Theory of magnetic cross valves

A PHYSICAL and mathematical theory of the interaction of two mutually orthogonal coils in a ferromagnetic medium is developed. For purposes of analysis, an idealized configuration with cross-sectional view, as shown in Fig. 1, is studied. Two coils, x and y, are wound at right angles to each other about a cylinder of ferromagnetic material of permeability μ. The structure is then immersed in a medium of infinite permeability. This last requirement is not stringent, it being required only that the saturation effects be confined to the central core for purposes of analysis. It is assumed further that the core material has no hysteresis or eddy-current losses while its typically nonlinear magnetization curve is as shown in Fig. 2. It is shown how the nonlinearity in the magnetization curve results in the interaction of the orthogonal circuits.