A Mixed-Signal Control System for Lorentz-Force Resonant MEMS Magnetometers

Abstract

This paper presents a mixed-signal closed-loop control system for Lorentz force resonant MEMS magnetometers. The control system contributes to 1) the automatic phase control of the loop, that allows start-up and keeps self-sustained oscillation at the MEMS resonance frequency, and 2) output offset reduction due to electrostatic driving by selectively disabling it. The proposed solution proof-of-concept has been tested with a Lorentz force-based MEMS magnetometer. The readout electronic circuitry has been implemented on a printed circuit board with off-the-shelf components. Digital control has been implemented in an FPGA coded with VHDL. When biased with 1 V and a driving current of <inline-formula> <tex-math notation= LaTeX >$300 \\mu ~A_{\\textrm {rms}}$ </tex-math></inline-formula>, the device shows 9.75 pA/<inline-formula> <tex-math notation= LaTeX >$\\mu \\text{T}$ </tex-math></inline-formula> sensitivity and total sensor white noise of 550 nT/<inline-formula> <tex-math notation= LaTeX >$\\sqrt {\\textrm {Hz}}$ </tex-math></inline-formula>. Offset when electrostatic driving is disabled is 793 <inline-formula> <tex-math notation= LaTeX >$\\mu \\text{T}$ </tex-math></inline-formula>, which means a 40.1% reduction compared when electrostatic driving is enabled. Moreover, removing electrostatic driving does not worsen bias instability, which is lower than 125 nT in both driving cases.