# Design of Broadband High-Frequency Multi-Throw RF-MEMS Switches
## 2 Structure and Theoretical Analysis  
A three-dimensional schematic of the switch is displayed in Figure 1a, featuring a cantilever beam design with six ports. Connections or isolations between different ports can be achieved by manipulating the driving electrodes. The local view provides a detailed top-view depiction of a single switch and its power divider. The switch comprises several components: signal lines, ground lines, CPW (coplanar waveguide) transmission lines, upper electrodes, anchor points, and a power divider. The power divider ensures an equitable energy distribution from the input port to each output port within this device. An upper electrode design close in width to the transmission line optimizes insertion loss performance. Additionally, the apertures in the upper electrode effectively accelerate the release speed of the beam, which is crucial for the yield of the beam structure and potential large-scale production. Regarding substrate material selection, we opted for a BF33 glass substrate with a dielectric constant of 4.6, given its attributes of low relative permittivity, minimal loss tangent, thermal stability, impact resistance, and high-temperature endurance. The intricate multi-channel signal regulation capability of the switch is demonstrated in Figure 1c. Notably, due to the switch's holistic symmetric design, any port can be the input, while the remaining ports can function as outputs. Through our optimization studies, each port exhibits exceptional RF performance. Amid the growing scarcity of spectral resources,such designs play a pivotal role in advancing the development of highly integrated and tunable devices. The primary design parameters of the switch are listed in Table 1.  
The following section provides a detailed analysis of the RF and physical characteristics of the switch. For the ohmic RF MEMS switch, when a sufficient bias voltage is applied between the upper and lower electrodes, the electrostatic force draws the upper electrode downwards, closing the signal. Upon removing the drive voltage between these electrodes, the upper electrode reverts to its original position due to the restoring force, \begin{table}
\begin{tabular}{c c} \hline \hline
**Parameters** & **Values (\(\upmu\)m)** \\ \hline CPW Size & 2/3.75/2 \\ CPW Thickness & 2 \\ Top Electrode Thickness & 0.5 \\ Top Electrode Length & 15.5 \\ Top Electrode Width & 3.75 \\ Gap & 0.5 \\ Overall Size & 63 \(\times\) 68 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Dimensions of the designed switch. Figure 1: Proposed switch. (**a**) 3D schematic; (**b**) Top view; (**c**) Operating modes. thereby disconnecting the signal. When analyzing the RF MEMS switch's RF performance, researchers often employ equivalent parameters. In high-frequency circuits, the lumped parameter equivalent circuit can describe the microwave performance of the RF MEMS switch. By establishing its resistance, inductance, and capacitance (\(RLC\)) model, one can gain a deeper understanding of the effect of each parameter on microwave performance. The switch's equivalent model is illustrated in Figure 2, where \(Z\) represents the characteristic impedance of the CPW signal input/output port. The coupling capacitance of the CPW signal input/output end is denoted as \(C_{p}\), and the equivalent resistance of the plane-type upper electrode is represented as \(Z_{s}\). The contact resistance of the upper electrode in the closed state is \(R_{c}\). When the switch is off, the coupling capacitance generated between the upper electrode and the signal line is \(C_{c}\). Microwave theory is utilized to compute the equivalent circuit results of the RF MEMS switch. The isolation expression obtained in the off state is as follows:  
\[S_{21}=20 lg\left|\frac{2 jwC_{c}Z}{1+2 jwC_{c}Z}\right| \tag{1}\]  
From this, it can be deduced that the coupling capacitance value between the upper electrode and the signal line significantly influences the isolation of the RF MEMS switch.