Hysteresis loss formula

Explore the hysteresis loss formula, its significance in magnetic materials, factors influencing loss, and a calculation example.

Hysteresis Loss Formula: Understanding Its Significance in Magnetic Materials

When dealing with magnetic materials in various applications, it is essential to understand the concept of hysteresis loss. In this article, we will delve into the hysteresis loss formula and its importance in the study of magnetic materials. We will also explore the factors that influence hysteresis loss and how it impacts the overall efficiency of electrical devices.

What is Hysteresis Loss?

Hysteresis loss is the energy dissipated as heat in a magnetic material due to the reversal of its magnetization. When a magnetic material is subjected to a varying magnetic field, the magnetic domains within the material rearrange themselves. This process, called hysteresis, causes energy to be expended in the form of heat, leading to a loss in efficiency in devices that use magnetic materials, such as transformers and inductors.

The Hysteresis Loss Formula

The hysteresis loss (P_h) in a magnetic material can be calculated using the following formula:

P_h = K × f × Bⁿ × V

Where:

• P_h is the hysteresis loss in watts (W)
• K is the Steinmetz hysteresis constant, a material-specific constant
• f is the frequency of the alternating magnetic field in hertz (Hz)
• B is the maximum magnetic flux density in the material, measured in tesla (T)
• n is the Steinmetz hysteresis exponent, another material-specific constant
• V is the volume of the magnetic material in cubic meters (m³)

Factors Influencing Hysteresis Loss

Several factors affect hysteresis loss, as indicated by the variables in the formula:

1. Material properties: The Steinmetz hysteresis constant (K) and the Steinmetz hysteresis exponent (n) are material-specific constants that determine the inherent hysteresis properties of a magnetic material. Different materials will have different values of K and n, affecting the hysteresis loss.
2. Frequency: The frequency (f) of the alternating magnetic field directly influences hysteresis loss. As the frequency increases, the hysteresis loss also increases. This factor is particularly relevant in devices that operate at high frequencies, such as switch-mode power supplies.
3. Magnetic flux density: The maximum magnetic flux density (B) affects the hysteresis loss, with higher flux densities resulting in increased hysteresis loss.
4. Volume of magnetic material: The volume (V) of the magnetic material is directly proportional to the hysteresis loss. A larger volume of magnetic material will result in a higher hysteresis loss.

In conclusion, the hysteresis loss formula is a valuable tool for understanding and predicting the energy loss in magnetic materials due to hysteresis. By controlling the factors that influence hysteresis loss, engineers can design more

Example of Hysteresis Loss Calculation

Let’s consider an example to demonstrate the calculation of hysteresis loss using the formula:

P_h = K × f × Bⁿ × V

Suppose we have a magnetic material with the following properties and operating conditions:

• Steinmetz hysteresis constant (K) = 0.001 W/(m³·Tⁿ·Hz)
• Steinmetz hysteresis exponent (n) = 1.6
• Frequency of the alternating magnetic field (f) = 60 Hz
• Maximum magnetic flux density (B) = 1.2 T
• Volume of the magnetic material (V) = 0.0002 m³

Using the formula, we can calculate the hysteresis loss as follows:

P_h = 0.001 × 60 × (1.2)^1.6 × 0.0002

First, calculate the value of Bⁿ:

(1.2)^1.6 ≈ 1.741

Next, substitute the calculated value and other variables into the formula:

P_h ≈ 0.001 × 60 × 1.741 × 0.0002

Now, calculate the hysteresis loss:

P_h ≈ 0.02088 W

Thus, the hysteresis loss in the given magnetic material under the specified conditions is approximately 0.02088 watts.

This example illustrates how the hysteresis loss formula can be used to calculate the energy loss due to hysteresis in a magnetic material. Engineers can use this information to optimize the design of devices that use magnetic materials, minimizing energy loss and improving overall efficiency.