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The skin effect is the tendency of an alternating electric current (AC) to distribute itself within a conductor so that the current density near the surface of the conductor is greater than that at its core. That is, the electric current tends to flow at the "skin" of the conductor.

The skin effect causes the effective resistence of the conductor to increase with the frequency of the current. The skin effect has practical consequences in the design of radio-frequency and microwave circuits and to some extent in AC electrical power transmission and distribution systems.

The current density J in an infinitely thick plane conductor decreases exponentially with depth δ from the surface, as follows:

J=J_\mathrm{S} \,e^{-{\delta /d}}

where d is a constant called the skin depth. This is defined as the depth below the surface of the conductor at which the current density decays to 1/e (about 0.37) of the current density at the surface (JS). It can be calculated as follows:

d=\sqrt{{2\rho}\over{\omega \mu}}

where

ρ = resistivity of conductor
ω = angular frequency of current = 2π × frequency
μ = absolute magnetic permeability of conductor

A type of cable called litz wire is used to mitigate the skin effect for frequencies of a few kilohertz to about one megahertz. 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.

Large power transformers will be wound with conductors of similar construction to Litz wire, but of larger cross-section.

In other applications, solid conductors are replaced by tubes, which have the same resistance at high frequencies but of course are lighter.

Solid or tubular conductors may also be silver-plated providing a better conductor (the best possible conductor excepting only superconductors) than copper on the 'skin' of the conductor. Silver-plating is most effective at micro wave frequencies, because the very thin skin depth (conduction layer) at those frequencies means that the silver plating can economically be applied at thicknesses greater than the skin depth.

In each kinds of materials, the skin depth at various frequencies is shown below.

 

 < cm>

Material

 

Frequency (Hz)

50

500

1K

3K

10K

400K

Iron

Norma Temperature
1,200C
Meting point

0.32

0.11

0.08

0.04

0.02

 

6.60

2.30

1.62

0.95

0.52

0.08

9.10

3.18

2.25

0.30

0.71

0.10

 

Norma Temperature
1,200C

5.70

1.97

1.39

0.80

0.44

0.07

7.50

2.60

1.84

1.06

0.58

0.09

Copper

Norma Temperature
850C

0.95

0.33

0.23

0.12

0.07

0.01

1.93

0.66

0.47

0.27

0.15

0.02

Aluminum

Norma Temperature
500C

1.07

0.37

0.26

0.14

0.08

0.01

1.93

0.60

0.47

0.27

0.15

0.02

Graphite

Norma Temperature

20.0

7.20

5.06

2.93

1.60

0.25

 




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