Skin Effect AC Resistance

Formula

Description

At high frequencies, the skin effect forces current to flow near the surface of a conductor, effectively reducing the useful cross-sectional area and increasing resistance. This simplified formula estimates the AC resistance increase as a function of the wire diameter relative to the skin depth. When the wire diameter is much less than the skin depth (d << δ), Rac ≈ Rdc and skin effect is negligible. When d >> δ, the AC resistance increases significantly. This effect is particularly important for power transmission at 50/60 Hz with large conductors and for RF applications.

Variables

• Rac — AC resistance at the operating frequency (Ω)
• Rdc — DC resistance of the conductor (Ω)
• d — Wire diameter (m)
• δ — Skin depth at the operating frequency (m)

Practical Notes

For copper at room temperature: skin depth at 60 Hz = 8.5 mm, at 1 kHz = 2.1 mm, at 1 MHz = 66 µm, at 1 GHz = 2.1 µm. Litz wire (multiple thin insulated strands) mitigates skin effect at kHz to low MHz frequencies. At microwave frequencies, only a thin surface layer carries current, so surface roughness and plating quality affect resistance significantly.