Passive Quadrature Reduction In Vibratory MEMS BAW Gyroscopes

This paper presents a comprehensive study on the design and characterization of a passive quadrature reduction method applied to electrostatic MEMS (Micro-Electro-Mechanical System) BAW (Bulk-Acoustic Wave) gyroscopes. The investigation primarily addresses the challenge of mode-to-mode coupling in axis-symmetric gyroscopes arising from fabrication imperfections. We demonstrate that, when quadrature is caused by a known and reproducible imperfection pattern, introducing a physical bias to the devices across a wafer counteracts the quadrature errors. The core concept involves adding or removing masses, referred to as notches, from the outer periphery of the gyro disk where the displacements from both modes are equal. Our study establishes that this targeted manipulation exclusively affects the stiffness coupling between the two modes. Utilizing measured data, we quantify the impact in terms of stiffness coupling, and by subsequently employing finite element analysis (FEA), we establish the correlation between coupling and the required notch size. By judiciously selecting and implementing the appropriate notches across a wafer, we successfully achieve more than 40% reduction in the standard deviation of quadrature nulling tuning voltage, all while preserving the performance parameters of the gyroscope.