An appraisal of several nonlinear hysteresis loop models

Several hysteresis loop models are evaluated including the well-known arctangent and hyperbolic tangent models. Other models are derived from the normal statistical distribution. A general method of deriving hysteresis loop models is shown. When the different models are compared, it is seen that the hysteresis loops are different even though φ
m
, (squareness), and H
c
are the same. These three parameters are seen not sufficient to characterize a hysteresis loop, and at least one other parameter is needed. The pulsewidth of the differentiated loop is sensitive to small changes in loop shape, and a suggested fourth descriptive parameter is W, the half-height width of the differentiated loop. This parameter is more useful if it is reduced by the coercive force H
c
. The several models are compared to actual hysteresis loops of various materials (powdered media, tapes, transformer laminations, etc.) and choices are made for applicability in each case. Only one of the models, the arctangent model, is useful for the purpose for which they were derived. Others should be adequate for reactor-transformer theory and magnetic amplifier theory, but of limited use in magnetic recording theory. To make them more functional as models, a natural way of deriving minor loops from the major loop is indicated.