Skin Effect in AC Conductors: Calculation and Impact
The Skin Effect Calculator determines how AC current concentrates near the conductor surface at high frequencies, increasing effective resistance and power loss. Critical for power cables, busbars, and RF design.
Skin Depth Formula
δ = √(ρ / (π f μ))
Where:
- δ = skin depth (m)
- ρ = resistivity (Ω·m)
- f = frequency (Hz)
- μ = μ₀μᵣ = 4π×10⁻⁷ H/m (non-magnetic)
AC Resistance Ratio
For solid round conductor (d >> δ):
R_ac / R_dc ≈ 1 + (d / (4δ))⁴ (approximate)
More accurate models use Bessel functions, but this suffices for f > 1 kHz.
Skin Depth at 60 Hz
| Material | Skin Depth (mm) |
|---|---|
| Copper | 8.5 mm |
| Aluminum | 10.9 mm |
Negligible for cables < 15 mm diameter at 60 Hz.
When Skin Effect Matters
- f > 1 kHz (audio, RF)
- Large conductors (> 500 kcmil)
- High-power transmission
- Induction heating
Examples
- Copper, d=10 mm, f=60 Hz → δ ≈ 8.5 mm, R_ac/R_dc ≈ 1.01
- Copper, d=5 mm, f=100 kHz → δ ≈ 0.21 mm, R_ac/R_dc ≈ 12
Mitigation
- Use stranded or Litz wire
- Hollow conductors (tubular bus)
- Lower frequency
- Silver plating (RF)
Conclusion
Skin effect increases I²R losses and heating. Use this calculator with Cable Sizing and Reactance tools for accurate high-frequency design.