Mathematical theory and calculations of magnetic hysteresis curves

Abstract

The constitutive law relating the time rate of change of the magnetic field H to that of the flux density B, via a differential equation, yields a faithful and yet computationally tractable representation of magnetic hysteresis. The equation is used to develop a theory of rate-independent and rate-dependent hysteresis in ferrites, ferromagnetic materials, magnetic thin films, and permanent magnetic materials. The theory provides mathematical expressions for the initial magnetization curve, the anhysteretic curve, the major loop, the symmetric and asymmetric minor loops, and the energy loss associated with their traversal. Functional forms for two material functions that appear in the equation can be scaled to measured values of the closure point, the remanence, the coercivity and, for rate-dependent applications, the nonlinear changes in the loop area and energy loss that accompany increases in dB/dt and dH/dt. Variations in loop shape and coercive point with angle observed in uniaxially anisotropic materials are described. Sample calculations are presented. >