The skin effect is the tendency of a high-frequency electric current to distribute itself in a conductor so that the current density near the surface of the conductor is greater than that at its core. It causes the effective resistance of the conductor to increase with the frequency of the current. The effect was first explained by Lord Kelvin in 1887. Nikola Tesla also investigated the Skin effect.
Mathematically speaking, the current density J in the conductor decreases exponentially with depth δ, as follows:
- ρ = resistivity of conductor
- ω = angular frequency of current = 2π × frequency
- μ = absolute magnetic permeability of conductor
- L = length of conductor
- D = diameter of conductor
Mitigation
A type of cable called litz wire (from the German Litzendraht, woven wire) is used to mitigate the skin effect. It consists of a number of insulated wire strands woven together in a carefully designed pattern, so that the overall magnetic field acts equally on all the wires and causes the total current to be distributed equally among them. Litz wire is often used in the windings of high-frequency transformers, to increase their efficiency.In other applications, solid conductors are replaced by tubes, which have the same resistance at high frequencies but of course are lighter.
Examples
In a copper wire, the skin depth at various frequencies is shown below.
frequency | δ |
60 Hz | 8.57 mm |
10 kHz | 0.66 mm |
10 MHz | 21 μm |