What is Skin Depth?

Skin depth (δ) is a measure of how far an alternating current (AC) flows into a conductor. As the frequency of the current increases, the magnetic field generates eddy currents that oppose the flow in the center of the conductor. This forces the current to concentrate near the outer surface, a phenomenon known as the Skin Effect.

In electrical engineering, skin depth is defined as the depth at which the current density drops to approximately 37% (1/e) of its surface value. Understanding this concept is critical for high-frequency PCB design, power transmission, and antenna engineering.

The Skin Depth Formula

The calculation is based on the following physical properties of the material and the signal frequency:

δ ≈ √(2ρ / (ωμ))

Where:

• ρ (Resistivity): Measured in Ohm-meters (Ω⋅m). High conductivity materials like copper have low resistivity.
• ω (Angular Frequency): Equal to 2πf.
• μ (Permeability): The product of the vacuum permeability (μ₀) and relative permeability (μᵣ).

Frequently Asked Questions

Why does skin depth decrease at high frequencies?

At high frequencies, the rate of change of the magnetic field increases, inducing stronger eddy currents. these eddy currents push the main current toward the surface of the conductor, resulting in a thinner "skin" layer.

What happens if the conductor is thinner than the skin depth?

If the physical thickness of a wire or trace is significantly less than the skin depth, the current distribution remains relatively uniform, and the DC resistance is nearly identical to the AC resistance.

How does permeability affect skin depth?

Ferromagnetic materials like iron have high relative permeability (μᵣ). This significantly reduces the skin depth, which is why materials like steel are poor choices for high-frequency signal transmission compared to copper.