Skin effect is the tendency of alternating current to flow near the surface of a conductor instead of through its whole cross-section. As the frequency rises, the current crowds into a thinner and thinner outer layer, so the conductor's effective cross-section shrinks and its resistance goes up. That is why a wire with low DC resistance can still show high loss at gigahertz frequencies.
In short:
- Skin depth is the depth at which current density has fallen to about 37% (1/e) of its value at the surface.
- In copper it is about 8.5 mm at 60 Hz, about 2 µm at 1 GHz, and about 0.37 µm at 32 GHz.
- At high frequency only the outer micrometers of the conductor carry signal, so surface finish, plating and roughness matter as much as the copper itself.
Why the Current Moves to the Surface
A changing current creates a changing magnetic field inside the conductor. That field induces eddy currents that oppose the current at the center and add to it near the surface. The result is that current flows mainly in the outer layer. With direct current there is no changing field, so the current spreads evenly across the whole cross-section.
Calculating Skin Depth
Skin depth (δ) is calculated from the material's resistivity and permeability and the frequency:
δ = √( ρ / (π × f × μ) )Where δ is skin depth in meters, ρ is resistivity in ohm-meters (about 1.68 × 10⁻⁸ Ω·m for copper), f is frequency in hertz, and μ is the absolute permeability (about 1.257 × 10⁻⁶ H/m for copper). For copper this simplifies to:
δ (mm) ≈ 66.1 / √f (f in Hz)Skin Depth in Copper at Different Frequencies
- 60 Hz — Skin depth: 8.5 mm; Where you meet it: Power distribution
- 10 kHz — Skin depth: 0.66 mm; Where you meet it: Switching power supplies
- 1 MHz — Skin depth: 66 µm; Where you meet it: Switched-mode power, AM radio
- 1 GHz — Skin depth: 2.1 µm; Where you meet it: RF and GHz-range signals
- 4 GHz — Skin depth: 1.05 µm; Where you meet it: Nyquist frequency of PCIe Gen 3 (8 GT/s NRZ)
- 16 GHz — Skin depth: 0.52 µm; Where you meet it: Nyquist frequency of PCIe Gen 5 (32 GT/s NRZ) and Gen 6 (64 GT/s PAM4)
- 32 GHz — Skin depth: 0.37 µm; Where you meet it: Nyquist frequency of PCIe Gen 7 (128 GT/s PAM4)
The Nyquist frequency is half the symbol rate, which is the frequency that dominates the channel's loss. For more on PCIe at these speeds, see our guide to PCIe Gen 7 connector signal integrity.
Worked Example: Copper Conductor at 16 GHz
Consider a conductor carrying a PCIe Gen 5 signal, where the Nyquist frequency is 16 GHz.
δ = 66.1 / √(16 × 10⁹) = 66.1 / 126,491 ≈ 0.00052 mm = 0.52 µmCurrent flows in a shell about half a micrometer thick, which is under 1% of the thickness of a human hair. For a round conductor much thicker than the skin depth, the AC resistance relative to DC is approximately the radius divided by twice the skin depth. For a conductor with a 0.25 mm radius (about 24 AWG), that works out to a ratio near 240, so the resistance at 16 GHz is roughly 240 times its DC value. Real cables use stranding, plating and different geometries, so treat this as an order-of-magnitude estimate.
What this means in practice
- The center of the wire does little work. Making the conductor thicker does not lower loss much once it is many skin depths across.
- Surface roughness matters. When roughness is comparable to the skin depth, current has to follow a longer path over the bumps, which adds loss. Smooth surfaces help.
- Plating becomes part of the signal path. At GHz frequencies a large share of the current flows in the outer micrometers, which is the plating and the surface of the base metal.
Reducing Skin Effect Loss
- Silver plating: silver has a lower resistivity than copper (about 1.59 × 10⁻⁸ Ω·m), so a thin silver layer on copper conductors helps where the current actually flows. The layer needs to be at least a few skin depths thick to be effective.
- Smooth copper foil on PCBs: very low profile (VLP) and hyper very low profile (HVLP) foils reduce surface roughness, which lowers insertion loss at high frequency.
- Litz wire: for kilohertz to low-megahertz power, Litz wire uses many thin, individually insulated strands so that each strand's skin depth covers most of its cross-section. It is not used for GHz signals.
- Mind the plating stack on contacts: a thin gold layer over a nickel barrier lets part of the current flow in the nickel. Nickel is magnetic and more resistive than copper, so the plating stack and thickness matter at GHz frequencies.
Skin loss is one part of a channel's total insertion loss, alongside dielectric loss and reflections. For the full picture, see insertion loss vs. return loss and our guide to cable impedance.
Skin depth values use standard resistivity and permeability for annealed copper at room temperature. Resistivity changes with temperature, so real values shift slightly in hot environments.