Skin Depth & Surface Resistance
Compute skin depth δs, surface resistance Rs, conductor attenuation and the ratio of trace thickness to skin depth for any conductor material and frequency. Essential for PCB trace, cavity and coaxial line loss budgets.
About the Skin Depth Calculator
At DC, current flows uniformly through the entire cross-section of a conductor. As frequency increases, electromagnetic induction pushes the current towards the surface of the conductor — a phenomenon called the skin effect. The skin depth (delta_s) is the depth at which the current density has fallen to 1/e (about 37%) of its surface value.
Skin Depth Formula
Skin depth is delta_s = 1/sqrt(pi * f * mu * sigma), where f is frequency, mu is the magnetic permeability and sigma is the electrical conductivity. For copper (sigma = 5.8 x 10^7 S/m) at 1 GHz, the skin depth is about 2.1 micrometres. At 10 GHz it shrinks to 0.66 micrometres — comparable to the surface roughness of PCB copper foil.
Surface Resistance
Because current flows only in a thin skin, the effective resistance of the conductor increases with frequency. Surface resistance Rs = 1/(sigma * delta_s) = sqrt(pi * f * mu / sigma) ohms per square. This resistance increases as the square root of frequency — conductor loss in transmission lines rises as sqrt(f).
Practical Impact on PCB Design
Standard 1 oz PCB copper is 35 micrometres thick. At 1 GHz this is about 16 skin depths — well-established current flow. At 100 GHz the skin depth is 0.2 micrometres and surface roughness dominates loss. This is why ultra-low-loss substrates and smooth copper foil matter for mmWave PCB design above 40 GHz.