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Towards a Parametrically Pumped Xylophone Microbar Magnetometer: Design Optimisation of Xylophone Bar Resonators
Keywords: Resonant Magnetometer, Xylophone Bar Resonator, Parametric Amplification
Xylophone Bar Magnetometers (“XBMs”) have considerable potential as a class of MEMS sensor, having desirable scale-invariance properties and being suited to fabrication via surface micromachining, as well as achieving high Q factors when carefully designed. Parametric amplification is a control technique which has attracted some attention in the sensor literature, being capable of augmenting resonator Q factors by two or more orders of magnitude. This work presents ongoing research aimed at developing a parametrically amplified XBM in a microscale integrated package. The operating principles of an XBM and parametric amplification are briefly reviewed, and an analytical model is developed for a prototype device under parametric amplification and electrostatic actuation, based on the method of multiple scales and local nonlinear theory. The predicted behaviour and regions of instability are compared to numerical results obtained via FEA and numerical solution of the nonlinear differential equation. Control of the device is then considered, and the analytical results are used to propose a sense/control scheme. The Q factor emerges from the analysis as the dominant design factor limiting the sensitivity of the device: on this basis, the prototype design is optimised for maximum Q, treating such sources of dissipation as gas damping, TMD, EMD, and support losses. It is shown that under certain reasonable assumptions, support loss dominates the Q factor. A novel expression for the support loss in an XBM is developed, which is shown to impose a tuning condition on the geometric design of the resonator. A lower-bound estimate for the device Q is thus obtained and compared with simulation and experimental results, leading to an estimated sensitivity on the order of nanoTesla – sufficient for inertial grade application.
Harry T.D. Grigg, PhD Student
Newcastle University
Newcastle upon Tyne, Tyne and Wear NE1 7RU

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