The theoretical output of a ring core fluxgate sensor

This article proves that the output from a ring core sensor is directly proportional to the first time derivative of the product of dynamic permeability and magnetic intensity perturbation within the core caused by an external, uniform magnetic field. (Dynamic permeability is defined to be the slope of the hysteresis loop at a given point in time.) Assuming that ellipsoidal shells can approximate the core, the demagnetization factor can be "estimated" in the first order to be proportional to the first power of the quantity tape thickness (or number of wraps) divided by the core diameter. The constant of proportionality is determined from laboratory data. When an additional scale adjustment is applied to the resulting sensor output formula, the computed output tracks laboratory data for a range of sensor geometries.