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)
| Frequency | Skin depth |
|---|---|
| 60 Hz | 8.5 mm |
| 1 kHz | 2.1 mm |
| 10 kHz | 0.66 mm |
| 100 kHz | 0.21 mm |
| 1 MHz | 66 µm |
| 10 MHz | 21 µm |
| 1 GHz | 2.1 µm |
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.
Was this article helpful?