In this paper, we propose a mode-localized resonant tilt sensor based on 3 degree-of-freedom (DoF) weakly coupled resonators (WCRs). The angle of rotation around the sensing axis causes gravity perturbation to the two outer resonators and influences the energy distribution of the WCRs system, finally resulting in a drastic change of the mode shape. The experimental results indicate that the sensitivity is improved by 326% compared with the 2-DoF mode-localized resonant tilt sensor. Under the closed-loop test, the resolution of the tilt sensor can achieve 2.4e-5 degrees within the range of 50 degrees.

A Mode-localized Tilt Sensor with Resolution of 2.4e-5 Degrees within the Range of 50 Degrees

Abstract This paper outlines the design of a novel mode-localized electric current sensor based on a mechanically sensitive element of weakly coupled resonator systems. With the advantage of a high voltage sensitivity of weakly coupled resonator systems, the current under test is converted to voltage via a silicon shunt resistor, which causes stiffness perturbation to one resonator. The mode-localization phenomenon alters the energy distribution in the weakly coupled resonator system. A theoretical model of current sensing is established, and the performance of the current sensor is determined: the sensitivity of the electric current sensor is 567/A, the noise floor is 69.3 nA/√Hz, the resolution is 183.6 nA, and the bias instability is 81.6 nA. The mode-localized electric current sensor provides a new approach for measuring sub-microampere currents for applications in nuclear physics, including for photocurrent signals and transistor leakage currents. It could also become a key component of a portable mode-localized multimeter when combined with a mode-localized voltmeter. In addition, it has the potential for use in studying sensor arrays to achieve higher resolution. 

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Micromechanical mode-localized electric current sensor

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This paper reports a mode-localized magnetometer with novel 3 degrees-of-freedom (DOF) weakly coupled resonators (WCRs) coupled by F-shaped coupling beams. In this coupling mechanism, the direct coupling between the two outer resonators can be effectively suppressed, which decreases the coupling coefficient and drastically increases the sensitivity. Utilizing these novel WCRs for Lorentz force sensing, a magnetometer is realized with the resolution of $6.9\ \text{nT}/\surd \text{Hz}$ in the range of 100 mT, which is an improvement of 234.78 times that of state-of-the-art mode-localized magnetometers ( $1.62\ \mu \mathrm{T}/\surd\text{Hz}$ ).

A Mode-Localized Magnetometer with Resolution of $6.9\ \text{NT}/ \surd \text{Hz}$ Within the Range of 100 mT

We present a mode localized mass sensor prototype based on a hybrid system excited at a fixed frequency slightly below the resonances. Indeed, we show, both theoretically and experimentally, that this condition yields higher sensitivities and similar sensitivity ranges than that of resonance peak tracking while being less time consuming than a classical open-loop configuration due to the absence of frequency sweep. The system is made of a quartz resonator and a hardware that includes a resonator and the coupling. The digital aspect allows maximum sensitivity to be achieved with a fine tuning of the different parameters and the implementation of a coupling, regardless of the physical resonator geometry. This allows the generation of mode localization on shear waves resonant structures such as the quartz cristal microbalance widely used in biosensing. This solution has been successfully implemented using resin micro balls depositions. The sensitivities reach almost their maximum theoretical values which means this fixed frequency method has the potential to reach lower limit of detection than the open loop frequency tracking method.

https://www.mdpi.com/1424-8220/20/18/5295/pdf

Towards an Ultra Sensitive Hybrid Mass Sensor Based on Mode Localization without Resonance Tracking.

This paper for the first time reports a resonant magnetometer based on the mode localization phenomenon. The proposed sensor utilizes a 3 degrees-of-freedom (DoF) weakly coupled resonators (WCRs) as the mechanical sensing element, with massive grill structures on both sides for converting magnetic field strength to stiffness perturbation. Stiffness perturbation will cause a drastic variation in the mode shape owing to the mode localization phenomenon. We use the amplitude ratio (AR) instead of the frequency as the readout metric, and the sensitivity of AR is 7800 times higher than that of frequency. And the best resolution of the magnetometer is 1.6μT/√Hz in the range of 90mT.

A Mode-Localized Lorentz Force Magnetometer with 1.6μT/√Hz Resolution

The invention discloses a high-sensitivity magnetic field measurement method and device and belongs to the field of an electronic measurement instrument. The device comprises a magnetic field measurement chip and a test signal processing method. The chip comprises at least two weakly coupled resonators, a driving electrode, a detection electrode and an outer gate-type structure. The AC current isapplied to the weakly coupled resonators through a driving electrode, and when the chip is placed in a vertical magnetic field, the resonators are subjected to changed Lorentz force to generate simpleharmonic vibration; when the external magnetic field changes, a vibration state of the resonators changes accordingly, moreover, the DC current is applied to the gate-type structure, the gate-type structure is subjected to Lorentz force in the horizontal direction, and the electrostatic negative stiffness between the gate-type structure and the weakly coupled resonators is changed, so energy distribution of a weakly coupled resonator system is severely unbalanced. Two sets of detection electrodes are designed on two sides of an output resonator, single-resonator amplitude difference detectionis achieved, feed-through capacitance interference is eliminated, and high-sensitivity measurement of the weak magnetic field intensity can be achieved by measuring resonator amplitude difference. The device is advantaged in that real-time measurement of the weak magnetic field can be realized, the anti-interference capability is high, and use significance is high.

Weak magnetic field measurement device and method based on modal localization effect

Disclosed are a high-sensitivity magnetic field measurement method and a device, pertaining to the field of electronic measurement instruments. The invention comprises a magnetic field measurement chip and a processing method for a test signal. The chip comprises no less than two weakly coupled resonators, a drive electrode, detection electrodes, a grid structure at an outer side. An alternating current is applied to the weakly coupled resonators by the drive electrode. When the chip is placed into a vertical magnetic field, the resonators are subjected to a changing Lorentz force and generate a harmonic oscillation. When the external magnetic field is changed, the oscillation state of the resonators changes accordingly. A direct current is applied to the grid structure, which is then subjected to a horizontal Lorentz force, changing the electrostatic negative stiffness between the grid structure and the weakly coupled resonators, such that a significant imbalance arises in the energy distribution of a system of the weakly coupled resonators. The invention provides two sets of detection electrodes at two sides of an output resonator, thereby achieving differential amplitude detection with a single resonator, eliminating interference of a feed-through capacitor, and achieving high-sensitivity measurements of a weak magnetic field strength by means of measuring an amplitude difference of resonators. The invention achieves real-time measurements of a weak magnetic field and has strong interference resistance, thereby providing superior practical value.

Li Wenmu

Papers

A Mode-Localized Lorentz Force Magnetometer with 1.6μT/√Hz Resolution

A Mode-Localized Magnetometer with Resolution of $6.9\ \text{NT}/ \surd \text{Hz}$ Within the Range of 100 mT

Weak magnetic field measurement device and method based on modal localization effect

Modal localization effect-based weak magnetic field measurement device and method