Dual-Resonator MEMS Magnetometer Based on Self-Clocking Sigma-Delta Modulation

This paper presents the design and experimental evaluation of a micromachined Lorentz force magnetometer with a dual-resonator structure, interfaced with an electromechanical sigma-delta modulation (EM- $\Sigma \Delta {\text {M}}$ ) force rebalancing control loop. The magnetometer chip comprises a matched pair of resonators on the same silicon die. The closed-loop control circuit relies on a self-oscillating architecture; the frequency of which is determined by first resonator. It is used to generate a drive current injected to the second resonator, and also generates all internal circuit clocks based on a self-clocking scheme. System level simulation indicate a signal-to-noise ratio (SNR) larger than 100dB in a bandwidth of 64Hz with a 10mT, 32Hz magnetic field input ( ${B}$ ). The system was implemented in hardware based on a dual quantization technique, which has the advantage of reduced quantization error of multi-bit quantization in a single sigma-delta modulator. Experimental results demonstrate that proposed dual-resonator magnetometer achieved a 7-fold improvement in bias instability (increasing the averaging time to reach the bias instability from 1s to 8s) and the bandwidth (BW) is increased to ~80Hz, 16-fold higher compared to an open-loop magnetometer with a single resonator. With a 1mA bias current, the output noise is less than $1\mu \text{T}/\surd $ Hz for the z-axis magnetic field.