Noise sources in miniature fluxgate sensors Part I: theoretical treatment

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A mathematical model for miniature fluxgate magnetometers is presented in the first part of this work. It is based on certain well-defined and easy-measurable parameters of the hysteresis loop exhibited by the fluxgate magnetic core, i.e., the coercive force and the field intensities at which the flux-reversal starts and saturates. Two signal extraction techniques are modeled, the classical second-order harmonic one, and the current sampling one. For both cases, analytical expressions (in time and frequency domains) are derived for the magnetometer transfer function (voltage vs field) and the influence of the aforementioned hysteresis loop parameters on the magnetometer response. Consequently the signal-to-noise ratio (SNR) in the ELF (Extremely Low Frequency) range and the effective magnetometer bandwidth are calculated for both cases. The SNR is a function of the variance of the aforementioned hysteresis loop parameters. Several noise-sources of different origin have been found to influence this variance, namely: (a) the magnetic (Barkhausen) noise, (b) the noise superimposed to the excitation waveform, (c) the noise generated due to electromagnetic-interference, and (d) the noise generated due to mechanical vibration of fluxgate cores. The extend, up to which the power of these noise-sources boost the variance of the aforementioned hysteresis loop parameters, is a function of certain fluxgate core characteristics, namely: (a) the saturation magnetization, (b) the coercive field, (c) the flux-reversal duration, (d) the dependence of flux-reversal duration on the excitation field slope (slew rate), (e) the core cross-section, and (f) the core frequency response (magnetic damping and magnetic viscosity). Finally, the conditions are investigated so that the current-sampling technique exhibits better SNR compared to the classical second-order-harmonic one. In the second part of this work the theory presented here is applied to explain the noise performance of miniature fluxgates employing amorphous wire cores.