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At higher frequencies, AC current in a conductor is not distributed evenly across its cross-section — it crowds toward the surface, leaving the core carrying little current. The skin depth δ is the distance from the surface at which current density has fallen to 1/e (≈37%) of its surface value; roughly 63% of the current flows within one skin depth of the surface. This effectively shrinks the usable conductive area at high frequency, raising the conductor's AC resistance above its DC resistance.
| Quantity | Formula |
|---|---|
| Skin depth | δ = √(ρ/(πfμ0μr)) |
| Copper resistivity | ρ ≈ 1.68×10−8 Ω·m (20°C) |
| Aluminum resistivity | ρ ≈ 2.65×10−8 Ω·m (20°C) |
| μ0 (permeability of free space) | 4π×10−7 H/m |
| AC/DC resistance ratio (thick wire, d≫δ) | Rac/Rdc ≈ d/(4δ) |
The AC/DC ratio formula shown is the simple high-frequency-limit approximation, most accurate when the wire diameter is much larger than the skin depth (d/δ > ~5); near d/δ≈1–2 the transition is more gradual and exact values require Bessel-function solutions or manufacturer/FEA data. For most 50/60Hz power conductors, skin effect is negligible; it becomes significant for switch-mode power supplies, RF, and induction heating.
The depth below a conductor's surface at which AC current density has fallen to about 37% (1/e) of its surface value. Most of the current flows within roughly one skin depth of the surface.
The tendency of AC current to concentrate near a conductor's surface as frequency increases, effectively reducing the usable cross-sectional area and raising AC resistance above the DC value.
Skin depth is inversely proportional to the square root of frequency (δ∝1/√f); higher-frequency currents induce stronger opposing eddy currents in the conductor's interior, pushing current flow further toward the surface.
Generally no for typical wire gauges — copper's skin depth at 50/60Hz is about 8–9mm, much larger than most household and industrial conductor radii, so DC resistance is a good approximation.
It matters once the conductor radius approaches or exceeds the skin depth — typically relevant above a few kHz for magnet wire, and always relevant at RF, in SMPS transformers, and induction heating.
Litz wire is made of many thin, individually insulated strands woven together, each thinner than the skin depth at the operating frequency, so each strand conducts efficiently and the bundle has much lower AC resistance than a single solid conductor of the same total area.
It is a simple high-frequency-limit approximation, accurate mainly when d/δ is large (roughly >5). Near d/δ≈1–3 the actual ratio transitions more gradually; exact values require Bessel function solutions or manufacturer/FEA data.
Yes — skin depth is inversely proportional to √μr, so magnetic materials (like steel, μr≫1) have much smaller skin depths than non-magnetic copper or aluminum at the same frequency.
The steel core provides mechanical strength; because it carries essentially no current at 50/60Hz (skin effect pushes current into the outer aluminum strands, and the steel's conductivity is also much lower), it does not need to be a good conductor.
Skin effect is current crowding due to a conductor's own field; proximity effect is additional current crowding caused by the magnetic field of nearby conductors (as in tightly wound transformer windings) — both raise AC resistance and often occur together.
Copper is about 1.68×10−8 Ω·m and aluminum about 2.65×10−8 Ω·m at 20°C; resistivity also rises with temperature, which should be accounted for in precise designs.
No — skin effect is purely an AC phenomenon caused by time-varying magnetic fields inducing opposing eddy currents; pure DC current distributes uniformly across a conductor's cross-section.
The induced eddy currents in a heated workpiece are concentrated within about one skin depth of the surface, so the induction heating frequency is chosen based on how deep into the material heating is desired.
Yes — using foil (flat, thin ribbon) conductors, hollow/tubular conductors, or simply keeping solid conductor diameter comparable to or smaller than the skin depth all reduce the AC resistance penalty.
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