The principles and practice of the Xylophone Bar Magnetometer

Abstract

This thesis reports on work undertaken to analyse, design, optimise, and fabricate a high-Quality factor mechanical resonant magnetometer, based on a Xylophone Bar Resonator (XBR). The principle of operation is based on the use of nodal supports to mechanically isolate a transverse beam vibrating in its fundamental mode. A control model is developed for the device, incorporating the effect of electromechanical parametric amplification. The device response and performance is shown to be strongly dependent on the Q factor of the sense element. The need for a quantitative model of XBR dynamics in order to design an optimal XBR is thus established. Using a Rayleigh-Ritz based approach, a model of the modal dynamics of an XBR is developed for the first time. In order to examine the efficacy of the nodal supports, a new model for support loss for resonators with two supports is developed and presented. Analytical models for other sources of dissipation are adapted for the first time to the XBR case. Combining these developments with a system level model allows for the development of a quantitative predictor of the fundamental and electronic noise limits on performance for an XBR. The model is solved over the operational range of geometric parameters, yielding optimisation criteria for the geometry. Corresponding predictions for the force and magnetic field sensitivity are presented. Based on the results, an optimised XBR design is exhibited for a macroscopic metal flexural XBM to be fabricated via Wire EDM. The fabricated devices are characterised, constituting the first demonstration of a macroscopic flexural XBR. The resulting Q factors and sensitivities are shown to be in agreement with the predictions. Fruitful directions for further work are suggested throughout the thesis and summarised in the conclusions. The original contribution to knowledge made by the thesis can be summarised as the development of an original and detailed theory of the principles of XBR optimisation for high Q, and demonstration of an operational macroscopic flexural XBM for the first time.