.Modelica.Magnetic.FluxTubes.UsersGuide.Hysteresis.StaticHysteresis.Tellinen

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The Tellinen hysteresis model

The Tellinen hysteresis model is described in more detail in [Te98, ZB12]. It is a simple model to describe the static magnetic hysteresis behavior of ferromagnetic materials. It only requires the Upper B_U(H) and lower B_L(H) branches of the limiting hysteresis loop for the adaption to a material specific hysteresis shape. Coming from negative magnetic saturation with increasing magnetic field strength H(t) the flux density B(T) travels along the B_L(H). Coming from positive saturation with a decreasing H(t), B(t) travels along B_U(H). The Tellinen model is defined by the following equation, which gives a calculation rule for time derivative of the magnetic flux density B(t) with respect to the current value of B(t), H(t) and its slope dH(t)/dt.

Therein, S_U(H) and S_L(H) are the derivatives of limiting branches of the hysteresis loop with respect to the magnetic field strength H, as illustrated in Fig 1.

Fig. 1: Upper B_U(H) and lower B_L(H) branches of the hysteresis envelope curve, their corresponding slope functions S_UH(H) and S_LH(H) and the actual operating point H(t), B(t).