Skin Effect
Understanding the Skin Effect
The skin effect is the primary mechanism causing conductor loss to increase with frequency. As frequency increases, current is confined to a thinner layer near the surface, increasing the effective resistance and thus the I^2R loss in the conductor.
Skin Depth
delta = 1/sqrt(pi f mu sigma)
delta = 2.1/sqrt(f_MHz) um
Examples:
1 MHz: delta = 66 um
100 MHz: delta = 6.6 um
1 GHz: delta = 2.1 um
10 GHz: delta = 0.66 um
100 GHz: delta = 0.21 um
Practical Implications
- Conductor thickness: Must be > 3-5 skin depths for minimum loss. At 10 GHz: > 3 um copper (standard PCB plating is 17-35 um, adequate).
- Surface roughness: Roughness comparable to skin depth increases loss. Critical above 10 GHz. Smooth copper (rolled annealed) preferred for mmWave.
- Plating: Gold or nickel plating must be thin relative to skin depth or use materials with comparable conductivity.
Frequently Asked Questions
What is the skin effect?
The skin effect confines AC current to a thin layer near the conductor surface. Skin depth = 2.1/sqrt(f_MHz) um for copper. At 10 GHz, current flows in only the outer 0.66 um. This increases resistance and loss with frequency.
Why does skin effect increase loss?
As frequency increases, current is confined to a thinner layer, reducing the effective conductor cross-section. Smaller cross-section = higher resistance = more I^2R loss. This is why conductor loss dominates at high frequencies.
Does surface roughness matter?
Yes, critically above 10 GHz. Surface roughness comparable to the skin depth forces current to follow a longer, rougher path, increasing resistance by 20-100%. Smooth copper (Ra < 0.3 um) is essential for mmWave circuits.