At what frequency does skin effect start to matter? Working it out for 1oz copper

Skin depth is inversely proportional to √f

Pass AC through a conductor and the current concentrates near the surface, falling off exponentially with depth. The depth at which current density drops to 1/e (37%) of the surface value is the skin depth δ, given by δ = √(ρ / (π·f·µ)). For copper (ρ = 1.72×10⁻⁸ Ω·m) that reduces to δ ≈ 66 / √f [mm] (f in Hz).

Quadruple the frequency and δ halves. It works out to 9.3mm at 50Hz, 0.21mm at 100kHz, 66um at 1MHz, 21um at 10MHz, 6.6um at 100MHz, and 2.1um at 1GHz.

Whether skin effect "matters" comes down to the ratio between δ and the conductor's thickness (or wire radius). If the thickness is below δ, current uses the full cross-section and skin effect is negligible. Once thickness exceeds δ by several times, the interior goes unused, the effective cross-section shrinks, and resistance rises.

For 1oz copper, 4MHz is the crossover

PCB 1oz copper is 35um thick. δ reaches 35um at (66 / 0.035)² ≈ 3.6MHz — above that, a trace's AC resistance starts to exceed its DC resistance.

The change is not abrupt. Where δ falls to half the thickness, around 14MHz, AC resistance runs about 1.3x DC; at 1/5 thickness, around 90MHz, about 2.5x; and at 1GHz, δ = 2.1um gives 35 / 2.1 ≈ 8x (a microstrip skews current toward the plane-facing surface, so the real figure runs worse than this).

The takeaway: there is no need to worry about skin effect on a PCB trace below a few tens of MHz. Power-trace voltage drop, motor drive, audio, and a few-MHz SPI or I2C bus can all be calculated with plain DC resistance. Above 100MHz, though, resistance rises by several times and becomes a real transmission-line loss term.

Switching-supply windings feel it at 100kHz

Before you ever meet skin effect on a PCB, you meet it in transformer and inductor windings. At 100kHz, δ = 0.21mm, so any wire over 0.4mm in diameter stops using its interior. Even a 1mm wire only carries current in a 0.21mm-thick annulus at the surface — about 0.52mm² of a 0.785mm² cross-section (for φ1.0mm) actually does the work.

The fixes are litz wire (many thin insulated strands bundled together) or flat wire / foil windings. A planar transformer (windings formed as PCB copper) works well with 1oz or 2oz copper precisely because that thickness sits below δ and skin effect barely touches it.

Proximity effect happens at the same time: the magnetic field of one winding skews the current distribution in a neighboring one, and loss grows with each added layer. In transformer designs above 100kHz, this often dominates over plain skin effect, and the fix is choosing the number of winding layers and interleaving them.

In the GHz range, copper roughness doubles the loss

At 1GHz, δ is 2.1um. PCB copper foil, meanwhile, has its back side roughened to bond with the resin, typically to a roughness (Rz) of 3–8um. The roughness exceeds the depth the current actually flows in, so current has to detour along the bumps, lengthening its path compared with a smooth surface.

Hammerstad's approximation puts the loss at about 1.6x when roughness is comparable to δ, saturating near 2x once roughness is well above δ. In other words, in the GHz range, the same trace width can carry twice the loss depending purely on the copper foil used. That is why low-roughness foils (VLP, HVLP) matter for high-speed boards — the effect is on the same order as the material's εr and tanδ.

As for the loss breakdown: in FR-4, conductor loss and dielectric loss become comparable around 1GHz, and above that dielectric loss (proportional to frequency) overtakes conductor loss (proportional to √f). Designs above 10GHz need a low-loss material mainly because of dielectric loss, so both that and roughness control end up being needed together.

What to check with the calculator

Use the skin-effect calculator to get δ from a frequency, and compare it against your conductor's thickness (oz to thickness). Where δ exceeds the thickness, stay with DC resistance; where it's smaller, estimate the AC resistance increase.

In practice, judge it in three bands: if δ ≥ thickness, ignore it. If thickness / δ is 2–5, resistance runs 1.3–2.5x — fold that into your power efficiency or loss budget. If thickness / δ exceeds 10, treat it as a transmission-line loss and bring trace width, material, and roughness into the design.