Skin Effect

Skin Effect

At high frequencies, current doesn't flow uniformly through a conductor — it concentrates near the surface. This is the skin effect, and it increases the effective resistance of traces at high frequencies.

The skin depth δ (how deep current penetrates) is:

δ = √(ρ / (π × f × μ))

Where:

• ρ = resistivity (copper: 1.72 × 10⁻⁸ Ω·m)
• f = frequency (Hz)
• μ = permeability = μ₀ × μᵣ = 4π × 10⁻⁷ × 1 for copper

At high frequency, the effective cross-section is only a thin shell of thickness δ, increasing resistance.

For a trace of width W and thickness T >> δ, the AC resistance per unit length is approximately:

R_ac ≈ ρ / (2 × δ × W)   (two sides carrying current)

Your Task

Implement:

• skinDepth(f_GHz) returning skin depth in micrometers (μm)
• acResistance(f_GHz, widthMm) returning AC resistance per meter in Ω/m (1oz trace, T >> δ assumption)