## 2 RF-MEMS Phase Shifter: Design Concept and Simulations  
The RF-MEMS phase shifters concepts operating at K and Ka frequency bands are designed capitalizing on True-Time Delay (TTD) technology [9, 10, 11, 12, 13, 14, 15] and are manufactured in the surface micromachining technology available at Fondazione Bruno Kessler (FBK) in Italy [16]. The resulting phase delay is defined by the lengths of the transmission lines. By selecting different propagating signal paths in the circuit, the total phase shift can be tuned by a predefined value. The designed phase shifters consist of 4 sections (i.e., 4 bits), connected in series. Each section has two RF paths with different lengths, as reported by the schematic in Figure 1.  
Figure 1: Top view of the 4-bit True-Time Delay (TTD) phase shifter schematic topology. The upper sections correspond to the reference path with a total 0\({}^{\circ}\) phase shift. The total phase shift is controlled by the combination of the four sections path lengths, selected using RF-MEMS ohmic switches monolithically integrated into the network. Once the switches are actuated (i.e., pulled-in), the RF signal travels through the selected delay line. Each bit can provide an additional 22.5 degrees phase shift at the operating frequency. Thus, a 4 bits phase shifter provides 24 = 16 different phase delays: 0\({}^{\circ}\), \(\pm\)22.5\({}^{\circ}\), \(\pm\)45\({}^{\circ}\), \(\pm\)67.5\({}^{\circ}\), \(\pm\)90\({}^{\circ}\), \(\pm\)112.5\({}^{\circ}\), \(\pm\)135\({}^{\circ}\), \(\pm\)157.5\({}^{\circ}\), and 180\({}^{\circ}\) at 19.5 GHz and 29.3 GHz center frequencies, for the K and Ka band specific design variant, respectively. The designed phase shifter is based on 50 \(\Omega\) Coplanar Waveguide (CPW) transmission line and the time delay switch option is based on series-type electrostatically driven RF-MEMS ohmic switches. Thus, the phase shift is controlled by the applied voltage signal to each of the four bits. The K band phase shifter is fitted with switches described by the authors in [17]. Figure 2a shows a schematic view of the transverse RF-MEMS switching unit integrated into the CPW transmission line. The Ka band device is almost twice smaller in size, so the same switch geometry cannot be fitted in it due to its dimensions and space needed for integration. One of the most compact configurations is related to cantilever-type geometry (i.e., single-hinged membrane) [18]. However, from a general point of view, cantilevered MEMS switches are not as robust as clamped-clamped designs [19; 20]. To avoid reliability issues, a compact longitudinal membrane with complex anchor geometry has been designed, as reported in Figure 2b. This membrane with optimized characteristics allows lowering the actuation voltage and reducing the area occupation, while still relying on double-hinged MEMS suspended membrane solution, as for the transverse micro-switch. Both the longitudinal and transverse switch geometries were optimized to achieve a wide operating frequency range in terms of low loss and high isolation. Table 1 shows that in the operating range 0-40 GHz, the simulated losses are less than \(-\)0.8 dB and isolation is better than \(-\)20 dB. Structural deformations due to the actuation voltage were simulated for 1.5 \(\upmu\)m membrane thickness and stiffening rib [16] of 2.5 \(\upmu\)m at varied air-gaps between the membrane and the actuation pads. Table 2 reports the applied actuation voltage depending on the air-gap for both membranes. The results of electromechanical simulations for the minimum gap of 2 \(\upmu\)m are illustrated in Figure 3, in which the actuation voltage (\(V_{PI}\)) is 28 V for the transverse MEMS membrane and 38 V for the novel compact longitudinal design concept.