What is skin effect?
Skin effect is the tendency of alternating current to flow in a thin layer at a conductor’s surface. Current density falls by 1/e at the skin depth δ = 1/√(π f μ σ). For copper (σ ≈ 5.8×107 S/m) δ is about 8.5 mm at 60 Hz, 66 µm at 1 MHz, 2.1 µm at 1 GHz and 0.66 µm at 10 GHz.[1]
How does skin effect increase loss?
The effective resistance of a conductor rises with frequency through the surface resistance Rs = 1/(σδ) = √(π f μ/σ), which grows as √f. Conductor loss in transmission lines therefore scales roughly with √f, while dielectric loss scales with f.[1]
Why does copper roughness matter?
When skin depth becomes comparable to the copper foil’s surface roughness (a few micrometers for standard electrodeposited foil), current follows the rough profile and loss increases. The classic Hammerstad correction multiplies conductor loss by 1 + (2/π)·arctan(1.4(Δ/δ)²), where Δ is rms roughness, saturating at 2×; more recent models (Huray “snowball”, Groisse) are used in simulators.[2] Low-profile and very-low-profile foils reduce this. See RF PCB materials.
What design choices follow?
- Plating thickness of several skin depths is sufficient; silver or gold plating only helps if thicker than δ.
- Litz wire helps below a few MHz, not at microwave frequencies.
- Inductor Q is limited by skin and proximity effects.
Frequently asked questions
What is the skin depth of copper at 2.4 GHz?
About 1.3 µm.
Does skin effect affect DC?
No; at DC current flows uniformly.
Is silver plating worth it?
Silver's conductivity is about 5% higher than copper's; the benefit is small and depends on finish quality.
See also
References
Online sources accessed October 21, 2026; printed works cited by edition. See all sources.
- “Microwave Engineering, 4th ed.”. D. M. Pozar, Wiley. 2012.
- “Accurate Models for Microstrip Computer-Aided Design”. E. Hammerstad and Ø. Jensen, IEEE MTT-S International Microwave Symposium Digest, pp. 407-409. 1980.