Skin Depth Calculator
Calculate AC current penetration depth.
What is the Skin Effect?
The Skin Effect is a tendency for Alternating Current (AC) to flow mostly near the outer surface of an electrical conductor, rather than uniformly through its cross-section. This happens because oscillating magnetic fields create eddy currents that cancel out current flow in the center of the wire.
The higher the frequency, the thinner this "skin" of current becomes. At microwave frequencies, the current flows in a layer so thin (microns) that the center of the wire is basically useless dead weight.
Calculating Skin Depth (Formula)
Skin Depth (δ) is defined as the depth below the surface where the current density has fallen to 1/e (about 37%) of the surface current.
δ = √(ρ / (π × f × μ))
Variables
- δ (delta): Skin depth (meters)
- ρ (rho): Resistivity of the material (Ω·m)
- f: Frequency (Hz)
- μ (mu): Magnetic permeability (H/m)
Common Depths (Copper)
- 60 Hz: ~8.5 mm (entire wire used)
- 1 MHz: ~0.066 mm (66 µm)
- 2.4 GHz: ~0.0013 mm (1.3 µm)
Practical Applications
- Litz Wire: In induction stoves and high-freq transformers, engineers use "Litz wire" (thousands of insulated strands thinner than the skin depth) woven together to force current to use the entire copper volume.
- RF Cabling: High-power coaxial cables often use a hollow copper tube as the center conductor. Since current only flows on the outside, a solid core adds weight/cost but no electrical benefit.
- Silver Plating: RF connectors are plated with silver. Since 100% of the signal is in the skin, you only need 3 microns of silver to get the conductivity of a solid silver wire!
FAQ
Does DC have skin depth?
No. Direct Current (DC), has a frequency of 0 Hz. Therefore, the skin depth calculation would result in infinity, meaning current flows uniformly through the entire cross-section of the wire.
Why does AC resistance increase with frequency?
Because the "effective" cross-sectional area of the wire shrinks. If you have a thick wire but current only uses the outer 1 micron, the resistance looks like that of a microscopic foil tube, which is very high.
Is Gold better than Copper?
Surprisingly, no. Gold is actually more resistive than copper. However, gold does not oxidize (rust). Copper oxide is a semiconductor/insulator. At RF, we use gold plating to prevent the surface from oxidizing, preserving that crucial outer skin layer.