How does skin depth affect conductor loss at millimeter wave frequencies and what materials perform best?
Skin Depth at mmWave
The skin effect forces high-frequency current to flow within a thin layer near the conductor surface. The skin depth δ = √(ρ/(πfμ)) decreases as the square root of frequency. At 77 GHz (automotive radar frequency), the skin depth in copper is just 0.24 μm, thinner than the roughness features on standard PCB copper (1-6 μm Rq). The current must follow the rough surface topology, traveling a longer effective path and experiencing higher resistance.
| Parameter | Semi-Rigid | Conformable | Flexible |
|---|---|---|---|
| Loss (dB/m at 10 GHz) | 0.8-2.5 | 1.0-3.0 | 1.5-5.0 |
| Phase Stability | Excellent | Good | Fair |
| Bend Radius | Fixed after forming | Hand-formable | Continuous flex OK |
| Shielding (dB) | >120 | >90 | >60-90 |
| Cost (relative) | 2-5x | 1.5-3x | 1x |
Frequently Asked Questions
Does plating help or hurt?
Depends on the plating material and thickness. Gold plating thicker than 3δ (>0.7 μm at 10 GHz) behaves as if the conductor is solid gold, which has higher resistivity than copper: loss increases by about 20%. Thin gold (<1δ) over copper sees mostly copper underneath. ENIG adds nickel (ferromagnetic, very lossy), which should be avoided on RF traces above 3 GHz.
What about aluminum waveguide?
Aluminum has 35% lower conductivity than copper, increasing conductor loss by about 17%. However, aluminum is lighter and cheaper. Silver plating aluminum waveguide provides near-optimum loss performance with aluminum's mechanical advantages. This is common in satellite and airborne applications where weight matters.
Can I calculate loss from skin depth?
Yes. For a microstrip line: conductor attenuation αc ≈ Rs/(Z0·W) in Np/m, where Rs = 1/(σδ). This gives the loss per unit length from the conductor alone. Add the roughness correction factor (Hammerstad or Huray model) for accurate mmWave loss prediction.