Force-rebalanced Lorentz force magnetometer based on a micromachined oscillator

This paper presents a 3-axis Lorentz force magnetometer based on an encapsulated micromechanical silicon resonator having three orthogonal vibration modes, each measuring one vector component of the external magnetic field. One mode, with natural frequency (f_n) of 46.973 kHz and quality factor (Q) of 14 918, is operated as a closed-loop electrostatically excited oscillator to provide a frequency reference for 3-axis sensing and Lorentz force generation. Current, modulated at the reference frequency, is injected into the resonator, producing Lorentz force that is centered at the reference frequency. Lorentz force in the first axis is nulled by the oscillator loop, resulting in force-rebalanced operation. The bandwidth and scale-factor of this force-rebalanced axis are independent of resonator Q, improving the sensor's temperature coefficient from 20 841 ppm/ °C to 424 ppm/ °C. The frequencies of the other two modes are closely spaced to the first mode's reference frequency and are demonstrated to track this frequency over temperature within 1 ppm/K. Field measurements in these two axes are conducted open-loop and off-resonance, ensuring that the scale-factor is independent of Q to first order and producing a measurement bandwidth of over 40 Hz.