A High-Frequency Resonant Framed-Annulus Pitch or Roll Gyroscope for Robust High-Performance Single-Chip Inertial Measurement Units

This paper introduces a novel resonator design for a high-frequency mode-matched pitch (or roll) gyroscope featuring large excitation amplitude and high Coriolis coupling to address the limitations of conventional designs in enabling robust high-performance single-chip inertial measurement units. The resonator consists of a compact framed-annulus structure with substrate-decoupled in-plane and out-of-plane high-frequency gyroscopic modes for high environmental robustness. The out-of-plane mode is carefully engineered to match the Coriolis force generated by the in-plane mode motion under rotation, providing high Coriolis coupling and improving the signal-to-noise ratio. Prototypes are implemented using HARPSS+ process with nano-gap slanted electrodes for quadrature tuning and nano-gap comb-drives for efficient largerange linear actuation. Mode-matched operation of the gyroscope at 657 kHz is demonstrated with a relatively large open-loop bandwidth of 73 Hz, showing a scale-factor of 150 pA/(°/s) with nonlinearity less than 0.08% over a measured 600°/s full-scale range. The gyroscope shows well-behaved Q-factor and scale-factor across temperature from -40°C to 80 °C, giving less than ±0.65% sensitivity variation after applying a quadratic correction curve to compensate for Q variation. The gyroscope demonstrates angle random walk of 0.55°/√h and bias instability of 17.9°/h, limited by package pressure and interface electronics. Resonant operation of the framed-annulus gyroscope with mechanical Q-amplification provides a solution to high-performance single-chip inertial measurement unit with robust large-bandwidth low-power gyroscopes.