Advantages of Dual Hyperbolic Tangent Function Over Single Hyperbolic Tangent Function in Description of Hysteresis Loops

Abstract

If the mathematical description of the magnetic hysteresis loop branches should be simple, easy to use and should credibly describe the waveform magnetic hysteresis loop with a minimum number of parameters, then it inevitably leads to the description of magnetic hysteresis loop branches with a hyperbolic tangent function. This paper presents the advantages in description of magnetic hysteresis loop branches with a hyperbolic tangent function over other functions. The advantages in description of magnetic hysteresis loop branches with dual hyperbolic tangent function versus description with a single hyperbolic tangent function when the magnetic hysteresis loop has a very pronounced saturation region are provided. Also, this paper presents numerical difficulties in describing of magnetic hysteresis loop branches with a hyperbolic tangent function. Using soft magnetic material, as an example, a numerical procedure for determining parameters in description of magnetic hysteresis loop branches with a single and two hyperbolic tangent functions is shown. The numerical results are analyzed and discussed.