There is strong interest in the use of small low-cost highly sensitive magnetic field sensors for applications (e.g. biomedical devices) requiring weak field measurements. Among weak-field sensors, the magneto-impedance (MI) sensor has demonstrated an absolute resolution of 10-11 T. The MI effect is a sensitive realignment of a periodic magnetization in response to an external field in small ferromagnets. However, design of MI sensors has relied primarily on trial and error experimental methods along with decoupled models describing the MI effect. To offer a basis for more cost-effective designs, this thesis research begins with a general formulation describing MI sensors, which relaxes assumptions commonly made for decoupling. The coupled set of nonlinear equations is solved numerically using an efficient meshless method in a point collocation formulation. For the problem considered, the chosen method is shown to offer advantages over alternative methods including the finite element method. Projection methods are used to stabilize the time discretization while quasi-Newton methods (nonlinear solver) are shown to be more computationally efficient, as well. Specifically, solutions for two MI sensor element geometries are presented, which were validated against published experimental data. While the examples illustrated here are for MI sensors, the approach presented can also be extended to other weak-field sensors like fluxgate and Hall effect sensors.
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