Silicon Substrate Thermal Diffusion Gradients and MEMS Stress Variations
Substrate thermal gradients induce anisotropic strain fields that degrade MEMS accuracy through piezoresistive offset shifts and capacitive gap distortion.
Mode Matching Frequency Pulling
Resonance Interaction
Dynamic coupling between the drive and sense modes of a vibratory gyroscope occurs when their respective resonant frequencies are brought close together to maximize sensitivity. In micromachined sensors, mode matching frequency pulling represents the mutual shift in these frequencies caused by electrostatic or mechanical cross-coupling as they approach degeneracy. This interaction limits the maximum usable sensitivity of the device.
The phenomenon ceases to dominate when the frequency separation between the modes is much larger than the bandwidth of the system.
Calibration Compensation
Tuning the resonant frequencies of the sensor involves applying DC voltages to dedicated electrostatic electrodes. However, mode matching frequency pulling complicates this tuning process because changes in the drive frequency lead to unexpected shifts in the sense frequency. The tuning algorithm must account for this non-linear interaction to achieve stable mode matching.
This requires a feedback loop that continuously adjusts the tuning voltages during operation.
Structural Optimization
Mechanical design can minimize the cross-coupling by ensuring that the drive and sense modes are mechanically orthogonal. Designers use symmetric suspension beams and balanced proof masses to reduce the parasitics that drive mode matching frequency pulling. This layout minimizes the dependence of the frequencies on manufacturing variations.
It also reduces the temperature sensitivity of the device.
Measurement Stability
Uncorrected frequency pulling results in unstable scale factor and bias drift over temperature. In precision navigation systems, this drift can cause errors in the calculated position. Therefore, active frequency tracking and control are needed to maintain sensor accuracy.