## 3 Performance Characterization and Reliability Assessment  
### RF Performance Measurement  
The RF performance of the filter designs was simulated prior to fabrication using the ANSYS HFSS (High-Frequency Structure Simulator) software (ANSYS, version 2023 R1, 17.2), which employs the Finite Element Method (FEM) for electromagnetic analysis. The 3D model incorporated the precise geometries of the L1, L2, and L3 configurations, including conductor and substrate thicknesses. The silicon substrate was defined with a relative permittivity of \(\varepsilon_{\mathrm{r}}=11.9\) and a loss tangent of approximately 0.004. The metal layers were modeled as finite-conductivity materials. The simulation utilized an adaptive meshing algorithm to ensure solution convergence, with higher mesh density applied around the resonator edges. The model was excited using wave ports, and the S-parameters were calculated across the frequency range of interest. Figure 8 presents a detailed comparison between these updated simulation results and the measured frequency response graphs for the three different resonator width configurations (L1, L2, and L3). The figure consists of three panels, each dedicated to one configuration, displaying S-parameter measurements that characterize the filters' RF performance. As shown, the new simulation results (red lines) demonstrate excellent agreement with the measured performance data (blue lines) across all three configurations. The updated model successfully predicts the measured center frequencies of approximately 17.5 GHz for L1, 17 GHz for L2, and 16.5 GHz for L3. This strong correlation validates that the previously observed frequency shift was systematically caused by the air gap inherent in the fabricated suspended stripline structure. Minor remaining deviations in insertion loss and return loss can be attributed to secondary factors, such as small tolerances in plating thickness and final conductor dimensions inherent in the manufacturing process. The analysis confirms the importance of accurately modeling such real-world packaging effects for high-frequency device design. Figure 7: Fabricated MEMS filters with stripline structures after wafer bonding. From left to right: L1 configuration with no resonator in the cap wafer (0% ratio), L2 configuration with cap wafer resonator width at 60% of the device substrate resonator width, and L3 configuration with identical resonator widths in both cap wafer and device substrate (100% ratio). All devices maintain the same overall dimensions of 5680 \(\upmu\)m \(\times\) 190 \(\upmu\)m \(\times\) 820 \(\upmu\)m with a stripline length of 5180 \(\upmu\)m, differing only in their cap-to-substrate resonator width ratios. Figure 9 displays a comparison of the measured frequency response graphs for three different resonator width configurations (L1, L2, and L3) of the wideband RF MEMS filters. Each configuration represents a different ratio of cap wafer resonator width to bottom wafer resonator width: L1 (0%), L2 (60%), and L3 (100%). The figure shows the S21 (insertion loss) and S11 (return loss) measurements for five different device samples (S1-S5). These S-parameters are critical RF performance metrics that measure how RF signals propagate through the filter. The x-axis represents frequency in GHz, while the y-axis shows the magnitude of the response in decibels. The measurements reveal how the electromagnetic wave behavior differs between the three configurations. L3, with matching resonator widths between cap and bottom wafers (100%), demonstrates the best overall RF performance profile compared to L1 and L2. This is consistent with the study's findings that matching resonator widths creates more symmetrical electromagnetic fields, minimizing mode distortion and reducing insertion loss. These frequency response graphs provide visual confirmation of the paper's central claim: that resonator width matching between cap and bottom wafers significantly impacts electromagnetic field distribution and overall filter performance.