Eddy Current Losses

Formulas

Skin depth δ

= √(2ρ / (ωμ)) = 1 / √(πfμσ)

Eddy loss (thin plate)

P ∝ (B · f · t)² / ρ (t = thickness)

Hysteresis loss

P_h ∝ f · B^α (α ≈ 1.6–2.5)

Core loss (Steinmetz)

P ≈ K · f^a · B^b

Skin depth in copper (20 °C)

Mitigation

• Laminations: thin insulated sheets stacked to reduce eddy-path area (transformers, motors).
• Powdered cores: ferrite or iron powder — particles isolated by binder.
• Litz wire: many thin insulated strands twisted — each smaller than skin depth at f.
• Ferrite instead of steel at high frequencies — high resistivity ≈ no eddy currents.
• Air-core: no core at all — used in high-frequency RF when losses dominate.

Proximity effect

• Nearby conductors carrying AC induce currents in each other — raises effective resistance.
• Matters at HF and in transformer / inductor windings.
• Mitigation: separate wires, use Litz, or bundle small strands.