Fluxgate Sensor Theory: Sensitivity and Phase Plane Analysis

In a previous paper [1] we have show+n that the transient behavior of fluxgate sensors in magnetometer and in gradiometer can be derived using a state space representation and expressing the solutions as matrices of sub-matrices involving the "monodromy." This present paper extends [1] to obtain the steady-state response to a static ambient magnetic field. The solutions are represented with trajectories on a phase plane, the presentation of which provides an insight into the nature of fluxgate operation from the energy point of view. These solutions also enable us to check the instability analysis with a forcing case and to extract expressions for the sensitivity of the magnetometer and the gradiometer. Results calculated with equations in this paper are compared with oscilloscope tracings for real sensors with comparable parameters. Among the design criteria and considerations that emerge are: 1) Total resistance of the sensor circuit should be kept small, consistent with stable operation. More precisely, the ratio R/L for the circuit, including the sensor, should be kept small. 2) The drive frequency should be as high as the magnetic properties of the core will reasonably permit. 3) The number of turns of a sensor winding should be kept as large as is practical, with an acceptable resistance in the sensor winding for a stable operation. 4) The duty cycle must be carefully optimized to achieve an appropriate combination of sensitivity and power consumption. 5) The gate ratio p is the most important design parameter from the sensitivity point of view.