Noise sources in miniature fluxgate sensors Part I: theoretical treatment

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