Skin Depth

Formula

Description

At high frequencies, alternating current concentrates near the surface of a conductor due to eddy currents generated by the changing magnetic field. The skin depth is the distance from the surface at which the current density drops to 1/e (about 37%) of its surface value. Beyond about 3-5 skin depths, virtually no current flows. This effect increases the effective resistance of conductors at high frequencies because less of the cross-sectional area is utilized. Skin effect is a major design consideration for RF circuits, power transmission at 50/60Hz, and high-speed digital signal traces.

Variables

• δ — Skin depth (m)
• f — Frequency (Hz)
• μ — Permeability of the conductor (H/m)
• σ — Conductivity of the conductor (S/m)

Practical Notes

For copper at room temperature (σ = 5.8×10⁷ S/m, μ = μ₀): skin depth at 60 Hz is 8.5mm, at 1 MHz is 66μm, at 1 GHz is 2.1μm. This is why RF PCB traces only need to be a few skin depths thick. Litz wire (bundles of thin insulated strands) is used at kHz-MHz frequencies to mitigate skin effect losses in inductors and transformers.