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 300 µA rms , the device shows 9.75 pA/µT sensitivity and total sensor white noise of 550 nT/ √ Hz. Offset when electrostatic driving is disabled is 793 µT, 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.

A CMOS-MEMS BEOL 2-axis Lorentz-Force Magnetometer with Device-Level Offset Cancellation

“…As a result, both the current and voltage driving generate a plate displacement defined as where Q is the device quality factor, k is the spring stiffness, is the electrostatic force, V is the device dc biasing voltage, v is the ac voltage or electrostatic driving, is the device capacitance and g is the nominal gap. The effect of electrostatic driving has been included because, being a resonant device, it is of utmost importance to track the resonance frequency, which is usually done by placing the device in a self-sustained oscillation loop [ 9 , 10 , 11 , 12 , 13 , 14 ]. When there is no magnetic field, some amount of electrostatic driving is required in order to keep the loop working correctly at resonance [ 14 ].…”

“…The effect of electrostatic driving has been included because, being a resonant device, it is of utmost importance to track the resonance frequency, which is usually done by placing the device in a self-sustained oscillation loop [ 9 , 10 , 11 , 12 , 13 , 14 ]. When there is no magnetic field, some amount of electrostatic driving is required in order to keep the loop working correctly at resonance [ 14 ]. In this situation, when the current and electrostatic drivings are in phase, the device works in amplitude modulation (AM), and the equivalent gap change in Equation ( 2 ) generates a change of the device capacitance that follows.…”

“…As a result, perfect resonance frequency tracking is not critical because the resulting sensitivity change at an offset frequency is minimized. Similarly, in [ 14 ], electrostatic driving is selectively enabled only when magnetic field is low enough to risk resonance unlocking. Although the resulting electrostatic ( ) and Lorentz ( ) forces are in quadrature, making it possible to remove the electrostatic driving offset with a synchronous demodulation, non-idealities due to this demodulation may arise, as well as capacitive bridge mismatch.…”

“…In Ref. [ 14 ], a capacitive network between the current carrying path and the amplifier input is used to partly compensate this offset source, similar to the solution proposed in Ref. [ 24 ].…”

Resonant MEMS Pressure Sensor in 180 nm CMOS Technology Obtained by BEOL Isotropic Etching

“…This work has a background in this kind of sensors. Some previously developed sensors in the research group are integrated magnetometers [ 9 ], resonant pressure sensors at 250 nm technology [ 10 ], and accelerometers [ 11 , 12 ]. Likewise, a technique has been patented that allows the construction of multilayer membranes, avoiding the technical problems caused by detachment [ 13 ].…”