The skin effect is the tendency of alternating electric current to flow primarily near the surface of a conductor. At higher frequencies, the current density decreases exponentially with depth from the surface, concentrating in a thin layer called the skin depth.

Skin Depth Formula

where \(\omega = 2\pi f\) is angular frequency, \(\mu\) is permeability, and \(\sigma\) is conductivity. Current density falls to \(1/e \approx 37\%\) of its surface value at depth \(\delta\).

Values for Common Conductors at 100 MHz

• Copper (\(\sigma = 5.8\times10^7\) S/m): \(\delta \approx 6.6\) µm
• Aluminium (\(\sigma = 3.8\times10^7\) S/m): \(\delta \approx 8.2\) µm
• Silver (\(\sigma = 6.3\times10^7\) S/m): \(\delta \approx 6.3\) µm

Impact on RF Resistance

Because current only flows in a thin annulus near the surface, the effective cross-sectional area of the conductor is reduced, increasing resistance compared to DC. The AC resistance of a round wire of radius \(r \gg \delta\) is approximately:

For a 1 mm diameter copper wire at 100 MHz, \(R_{AC}/R_{DC} \approx 38\). This is why multi-strand (Litz) wire is used in high-Q inductors at lower RF frequencies — many thin strands, each smaller than the skin depth, provide more effective conductor area.

Design Implications

• Conductor thickness in PCBs should be at least 3–5 skin depths to minimise resistive loss.
• Silver plating adds only marginal benefit over copper above ~100 MHz (skin depth ~6 µm) as long as the copper is thicker than a few skin depths.
• In MRI coils at 128 MHz (3 T), copper tubing (thick wall) is preferred over solid wire for high-Q resonators.