Magnetic Field Sensing Using Micromechanical Oscillators

In the first part of this study, a method for improving bandwidth and thermal stability of the scale factor is presented. The method is successfully demonstrated using two nominally-identical, resonator-based AM magnetometers: the first is operated off-resonance in open-loop to measure magnetic field, and the second is operated as a closed-loop oscillator to provide a frequency reference for Lorentz force generation. With the proposed method, the sensor’s temperature sensitivity is reduced by a factor of 24, and a wide bandwidth (38 Hz) that is independent of the sensor’s mechanical bandwidth (3.2 Hz) is achieved. However, it is observed that the open-loop AM sensor operating off-resonance suffers from poor bias instability that is found to be limited by offset-related 1/f (flicker) noise. The root cause of 1/fnoise is demonstrated to be 1/f noise on the ac and dc bias voltages applied to the sensor, and the effects of 1/f noise sources on the sensor’s bias instability are explored. To reduce offset-related 1/f noise, an innovative method based on chopping the dc bias voltage applied to the resonator is described. Using the chopping method, the sensor’s bias instability is reduced from 27 nT to 7 nT (the best bias instability reported to date for a resonant MEMS magnetometer).

The second part of this study focuses on closed-loop AM operation. A force-rebalanced Lorentz force magnetometer is demonstrated, which is the first demonstration of a three-axis magnetic field sensing oscillator incorporating force-rebalanced operation. The proposed force-rebalanced magnetometer shows significantly superior scale factor stability performance over temperature change and allows larger bandwidth compared to conventional closed-loop magnetometers. However, the force-rebalanced sensor is plagued by offset arising from the electrostatic force used to drive the sensor into resonance. Because the offset is strongly temperature-dependent, the sensor’s bias instability degrades in the presence of temperature variations. This problem is successfully solved by designing a dual-resonator magnetometer, having two identical resonators with opposing axes of field sensitivity.

In the last part, sensor operation is demonstrated using quadrature FM (QFM) readout, where the field is measured by monitoring the change in oscillation frequency. It is theoretically and experimentally demonstrated that FM sensors potentially provide wide bandwidth and improved stability over temperature as compared to conventional AM sensors. However, their output stability is still poor due to the temperature dependence of the sensor’s resonant frequency. To solve this problem, a dual-resonator QFM magnetic sensor composed of a matched pair of differentially operated resonators on the same silicon die are developed. Experimental data show that a differential measurement scheme using the dual resonator significantly improves the sensor’s bias instability.