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 ¥ä from the surface, as follows:
-
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:
-
where
- ¥ñ = resistivity of
conductor
- ¥ø = angular
frequency of current = 2¥ð × frequency
- ¥ì = 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.
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
|
|