# MEMS-Switched Triangular and U-Shaped Band-Stop Resonators for K-Band Operation
## 1 Introduction  
Multi-band systems have begun to be widely adopted in modern satellite communication [1], where complex arrangements of frequencies and spatial coverage constraints require miniaturization [2, 3] and frequency band selection. RF MEMS switches have been used for the last two decades to tune or reconfigure high-frequency devices instead of pin diodes or transistors to overcome their intrinsic limitations using an all-passive solution. Despite the obvious advantages of using microelectromechanical systems, a fully reliable and long-lifetime solution has not yet been certified for the space environment. On the other hand, a few examples [4, 5, 6, 7, 8] used in signal routing have also been studied in the past years [9, 10, 11] and, more recently, also for the small satellites domain [12, 13, 14]. For this reason, the RF MEMS solution is still appealing to substitute semiconductor conventional switches or even bulky waveguide switches with planar, miniaturized, and fully passive devices. The ongoing interest in researching RF MEMS is also devoted to RF applications towards reconfigurability; for instance, the frequency agility of resonators [15, 16] and antennas [17, 18]. A new perspective for the feasible application of RF MEMS is opening up with regard to 5G/6G telecommunications technologies [19, 20, 21], where the lowest power consumption will be a key aspect [22, 23]. In this paper, RF MEMS devices will be used in a single-pole-double-through (SPDT) configuration to address the microwave signal in two branches loaded by resonators working at frequencies very close to each other (fine-tuning around 20 GHz or 26 GHz) or to switch the signal between approx. 20 GHz and 26 GHz. The general structure of the proposed devices was designed in a coplanar waveguide (CPW) configuration for possible implementation within staked modules, i.e., in situations where the electromagnetic interference between different layers must be minimized. CPWs naturally fulfill this requirement, because the electric field is confined in the plane of the substrate. Due to their robustness and reliability, double-clamped metal beams arethe best mechanical structure for RF MEMS switches. Manufacturing micromechanical devices using lateral ground planes for supporting the entire structure is convenient from a mechanical and electrical standpoint, because it is easier to separate the RF and DC paths, as generally required by high-frequency sub-systems. Two geometries were considered in this contribution: (i) triangular resonators with a Sierpinski geometry and (ii) U-shaped resonators. Sierpinski structures were introduced for a few reasons. First, triangular geometries are rarely used, but have some advantages regarding their footprint and coupling possibilities, as discussed in [24], concerning square or circular resonators. Secondly, there is no systematic work on or a straightforward analytical approach to determining the spectrum of Sierpinski triangles depending on their internal complexity, and an experimental approach supporting or modifying the theory is necessary for CPW-fed configurations. This paper also studied the U-shape, combining two resonators with SPDT RF MEMS devices. In this case, we selected this configuration for miniaturization purposes and the implementation in coupled structures analogously to the classical hairpin filters developed in a microstrip configuration [25]. So far, the novelty of this basic work is mainly related to introducing the design of triangular and U-shaped resonators in a non-conventional configuration hosted by a CPW environment and driven by RF MEMS switches. Results about the design, manufacturing, and testing of devices mounting RF MEMS SPDT switches will be presented for applications in K-Band, specifically working around 20 GHz and 26 GHz. The technology for realizing switches in MEMS technology has already been discussed in [24] and will be briefly reviewed here.