Chapter 38: Magnetic Materials (Continued)

Date: 11/08/2021

38.4 Eddy Current Loss

If a coil is wound round a ferromagnetic core (such as in a transformer) and an alternating current is passed through the coil, an alternating flux is set up in the core. The alternating flux induces an EMF in the coil and also in the core. Since the core possesses resistance, the EMF induced in the core by the alternating flux causes “eddy currents” to flow. These eddy currents cause power loss and undesirable heating. Lominating the core is the standard way of reducing eddy current loss.

The total eddy current power lost (P_e) in a constant volume of material is given by the equation:

Where:

• k_e is a constant based on the material
• B_m is the maximum flux density
• f is the frequency of the alternating flux
• t is the thickness of the laminations

The equation shows that core losses are proportional to the square of the thickness of the lamination strip. Therefore, it is desirable to make the strip as thin as possible. However, this is not always necessary or possible at high frequencies. At high frequencies, “dust cores” consisting of carbonyl iron dust mixed with a binding material are used to limit eddy currents.

38.5 Separation of Hysteresis and Eddy Current Losses

The total core loss (P_c) is the sum of hysteresis loss (P_h) and eddy current loss (P_e).

If the maximum flux density in a transformer or inductor core is maintained constant, the terms can be simplified to constants k₁ and k₂:

• P_h = k₁ f (where k₁ = k_h v B_m^n)
• P_e = k₂ f² (where k₂ = k_e B_m^2 t^2)

Thus, total core loss becomes:

Dividing by frequency f gives an equation in the form of a straight line (y = mx + c):

If P_c/f is plotted vertically against f horizontally, a straight line results having a gradient of k₂ and a vertical intercept of k₁.

If the total core loss (P_c) is measured over a range of frequencies, the constants k₁ and k₂ may be determined. Once k₁ and k₂ are known, the individual losses at any given frequency can be evaluated:

• Hysteresis Loss (P_h) = k₁ f
• Eddy Current Loss (P_e) = k₂ f²

This method provides a reasonable approximation for evaluating the relative magnitudes of hysteresis and eddy current losses in an iron core.