Hysteresis loss and eddy current loss

Iron (core) loss in a magnetic core carrying alternating flux has two parts: hysteresis loss and eddy current loss.

Hysteresis loss

When the core is taken round a complete magnetisation cycle, the domains are repeatedly re-oriented. The energy spent on this, equal to the area of the B-H loop per cycle per unit volume, is lost as heat.

$$P_h = k_h\, B_m^{x}\, f\, V \quad \text{watts}$$

• $k_h$ = hysteresis constant of the material
• $B_m$ = maximum flux density
• $x$ = Steinmetz exponent (1.6 for older steels, about 1.6–2 for modern ones)
• $f$ = frequency, $V$ = volume of core

Reduction: use a soft material with a narrow loop (silicon steel, CRGO), work at a moderate $B_m$, and anneal the laminations.

Eddy current loss

The alternating flux induces emfs in the core itself. These drive circulating (eddy) currents in closed paths in the iron, causing $I^2R$ loss.

$$P_e = k_e\, B_m^2\, f^2\, t^2\, V \quad \text{watts}$$

For thin laminations of thickness $t$ and resistivity $\rho$, the loss per unit volume is

$$p_e = \frac{\pi^2 B_m^2 f^2 t^2}{6\rho} \quad \text{W/m}^3$$

Reduction:

• Laminate the core (0.23–0.5 mm sheets) insulated by varnish or oxide, so the eddy paths are broken up. The loss varies as $t^2$.
• Raise the resistivity by adding silicon.
• Use ferrite or powdered cores at high frequency.

 solid core: large eddy loop    laminated: small loops
 +-------------+               +--+--+--+--+
 |  .-------.  |               |()|()|()|()|
 |  |  ->   |  |               |  |  |  |  |
 |  '-------'  |               |()|()|()|()|
 +-------------+               +--+--+--+--+