# Design of Broadband High-Frequency Multi-Throw RF-MEMS Switches
## 3 Results and Discussion  
### Low Voltage and Rapid Response  
This section details the design and optimization of the switch cantilever beam and the associated upper electrode. To reduce the driving voltage in MEMS switches, engineers often adopt one fundamental approach: diminishing the spring constant of the cantilever beam. The spring constant \(k\) for multi-cantilevers can be derived from Equation (5). It is analytically determined that the overall value of \(k\) is significantly influenced by the minimal value of \(k_{1..7}\). Thus, it is imperative to minimize this value. Another point of consideration is that the pull-in voltage is directly proportional to the material's Young's modulus. Following a thorough analysis, gold has been chosen as the beam material due to its excellent conductivity, chemical stability, and low contact resistance for the electrical contacts, which reduces reactions with ambient air or humidity. It is worth noting that while gold offers many advantages, it also has some limitations such as creep and low softening/melting temperatures, which can affect power handling and long-term reliability. Despite these challenges, the overall benefits of using gold in our design, particularly its excellent conductivity and low contact resistance, make it a suitable choice for the beam material. The designed folded-beam structure is depicted in Figure 3a, whereas Figure 3b elaborates on the relationship between the drive voltage and displacement for the proposed RF MEMS switch. The relationship between the pull-in force and displacement can be seen in Figure 3c. The lengths of each beam segment are provided in Table 2, where each portion of the folded beam maintains a consistent width of 1 \(\upmu\)m. According to Equations (2) and (3), the cantilever beam undergoes pull-in at a force of 1.3 \(\upmu\)N. COMSOL simulation results indicate that the switch pulls in at a force of 1.2 \(\upmu\)N. From Equations (2)-(7), it can be derived that the cantilever beam's spring constant (\(k\)) is 0.8254, which corresponds to a driving voltage of 6.8 V and a response time of 2.28 \(\upmu\)s. From Equations (8) and (10), the self-actuation power of the proposed switch is calculated to be approximately 1.58 W. The contact force is about a kilo \(\upmu\)N. From these metrics, our curved folded-beam ohmic RF MEMS switch design boasts a diminished spring constant, excelling in pull-down voltage and response time characteristics. Figure 3: (**a**) Designed folded beam; (**b**) Pull-down voltage versus displacement relation; (**c**) Load–displacement relationship diagram. A finite element simulation analysis was executed using COMSOL Multiphysics 6.0 software to evaluate the structure's reliability further. As portrayed in Figure 4, materials with a high Poisson's ratio and thermal expansion coefficients are optimal for control voltage minimization. Consequently, gold was chosen as the material for the upper electrode in this study. Given the short length of the designed cantilever beam, the critical stress value is relatively high, and through calculation, this value is found to be 800 MPa. The simulation results highlight that the root of the cantilever beam, where it connects to the fixed end, is the primary location for stress concentration. Due to significant bending stress in this region, the root of the cantilever beam endures the maximum bending and shear stress when a voltage is applied. The simulation images show that the stress is highest in the root area, represented in red. Similarly, the corner regions of the cantilever beam also experience stress concentration due to geometric discontinuities, exhibiting higher stress when subjected to forces. These regions are shown with high stress values, with colors approaching red in the simulation. By comparing Figure 4a with Figure 4c, it becomes evident that our proposed curved folded-beam design significantly reduces stress concentration compared to conventional straight beams. This enhances the cantilever beam's reliability and stability [28].