What is Hysteresis loss? Magnitude Formula

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Hysteresis loss

Hysteresis loss, also known as magnetic hysteresis loss, is a phenomenon that occurs in ferromagnetic materials when they are subjected to cyclic magnetic fields. It refers to the energy dissipated in the form of heat as the magnetic domains within the material undergo repeated alignment and realignment with the changing magnetic field. Hysteresis is a significant factor to consider in various electrical and magnetic applications.

Ferromagnetic materials, such as iron and its alloys, exhibit a unique property known as hysteresis. When a ferromagnetic material is exposed to an external magnetic field, the magnetic domains within the material align themselves with the applied field.

As the field strength is increased, the domains progressively align in the same direction, leading to an increase in the magnetization of the material. This alignment process is reversible and exhibits a lag between the changes in the applied magnetic field and the magnetization of the material. This lag gives rise to a hysteresis loop on a magnetization curve as shown in below figures.

What is Hysteresis loss? Magnitude Formula

The hysteresis loop represents the relationship between the magnetic field strength (H) and the magnetic induction (B) of the material. It consists of two branches: the magnetization curve when the magnetic field is increasing (ascending branch) and the curve when the magnetic field is decreasing (descending branch). The area enclosed by the hysteresis loop represents the energy dissipated during one complete cycle.

As the magnetic field is cycled, the magnetic domains within the material experience friction and resistance, causing energy losses in the form of heat. These losses are attributed to the realignment of the magnetic domains and the movement of the magnetic moments within the material. The energy required to overcome these frictional forces is dissipated as hysteresis loss.

The magnitude of hysteresis depends on several factors, including the properties of the ferromagnetic material, the shape and size of the magnetic core, and the frequency of the magnetic field. Materials with high coercivity (ability to resist magnetization) exhibit larger hysteresis losses, while materials with low coercivity have smaller losses.

How to Mitigate Hysteresis Loss?

To mitigate hysteresis losses in practical applications, soft magnetic materials with low coercivity, such as silicon steel and ferrites, are used in transformer cores and magnetic components. These materials have a narrow hysteresis loop, indicating lower energy dissipation during each cycle and higher energy efficiency.

It’s important to note that hysteresis loss is separate from other losses in transformers and electrical devices, such as eddy current losses and copper losses. However, hysteresis loss can be a significant factor, particularly in applications with rapidly changing magnetic fields or where high energy efficiency is crucial.

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Hysteresis Loss Formula

The magnitude of hysteresis loss can be estimated using the Steinmetz equation, which provides an approximation of the hysteresis per unit volume of the magnetic material. The equation is as follows:

P_h = η * B_max^1.6 * f * V


  • P_h is the hysteresis loss per unit volume (W/m³ or J/m³)
  • η is the Steinmetz hysteresis coefficient (dimensionless), which is a material-specific constant.
  • B_max is the maximum value of the magnetic flux density (T) during one complete magnetic cycle.
  • f is the frequency (Hz) of the magnetic field.
  • V is the volume (m³) of the magnetic material.

The Steinmetz hysteresis coefficient, η, depends on the material properties and is typically provided by manufacturers or can be obtained from experimental data. It is a constant that accounts for the material’s specific hysteresis characteristics.

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