Definition
At RF frequencies, current concentrates near the surface of conductors — the skin effect. The skin depth δ is the distance from the surface at which current density falls to 1/e (≈37%) of its surface value:
δ = √(2 / (ω·μ·σ)) = √(ρ / (π·f·μ₀·μᵣ)) [meters] For copper (σ = 5.8×10⁷ S/m, μᵣ = 1): δ_Cu = 66.2 / √f_MHz [µm] or δ_Cu = 2.09 / √f_GHz [µm]
Skin Depth vs Frequency for Common Conductors
| Frequency | Copper δ | Aluminum δ | Gold δ | Silver δ |
|---|---|---|---|---|
| 100 MHz | 6.6 µm | 8.6 µm | 7.9 µm | 6.4 µm |
| 1 GHz | 2.1 µm | 2.7 µm | 2.5 µm | 2.0 µm |
| 2.4 GHz | 1.35 µm | 1.76 µm | 1.61 µm | 1.30 µm |
| 10 GHz | 0.66 µm | 0.86 µm | 0.79 µm | 0.64 µm |
| 28 GHz | 0.40 µm | 0.51 µm | 0.47 µm | 0.38 µm |
Impact on PCB Conductor Loss
Standard 1 oz copper: t = 35 µm >> δ at all RF frequencies → OK
Surface roughness matters:
Smooth copper (Ra <0.5 µm): αc ≈ Rs/(Z₀·W)
Rough copper (Ra ~3 µm): αc increases by ×1.5–2 above 5 GHz
Rs = surface resistance = 1/(σ·δ) = √(π·f·µ₀/σ) [Ω/sq]
Rs_Cu(1 GHz) = 8.25 mΩ/sq
Rs_Cu(10 GHz) = 26.1 mΩ/sq
Practical Design Implications
- Above 5 GHz: use low-roughness copper foil (LD, HVLP grade) to minimize conductor loss
- Gold plating thickness: must be >3δ at operating frequency for good conductivity (at 10 GHz: >2 µm gold)
- Via walls: standard 25 µm plating is adequate for all cellular frequencies (δ_Cu = 2.1 µm at 1 GHz)
RF View Skin Depth Calculator: Enter frequency and conductor type in RF View's Utilities tab to compute skin depth δ and surface resistance Rs for design verification. Offline on Android.