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

"At high frequency, current only flows near the surface" is true, but what counts as "high frequency" depends on the conductor's thickness. For 1oz copper on a PCB that is around 4MHz; for a power winding, it starts at 100kHz.

Last updated: 2026-10-28 Skin effectCopper thicknessHigh frequencyLoss

Skin depth is inversely proportional to √f

AC current concentrates near the surface and falls off exponentially with depth. The depth at which current density drops to 1/e (37%) of the surface value is the skin depth δ. For copper (ρ = 1.72×10⁻⁸ Ω·m) it is δ ≈ 66 / √f [mm] (f in Hz).

If the conductor is thinner than 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.

Skin depth in copper
FrequencySkin depth δCompare to
50Hz9.3mmthickness of a power cable
10kHz0.66mmstarts to matter for φ1.2mm wire
100kHz0.21mmswitching-supply windings
1MHz66um2oz copper (70um)
4MHz33um1oz copper (35um)
100MHz6.6umabout the same as copper surface roughness
1GHz2.1umsmaller than surface roughness
High-frequency current concentrating near a conductor’s surface
High-frequency current concentrating near a conductor’s surface. AI-generated conceptual illustration; see the article’s diagrams and text for circuit details and conditions.
Current density distribution under skin effectTwo conductor cross-sections with current density curves. Left: thickness below δ, so current fills the cross-section. Right: thickness several times δ, so density falls exponentially from the surface to 1/e (37%) at depth δ and the interior is barely used. Current density falls off exponentially from the surface At depth δ, current density is 1/e (37%) of the surface value Thickness < δ Skin effect is negligible Surface Current density Current fills the section Thickness several × δ Interior unused, resistance rises Surface Current density δ 1/e (37%) Interior barely used
Figure 1: current density falls off exponentially from the surface.

For 1oz copper, 4MHz is the crossover

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

About 1.3x DC around 14MHz (δ at half the thickness) and 2.5x at 90MHz (1/5). At 1GHz (δ = 2.1um), with current on both faces, 35 / (2 × 2.1) ≈ 8x; a microstrip skews current toward the plane side, so the real figure is worse.

There is no need to worry about skin effect on a PCB trace below a few tens of MHz. Power traces, motor drive, audio, and a few-MHz SPI or I2C bus can use plain DC resistance. Above 100MHz, resistance rises several times and becomes a transmission-line loss.

Copper skin depth versus frequency, and its crossing with copper thicknessLog-log plot, x-axis 10kHz to 10GHz, y-axis 1um to 1mm. The skin-depth curve is overlaid with horizontal lines for 0.5oz, 1oz, and 2oz copper thickness, marking the 3.6MHz crossing with 1oz. Skin effect kicks in once skin depth falls below the copper thickness δ = 66 / √f [mm] (copper, 20°C) 10kHz100kHz1MHz10MHz100MHz1GHz10GHz 1µm10µm100µm1mm Skin depth δ Frequency δ (copper) 1oz = 35µm 2oz = 70µm 0.5oz = 18µm Crossing with 1oz: about 3.6MHz ← still DC resistance AC resistance rises →
Figure 2: skin depth versus copper thickness.

Switching-supply windings feel it at 100kHz

Windings feel it before a PCB does. At 100kHz, δ = 0.21mm, so any wire over 0.4mm in diameter stops using its interior. In a φ1.0mm wire only a 0.21mm surface annulus carries current: about 0.52mm² of the 0.785mm² cross-section (Figure 3).

The fixes are litz wire (thin insulated strands bundled together) or flat wire / foil windings.

Proximity effect also occurs: the field of one winding skews current in its neighbor, and loss grows with each layer. Above 100kHz it often dominates over skin effect; the fix is the layer count and interleaving.

Where current flows in a φ1.0mm wire at 100kHzCross-section of a φ1.0mm wire. At 100kHz, current flows only in an annulus δ = 0.21mm deep from the surface and the core is unused. About 0.52mm² of the 0.785mm² cross-section does the work. In a φ1.0mm wire, only the surface annulus carries current δ = 0.21mm in copper at 100kHz Unused δ = 0.21mm φ1.0mm Wire cross-section 0.785mm² Annulus carrying current 0.52mm² Wires over 0.4mm in diameter stop using their interior
Figure 3: where current flows in a φ1.0mm wire at 100kHz.

In the GHz range, copper roughness doubles the loss

At 1GHz, δ is 2.1um. PCB copper foil is roughened on the back to bond with the resin, typically to Rz 3-8um. The roughness exceeds the depth the current flows in, so current detours along the bumps and its path is longer (Figure 4).

Hammerstad's approximation gives about 1.6x loss when roughness is comparable to δ, saturating near 2x when well above. Foil choice alone can double GHz loss, which is why high-speed boards use low-roughness foils (VLP, HVLP).

In FR-4, conductor and dielectric loss are 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 too.

Copper roughness and the current pathCross-sections of a copper surface. On a smooth surface, current runs straight in the δ layer. On a rough surface (Rz 3-8um), the bumps are larger than δ = 2.1um at 1GHz, so current detours along them and the path is longer. At 1GHz, the bumps are larger than δ Dashed line: depth δ (2.1um) below the surface. Current flows in this layer Smooth surface Current runs straight Short path Rough surface Current detours along the bumps Rz 3-8um Longer path, more loss Hammerstad's approximation: about 1.6x loss when roughness is comparable to δ, saturating near 2x when well above
Figure 4: current detours around bumps.

What to check with the calculator

Use the skin-effect calculator to get δ, and compare it with the thickness (oz to thickness). If δ ≥ thickness, ignore it. If thickness / δ is 2-5, resistance runs 1.3-2.5x, so put it in the loss budget. Above 10, treat it as transmission-line loss and bring width, material, and roughness into the design.

Frequently asked questions

How much does resistance increase from skin effect?
Once t is well above δ and current flows on both faces, resistance is about t / 2δ times DC: around 2.7x for 1oz at 100MHz (δ = 6.6um). With current on one face, as in a microstrip, it is t / δ, around 5x.
Does going to 2oz copper reduce high-frequency loss?
Where skin effect dominates (a few tens of MHz and up for 1oz), thickness barely changes AC resistance. To cut high-frequency loss, widen the trace or use a low-roughness foil.
Does gold or tin plating on copper make a difference?
If the plating is comparable to or thicker than δ, its resistivity matters. Gold (2.4×10⁻⁸ Ω·m) is higher than copper and tin (1.1×10⁻⁷) higher still, so thick tin adds GHz loss. ENIG's nickel is magnetic with an extremely small δ, a common culprit.
At what frequency does skin effect matter for a flat copper power busbar?
For a 5mm bar, δ = 5mm at (66 / 5)² ≈ 174Hz, so the effect is small at 50/60Hz. Against inverter harmonics (a few kHz to tens of kHz), δ drops below 1mm and shows up as heating.

Standards and references

  • H. W. Johnson, M. Graham, High-Speed Signal Propagation — Skin effect, proximity effect, and the relationship between surface roughness and loss
  • E. Hammerstad, O. Jensen (1980) — Approximation for the increase in conductor loss from copper surface roughness
  • IPC-4562 — Classification of copper foil types and surface roughness (standard, low-profile, etc.)

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