Phase Sensitivity and Phase Noise of Cantilever-Type Magnetoelastic Sensors Based on the $\Delta$E Effect

TL;DR

This paper investigates the phase sensitivity and intrinsic phase noise of cantilever-type magnetoelastic sensors, revealing that thermal and magnetic losses primarily limit their detection capabilities, with implications for future sensor design.

Contribution

It provides a comprehensive mathematical and experimental analysis of phase noise sources in magnetoelastic sensors, emphasizing the role of magnetic losses over sensitivity.

Findings

Thermal-mechanical and electrical noise set the fundamental detection limit.

Magnetic losses, not sensitivity, dominate the phase noise and detection limit.

Magnetic loss parameters are key targets for improving sensor performance.

Abstract

Magnetoelastic sensors for the detection of low-frequency and low-amplitude magnetic fields are in the focus of research since more than 30 years. In order to minimize the limit of detection (LOD) of such sensor systems, it is of high importance to understand and to be able to quantify the relevant noise sources. In this contribution, cantilever-type electromechanic and magnetoelastic resonators, respectively, are comprehensively investigated and mathematically described not only with regard to their phase sensitivity but especially to the extent of the sensor-intrinsic phase noise. Both measurements and calculations reveal that the fundamental LOD is limited by additive phase noise due to thermal-mechanical noise of the resonator, i.e. by thermally induced random vibrations of the cantilever, and by thermal-electrical noise of the piezoelectric material. However, due to losses in the magnetic material parametric flicker phase noise arises, limiting the overall performance. In particular it is shown that the LOD is virtually independent of the magnetic sensitivity but is solely determined by the magnetic losses. Instead of the sensitivity, the magnetic losses, represented by the material's effective complex permeability, should be considered as the most important parameter for the further improvement of such sensors in the future. This implication is not only valid for magnetoelastic cantilevers but also applies to any type of magnetoelastic resonator.