# MEMS-Switched Triangular and U-Shaped Band-Stop Resonators for K-Band Operation
## 4 U-Shaped Resonators  
Until now, U-shaped resonators have been studied mainly in microstrip configurations for filtering applications or combined in arrays for antenna and high-frequency absorber purposes. A U-resonator alone is not necessarily suitable for a metamaterial response, at least the resonators studied in [24]. Still, their collective excitation is usually referred to as a metamaterial-inspired structure. The main advantage of a U-shape in filtering applications is the possibility of bending a resonating line with a consequent decrease in the footprint. This solution allows for a designer to use the U-elements in the well-established coupled-line filters designed in a microstrip configuration, substituting straight lines with bent ones. Preliminary work on filters implemented by RF MEMS switches was performed in [33]. The hairpin filter is a well-known example of using U-bended lines [34; 35]. The drawback of the line-bending procedure is to account, during the design of the device, for the discontinuity created by the bending itself, whose equivalent circuit modifies the resonant frequency. Another delicate point to be considered is the coupling between the resonator and the feeding line, either a microstrip or a CPW. The structures studied in this paper combined a 20 GHz resonator and a 26 GHz resonator coupled to the central conductor of a CPW and were placed on two branches separated by an SPDT RF MEMS switch. The SPDT drove the signal on the branch selected by the actuation of the corresponding membrane. In the following Figure 13, the configuration used for the double-frequency filter is shown during an on-wafer measurement. Figure 13: Layout of the U-switched resonators. In this picture, the upper resonator allows the 26 GHz output, while the 20 GHz resonator is shown on the bottom side. The size of the full structure and detailed dimensions of the single resonators are also given. In Figure 14, the predicted performance of the switched filter based on the U-resonators is shown, where the selected frequencies around 20 GHz and 26 GHz resulted from the simulation of the individual filter response. As previously discussed, additional resonances can appear in the spectrum, but having a series of resonances is intrinsic to the nature of all resonators, depending upon the size of the resonators, and corrected by their effective lengths because of electromagnetic boundary effects and the coupling conditions. The main mode was almost correctly predicted at 20 GHz; the same happened for the 26 GHz resonator. Experimentally, the situation was more complicated. The presence of the switches and the feeding lines, together with the intrinsic nature of the resonators of being multi-resonant, allowed for the excitation of multiple peaks because non-perfect matching or unwanted inhomogeneities created discontinuities that could excite higher-order modes, thus hindering the possible selection of two single resonances. This situation is clearly shown in Figure 15, where the measured response of the U-structures is plotted. An arrow is used to indicate the main resonance due to the single resonator (big or small) activated by the branch selected using the SPDT. Like in the case of the already discussed triangles, a further improvement of this configuration should include a shift in the position of the two individual resonators to provide a better physical separation and mitigate the possible interaction between them. Additionally, both the main resonance modes were shifted with respect to the expected single resonances because of the influence of the entire network. For clarity, the main modes were isolated from the previous figure and are plotted separately in Figure 16.  
Figure 14: Expected resonances for the structure with two U-shaped resonators working at 20 GHz and 26 GHz, respectively. (from Figure 15). So far, a downward shift of approx. 2 GHz was experienced when comparing the theory and experiment. In conclusion, the studied resonators are promising as individual devices.