Aspect Ratio Influence on Anchor Loss Using Rapid Analytical FEA Technique

Aspect ratio and its effect on quality factor and coupling factor in length-extensional resonators is analyzed through a rapid analytical/3D-FEA hybrid approach. The approach uses modal analysis to quickly solve for displacements at anchor points, a proxy for energy radiated out of the resonator. Results are compared to experimental data, explaining variations in quality factor from 100 to 2000 based on aspect ratio. Specific aspect ratios which mitigate anchor loss were found to occur for different material stacks, in this case a width to length ratio of 1.4 exhibits a peak in quality factor, in addition to increased coupling compared to extremely low width to length ratios. Flexure due to stack asymmetry limits this effect at higher harmonics. Methods to reduce anchor loss through tethering and acoustic reflectors can be used in parallel with this work to further reduce anchor loss.