Eddy current loss and its minimization

Eddy current loss is the $I^2R$ heat loss caused by circulating currents (eddy currents) induced in the body of a conducting magnetic core when the flux through it changes.

How it takes place with ac excitation

• With an ac supply the core flux alternates: $\phi = \phi_m \sin\omega t$.
• The iron core is itself a conductor. It can be regarded as many closed loops lying in planes perpendicular to the flux.
• By Faraday's law an emf $e = d\phi/dt$ is induced in each loop, so currents circulate in the core in closed paths, like whirlpools ("eddies").
• These currents flow through the resistance of the iron and produce heat $I^2R$. They also set up their own flux opposing the main flux (Lenz's law).

  Solid core              Laminated core
  +-----------+          +-+-+-+-+-+-+
  |  .-----.  |          |o|o|o|o|o|o|
  | (   o   ) |  phi     | | | | | | |  small loops,
  |  '-----'  | (out)    |o|o|o|o|o|o|  high resistance
  +-----------+          +-+-+-+-+-+-+
  large eddy loop        insulated sheets

Expression

$$P_e = K_e B_m^2 f^2 t^2 V \quad \text{W}$$

where $B_m$ = peak flux density, $f$ = frequency, $t$ = lamination thickness, $V$ = core volume, $K_e$ = a constant that falls as the resistivity of the material rises. Since the induced emf ∝ $fB_m t$ and loss ∝ emf², the loss depends on the square of each.

Methods of minimising eddy current loss

1. Laminating the core: build the core from thin sheets (0.25–0.5 mm) insulated from each other by varnish or oxide, with the sheets parallel to the flux. Each eddy path is confined to a thin sheet, its emf is small and its resistance high. Loss ∝ $t^2$, so halving thickness quarters the loss.
2. Using high-resistivity material: adding 3–4% silicon to steel raises its resistivity and lowers the eddy currents (and also reduces hysteresis loss).
3. Ferrite or powdered-iron cores for high-frequency use, where resistivity is very high.
4. Limiting $B_m$ and frequency in design, since loss ∝ $B_m^2 f^2$.