\ \hline _gap1_ & 15.4 & _gap3_ & 15.3 \\ _gap2_ & 16.8 & _gap4_ & 14.9 \\ \hline \end{tabular}
\end{table} 
Table 7: The values of the physical dimensions of the eighth-order filter, considering fabrication. Figure 7: Realistic geometry of the eighth\(-\)order WG ZOR BPF. (**a**) Front-view of the thin resonator with the round corners. (**b**) and (**c**), 3D structure. (**d**) S\({}_{11}\) and S\({}_{21}\). Figure 8: _Cont._  
Figure 9 provides variation in L3 generated by the error of the rounded corner, which is critical to the change in the frequency response. For a quick simulation, a second-order case of the proposed filter is dealt with. L3 varied from 2.9 mm to 3.3 mm, mainly causing the frequency shift in S\({}_{11}\), S\({}_{21}\), S\({}_{11}\) and S\({}_{21}\) as in Figure 9a-c, respectively. Figure 8: Prototyped eighth\(-\)order WG ZOR BPF via the CNC milling process. (**a**) Bird’s eye\(-\)view of the thin resonator with the round corners embedded in the flange body. (**b**) Front\(-\)view of the manufactured filter. (**c**) Top\(-\)view of the manufactured filter. (**d**) The device under test having the adaptors matched with the flanges. (**e**) S\({}_{11}\) and S\({}_{21}\). Figure 9: _Cont._  
The characteristics of the proposed filter and reference BPF structures are compared as in Table 8. Most of all, the proposed filter has the shortest resonator as the WG metamaterial, which results in a good insertion loss from the complete structure at the length of 3.5 \(\lambda_{g}\) for a relatively low frequency, while [5; 7] have lengths of around 4.7 \(\lambda_{g}\) and 8.5 \(\lambda_{g}\), each for a relatively high frequency. If the proposed method is applied to 11 GHz, the total length is expected to be 3.5 \(\lambda_{g}\), which is shorter than [5] according to a quick estimation. This work and refs. [5; 7] are high-order filters, giving high levels of attenuation in the stopbands, but [17; 18; 19] take four cavities, showing poor noise-suppression effects. If [15; 16; 17] are elongated to high-order filters, the lengths and insertion loss will be larger. Because the operation frequency of this work is much lower than others' and has to use a WR-112 cross section as the largest, the 7.5 GHz filter might be the heaviest from Table 1 when the same order is assumed for all the compared cases. Thus, the total length must be as small as possible, enabled by the metamaterial resonators. The proposed filter is compared with the non-metamaterial filter in terms of size and function.