Technology / Technical guide
Winding Skin Effect & Proximity Effect: Current Distribution
Copper’s bulk resistivity is not the only factor controlling AC winding behaviour. Time-varying fields can change how current occupies the conductor cross section. Skin effect concerns the conductor’s own field interaction, while proximity effect adds the influence of surrounding conductors and fields.
Current distribution can change without changing the metal.
Frequency, dimensions and neighbouring fields determine how useful a uniform-current approximation remains.
01 / Uniform reference
A DC resistance model assumes a useful current distribution.
For a simple straight uniform conductor under steady conditions, the familiar resistance relation uses resistivity, length and cross-sectional area.
For a simple straight uniform conductor under steady conditions, the familiar resistance relation uses resistivity, length and cross-sectional area. Its usefulness depends on the represented geometry and current distribution. Physical copper area and effective AC behaviour need not be interchangeable.
The temperature guide treats a change in material resistance with temperature. Skin and proximity effects address another mechanism: the electromagnetic distribution of alternating current, even when the material’s reference temperature is held fixed.
02 / Skin mechanism
The changing self-field redistributes current.
An alternating conductor current produces a changing magnetic field.
An alternating conductor current produces a changing magnetic field. Induced electromagnetic effects alter the current distribution within the conductor. Under applicable conditions, current density becomes more concentrated near the surface than in a uniform DC approximation.
COMSOL’s conductor-model explanation relates this behaviour to field penetration and losses. The effect does not mean all current suddenly occupies an infinitesimal surface, or that the metal’s inner region disappears. It is a frequency-dependent distribution with a characteristic penetration scale.
03 / Depth scale
State the assumptions behind the skin-depth relation.
For a good conductor in the usual linear sinusoidal approximation, skin depth is δ ≈ √(2ρ/(ωμ)), with resistivity ρ, angular frequency ω and magnetic permeability μ.
For a good conductor in the usual linear sinusoidal approximation, skin depth is δ ≈ √(2ρ/(ωμ)), with resistivity ρ, angular frequency ω and magnetic permeability μ. The scale depends on material properties as well as frequency; it is not a fixed number for every copper winding.
As a mathematical comparison at unchanged ρ and μ, increasing frequency fourfold halves δ. Whether that change materially affects an actual winding depends on conductor dimensions relative to δ. The comparison does not identify MARSTON strand diameter, frequency spectrum or measured AC resistance.
04 / Proximity mechanism
Neighbouring fields create a different distribution.
Nearby alternating-current conductors generate fields that influence one another’s current distribution.
Nearby alternating-current conductors generate fields that influence one another’s current distribution. This proximity effect can concentrate current unevenly around a conductor rather than producing only the isolated conductor’s approximately symmetric skin distribution.
Cooke and Shatz’s original proximity-effect study separates the added effect from an isolated wire’s skin-effect reference. Geometry, spacing and current directions affect that interaction. Their particular simulated wire arrangements and numerical results are not transferred to a wind-generator winding.
05 / Loss consequence
Nonuniform current changes the heating integral.
For a stated conductive model, local resistive heating depends on current density as well as material resistivity.
For a stated conductive model, local resistive heating depends on current density as well as material resistivity. Concentrating the same total current into a smaller effective region can increase dissipation relative to a more uniform distribution. Frequency-dependent AC resistance summarises that effect over a stated model boundary.
A nonsinusoidal waveform contains several frequency components, so one low-frequency resistance value cannot necessarily represent every contribution. Winding electromagnetic loss also remains distinct from magnetic-core loss, explained in the core-loss guide.
06 / Interpretation scope
Frequency effects do not disclose a winding construction.
Strand arrangement and electromagnetic geometry matter to a winding model, but a photograph or the phrase high-temperature copper wire does not establish them.
Strand arrangement and electromagnetic geometry matter to a winding model, but a photograph or the phrase high-temperature copper wire does not establish them. Temperature dependence, skin effect and proximity effect can coexist without one serving as evidence for the magnitude of another.
No MARSTON strand structure, litz construction, AC/DC resistance ratio or winding-loss figure is assigned here. The page explains current-distribution physics without rewinding, conductor selection, field measurement or any operational change.
Related technical guides: Generator Core Loss: Magnetic Hysteresis & Eddy Currents · Generator Internal EMF, Terminal Voltage & Load Response · Parasitic Inductance, Current Slew & Switching Overshoot.
General background: COMSOL: field penetration and skin-depth modelling · Cooke and Shatz: original proximity-effect current-distribution study. These references explain industry concepts; they are separate from the applicable MARSTON product and project documents.
Key concepts and conditions.
Read each quantity with its reference, units and stated conditions. A general relation does not establish a model-specific value.
| Concept / quantity | Meaning / relation | Conditions / limits |
|---|---|---|
| DC reference | Resistance for a stated geometry and temperature | Uniform-current approximation has a defined scope. |
| Skin effect | Self-field current redistribution | Not a change in copper composition. |
| Skin depth | δ ≈ √(2ρ/(ωμ)) in m | Good-conductor linear sinusoidal approximation. |
| Proximity effect | Neighbour-field current redistribution | Arrangement and current relationships matter. |
| Loss representation | Spatial heating or applicable AC resistance | Frequency and model boundary accompany the value. |
Engineering questions.
Is skin effect the same as copper becoming hotter?
No. Current redistribution and temperature-dependent resistivity are different mechanisms.
Does the interior carry exactly zero current?
Not generally. Field penetration and current density vary continuously within the applicable model.
Does four times frequency halve skin depth?
Yes in the stated approximation with unchanged resistivity and permeability.
Is proximity effect just another name for skin effect?
No. It includes the influence of surrounding conductors and fields.
Can one DC resistance determine all harmonic heating?
Not generally when AC resistance depends on frequency and distribution.
Does high-temperature wire establish litz construction?
No. No actual MARSTON strand arrangement or AC-loss result is assigned.
Technical enquiry
Discuss the technical question.
Copper’s bulk resistivity is not the only factor controlling AC winding behaviour. Share the model and applicable operating or design information for an engineering discussion.