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A new mathematical model of dynamic hysteresis loops is presented. The model is completely specified by two strictly monotonically increasing functions: a restoring function f(.) and a dissipation function g(.). Simple procedures are given for constructing these two functions so that the resulting model will simulate a given hysteresis loop exactly. The model is shown to exhibit many important hysteretic properties commonly observed in practice such as the presence of minor loops and an increase in area of the loop with frequency. In the case of an iron-core inductor, the mathematical model is shown to be equivalent to a lumped-circuit model, consisting of a nonlinear inductor in parallel with a nonlinear resistor. Extensive experimental investigations using different types of cores show remarkable agreement between results predicted by the model with those actually measured. The most serious limitation of this dynamic model is its inability to predict dc behaviors. For the class of switching circuits where dc solutions are important, a special dc lumped-circuit model is also presented.