Table of Contents
What is Skin Depth?
Skin depth (also called penetration depth) is the distance into a conductor at which the current density falls to 1/e (about 37%) of its surface value. At high frequencies, alternating current tends to flow near the surface of a conductor rather than uniformly through its cross-section -- this is called the skin effect.
The skin effect is a direct consequence of electromagnetic induction. Changing magnetic fields inside the conductor induce eddy currents that oppose the flow of current in the interior, forcing the current to concentrate near the surface. This effect becomes more pronounced at higher frequencies.
Skin Depth Formula
Where ρ is resistivity, f is frequency, μ0 is permeability of free space (4π x 10^-7 H/m), and μr is relative permeability.
| Material | Resistivity (Ω·m) | μr | Skin Depth at 1 MHz |
|---|---|---|---|
| Copper | 1.68 x 10^-8 | 1 | 0.066 mm |
| Aluminum | 2.65 x 10^-8 | 1 | 0.082 mm |
| Silver | 1.59 x 10^-8 | 1 | 0.064 mm |
| Steel | 1.0 x 10^-7 | ~200 | 0.011 mm |
Applications
- PCB design: Skin depth determines the effective cross-section of copper traces at high frequencies, affecting impedance and signal integrity.
- RF shielding: Shield thickness should be several skin depths to provide adequate attenuation of electromagnetic interference.
- Induction heating: Skin depth determines how deep the heating penetrates into the workpiece, critical for proper heat treatment.
- Power transmission: At 50/60 Hz, skin depth in copper is about 9 mm, affecting the design of large power conductors.
Frequently Asked Questions
Why does skin depth matter in wire design?
At high frequencies, the effective cross-section carrying current is limited to approximately one skin depth from the surface. This increases the AC resistance compared to DC resistance. For this reason, high-frequency cables often use Litz wire (multiple thin insulated strands) to increase the effective surface area.
How does temperature affect skin depth?
Higher temperatures increase the resistivity of metals, which increases the skin depth. For copper, resistivity increases about 0.4% per degree Celsius, so skin depth increases at elevated temperatures.
What is the skin depth at 60 Hz for copper?
At 60 Hz, copper has a skin depth of approximately 8.5 mm. This means that for round conductors with radii much larger than 8.5 mm, the current concentrates near the surface and the full cross-section is not effectively utilized.