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Electrical hysteresis typically occurs in ferroelectric material, where domains of polarization contribute to the total polarization. Polarization is the electrical dipole moment (either C·m −2 or C·m). The mechanism, an organization of the polarization into domains, is similar to that of magnetic hysteresis.
The hysteresis loop (P x versus E x) may be obtained from the free energy expansion by including the term −E x P x corresponding to the energy due to an external electric field E x interacting with the polarization P x, as follows:
Hysteresis vs single-valued: Devices which have hysteresis; that is, in which the current–voltage relation depends not only on the present applied input but also on the past history of inputs, have I–V curves consisting of families of closed loops. Each branch of the loop is marked with a direction represented by an arrow.
A family of hysteresis loops for grain-oriented electrical steel, a soft magnetic material. B R denotes retentivity and H C is the coercivity. The wider the outside loop is, the higher the coercivity. Movement on the loops is counterclockwise.
Magnetic hysteresis can be characterized in various ways. In general, the magnetic material is placed in a varying applied H field, as induced by an electromagnet, and the resulting magnetic flux density (B field) is measured, generally by the inductive electromotive force introduced on a pickup coil nearby the sample.
The magnetic properties of electrical steel are tested using the internationally standard Epstein frame method. [18] The size of magnetic domains in sheet electrical steel can be reduced by scribing the surface of the sheet with a laser, or mechanically. This greatly reduces the hysteresis losses in the assembled core. [19]
Saturation is most clearly seen in the magnetization curve (also called BH curve or hysteresis curve) of a substance, as a bending to the right of the curve (see graph at right). As the H field increases, the B field approaches a maximum value asymptotically , the saturation level for the substance.
In control theory, a bang–bang controller (hysteresis, 2 step or on–off controller), is a feedback controller that switches abruptly between two states. These controllers may be realized in terms of any element that provides hysteresis. They are often used to control a plant that accepts a binary input, for example a furnace that is either ...