Skin effect

The skin effect (of English. Skin for skin), and skin effect, is an effect in carrying higher frequency of alternating current electrical conductors through which the current density inside a conductor is lower than in outer areas.

It occurs in relatively thick for the skin depth ladders and even in electrically conductive screens and cable sheaths. The skin effect favored with increasing frequency, the transfer impedance of shielded cables and the shielding effectiveness of conductive shields, but increases the resistance per unit length of an electrical line.

A similar effect of related adjacent electrical conductor is known as the proximity effect.

Cause

Within a carrying direct current electrical line located just builds up a magnetic field, as it happens around the conductor. With direct current, the current density in the cross section is identical everywhere.

This is different for AC: Any change of the polarity of the current flow also changes the magnetic field and produces in the conductor material, eddy currents, which are opposed to the producer stream and weaken in the central axis of the conductor. The magnetic field surrounding the current affects such that the electrons are enclosed in the center of the conductor of the field lines more than the electron further outward. With alternating current the changing magnetic field induced inside the head of a greater braking voltage ( back pressure) than at the edge.

In the center line, the counter voltage is thus at its greatest, which leads to a displacement of the current at the edge. This acts like a reduction of the effective conductor cross -section, so that increases the impedance ( impedance ) of the conductor. The higher the frequency, the greater is this effect, to high frequencies, only a thin portion of the surface leads to the greater part of the current.

The skin depth decreases with increasing electrical conductivity - a highly electrically conductive coating is therefore often only poorly conductive base materials useful. The fact that the skin depth decreases with increasing permeability, leading for example to the fact that iron ( ) is particularly suitable as a high frequency head. Iron also has a low electrical conductivity.

Calculation

The current density in the conductor increases at a distance from the edge by the following equation exponentially:

With the marginal current density and the equivalent Leitschichtdicke which can be described in many cases good electrical conductors, having the following approximation equation:

With

This measure describes the wall thickness of a fictitious conductor with a round conductor, the thickness of the annulus, at the direct current having the same resistance as the solid wire due to the skin effect at the angular frequency. This approximation is valid for a round conductor, whose radius is very small compared to the length, but significantly greater than. In this case, the depth at which the current density has dropped to a factor.

Is a good approximation for the ratio between the effective resistance of the conductor to the DC resistance is

With.

It also applies to deep penetration, but is at x = 1 is not quite steadily.

A more accurate form for the equivalent Leitschichtdicke, which especially in poor electrical conductors and non- metals is applied and observed the influence of the permittivity, provides the following equation is:

This equation can be applied in approximation up to frequencies well below the plasma oscillation of the material. Is the angular frequency significantly less than, the additional factor falls away with the permittivity and the result is above simple equation. For good electrical conductor such as copper, the equivalent Leitschichtdicke can be expressed up to frequencies around 1 eHz (1018 Hz) without regard to the permittivity. In poor electrical conductors, however, the right factor increases at frequencies well above takes the equivalent Leitschichtdicke from stuck, but is approaching an asymptotic value, which no longer depends on the frequency:

A material example of a poor electrical conductor is undoped silicon which has the intrinsic conductivity at 100 Hz Leitschichtdicke an equivalent of approximately 40 m. If the frequency is increased to a few MHz and above, the equivalent Leitschichtdicke does not fall below 11 m. Due to the comparatively high for good conductors values ​​of the equivalent of a few meters Leitschichtdicke the frequency- dependent component of the skin effect need not be considered in these materials.

Depending on the ratio of depth to the mean free path of the charge carriers is different cases:

The anomalous skin effect is used to measure the Fermi surfaces of materials. For low temperatures ( ≈ 1 K) and pure materials are necessary so that the mean free path is large.

Measures against the increase of the resistance coating

In order to minimize the impact of the skin effect as small as possible, lines with the greatest possible surface conditions, for example in the form of thin-walled hose pipes, wires or bands in the high frequency technology. The low loss of the hollow fibers are partly that a large part of the inner surface is involved in current flow.

Furthermore, the surfaces of high-frequency or high -frequency lines are often coated with highly conductive metals such as silver or gold, in order to reduce the resistivity of the outer surface of the wire, which passes by far the largest part of the current. In this case the fact is utilized mainly for gold in that this metal is not oxidized in the air, so that the surface maintains a long-term stable conductivity. For there has gold a lower electrical conductivity than copper, but much better than copper.

Also make sure that the conductor surface is very smooth, as rough surfaces represent a longer path and thus greater resistance for the current. Particularly disadvantageous are also ferromagnetic conductor materials, as greatly reduced at this penetration depth. They are also often coated with metal for this reason.

RF lines and coil windings are often made from twisted or braided, mutually insulated single wires ( Litz ). The strands are constructed as so-called Millikan conductors, wherein the individual wires are insulated from each other alternately inside and outside the overall cross-section. Thus in each wire the same current flows between them and induced voltages cancel each other out.

High voltage overhead lines are twisted conductors. In them, the supporting cables of steel on the inside and the line conductors made ​​of aluminum are outside. The skin effect comes here, however, because of the low power frequency of 50-60 Hz only with large cross sections for carrying. By the skin effect, the current flows mainly in the outer layer of aluminum. This cable structure also has structural advantages: The soul of steel inside can accommodate much larger forces than aluminum. The steel can be also inside to better protect from the weather.

The ever-increasing operating frequencies of switching power supplies require consideration of the skin effect in the interpretation of their transformer windings. One uses therefore also increasingly HF wire or bands.