How does Skin Effect work with a Wire?

By Douglas Krantz | Electronics

Greetings Douglas,

When we say electrons flow through the conducting wire, then what does actually happen? Do the electrons flow inside the wire, or flow over the surface of the wire?

Thank You, AN

Rather than an absolute "either the electrical current flows through the entire cross section of the wire or the electrical current only flows on the surface of the wire", the effect that you're talking about, Skin Effect" is really a gradual change from an even amount of current flowing through the entire cross section of the wire (DC current), to a tendency of the current to flow at the edge of the conductor compared to the inner part of the wire (AC current).

The longer the wire, the greater the difference between the surface of the wire versus the inner part of the wire; the higher the frequency of the AC current, the greater the difference between the surface of the wire versus the inner part of the wire.

Even the diameter of the wire makes a difference. Very thin wire won't have much difference between the surface and the inner parts of the wire. But then again, very thin wire won't carry very much current.

The Short and Long of It

The short answer to the question is "The impedance (equivalent to AC resistance) of the inside of the conductor (wire) is greater than the impedance (equivalent to AC resistance) of the outside of the conductor."

Skin Effect

Electricity doesn't really use exclusively use the skin of the wire or else it exclusively uses the core. Instead, electricity uses all available routes at once. If the route has lower resistance or impedance (in other words, the route is easier), more current goes through that route. If the route has higher resistance or impedance (in other words, the route is harder), less current goes through that route.

When both an easy route and a hard route are available to electricity (the skin or then core of the wires), both routes for the electricity will be used at once.

The distribution of the electricity between the two routes can be considered two different ways: the total current is split up to go through both routes, and the current through the two routes is added up to be the total current.

The question that is asked, however, seems to be about the phenomena known as "Skin Effect".

When looking at the current in a cross section of a wire, "Skin Effect" is the tendency of AC electrical current to flow more toward the outside, or "Skin" of the wire, than in the center of the wire. See:

https://en.wikipedia.org/wiki/Skin_effect

Low Frequency

• Steady DC electrical current is exclusively affected by resistance. Inductance in the cross section of a wire doesn't affect DC current, so DC current does not have this Skin Effect tendency.

• With a low frequency (50 Hz or 60 Hz) in high tension power lines, because the wires span great distances (hundreds of miles or kilometers), the outside strands of the wire carry more current than the insides.

See, partway down the page under the title "Overhead":

https://en.wikipedia.org/wiki/Electric_power_transmission

Medium Frequency

• With high power, medium frequency (0.5 MHz to 200 MHz), commercial radio and TV coaxial cables, because the coax cable spans a distance of feet or meters, up to hundreds of feet or meters, the inner conductor of the coax cable is just a hollow copper pipe. In essence, since only a little of the current flows through the center area of the pipe, they don't waste copper in the center.

See:

The reason for this Skin Effect is that with AC electricity in a solid conductor, the impedance is higher on the inside of the conductor than on the outside skin of the same conductor.

High Frequency

Going above 200 MHz, skin effect starts to become extreme. As the frequency increases, the depth of the current carrying skin of the conductor gets thinner and thinner. The ability to carry power becomes difficult, so rather than trying to use electrical conductors, waveguides are used instead.

See:

https://en.wikipedia.org/wiki/Waveguide

Impedance versus Resistance

In a conductor, resistance can be looked at as a power converter; resistance converts electrical power to heat power. Heat power, of course, is usually wasted power. In many cases, like in power lines, the heat energy is just radiated into the atmosphere, never to be used again.

With DC electricity, the conductor is all resistance, there is no added AC impedance.

Impedance, on the other hand, can be looked at as hindering the flow of AC electricity. AC impedance is kinda added to DC resistance to come up with an overall AC/DC impedance.

AC electrical current is always changing. In an AC current cycle, the polarity changes from positive to negate, and back to positive. The current is also changing level throughout the positive half the cycle, and throughout the negative half.

Inside a single wire, inductance is caused by the changing movement of electrons creating a changing magnetic field, and the changing magnetic field also causing electrons to flow. In other words:
• Some of the power used to change the flow of electricity is converted to changes in the magnetic field.

• When the magnetic field is changed, some of the power from the changes in the magnetic field is converted to electrical power, looping around, inside the conductor.

In addition, remember, no matter what causes the electrons to flow, if the electrons are flowing through a resistor (the wire has resistance), the resistance is converting some of the power to wasted heat.

Inductance never reduces total resistance; adding the inductance to the resistance already in the wire only increases the total impedance (similar to resistance) of the wire.

Parasitic Eddy Currents

See again, partway down the page, under the title "Cause":

https://en.wikipedia.org/wiki/Skin_effect

In the center of a conductor, the parasitic eddy currents (looping electrical currents) happen throughout the conductor. AC current in the center of the conductor can cause eddy currents in all directions, so the core impedance is higher. Example: 6 ohms of impedance.

Important: The eddy currents inside a wire are electrical current, and the eddy currents go through the resistance inside of the wire. Some of the AC power is turned into eddy currents. Electrical power in the eddy currents are then converted to heat by the wire's resistance, which is wasted. In other words, the eddy current is parasitic current.

On the outside of a conductor (it's skin), the parasitic eddy currents happen only on the inside the conductor. Because the atoms on the skin of the conductor can cause eddy currents only inside the conductor, and not on the outside the conductor, the impedance is somewhat lower. Example: 5 ohms of impedance.

Keep in mind that impedance is similar to resistance. Looking at Skin Effect in a different way, the impedance of a wire is less near the skin of the wire than in the core of the same wire.

In other words, because of the differences in impedance between the core and the skin of a wire, more eddy currents are going to be converted to heat closer to the core of a wire than in the skim of the same wire.

Distance Between the Ends of a Wire and Skin Effect

The total impedance of a wire can be considered in terms of series resistance.

As distance from one end of the wire to the other end increases, the difference in impedance of the cross-section parts of the wire also increases. When the wire is doubled in length, the impedance of the skin of the wire doubles, and the impedance of the core of the wire also doubles. Mathematically, the difference in impedance between the skin of a wire and the core also doubles, so the skin effect doubles.

Distance Examples:

We are using some arbitrary values for the impedance (equivalent to resistance) of the wire to show what is happening in the core of a wire and the skin.
• At a fixed distance:

• Impedance of the core of a wire - 6 ohms of impedance

• Impedance of the skin of a wire - 5 ohms of impedance

• Difference in impedance between skin and core of a wire - 1 ohm of impedance

When doubling the distance, the impedance of the wire is doubled.
• At doubled the fixed distance:

• Impedance of the core of a wire - 12 ohms of impedance

• Impedance of the skin of a wire - 10 ohms of impedance

• Difference in impedance between skin and core of a wire - 2 ohms of impedance

When increasing the distance to 10 times, the impedance of the wire is multiplied by 10 times.
• At 10 times the fixed distance:

• Impedance of the core of a wire - 60 ohms of impedance

• Impedance of the skin of a wire - 50 ohms of impedance

• Difference in impedance between skin and core of a wire - 10 ohms of impedance

Frequency and Skin Effect

As frequency is increased, the impedance caused by internal inductance (eddy currents) increases. The parasitic eddy currents effects convert more electrical power to wasted heat, and the skin effect increases.

Frequency Examples:

At a fixed distance, but at low frequency:
• Impedance of the core of a wire - 12 ohms of impedance

• Impedance of the skin of a wire - 10 ohms of impedance

• Difference in impedance between skin and core of a wire - 2 ohms of impedance

At the same fixed distance, but at high frequency:
• Impedance of the core of a wire - 100 ohms of impedance

• Impedance of the skin of a wire - 15 ohms of impedance

• Difference in impedance between skin and core of a wire - 85 ohms of impedance

The total amount of resistance and impedance in a straight wire is very much affected by the frequency of the signal.

Bottom Line

When conducting steady DC current, no matter how much distance a wire spans, the DC current will always use the entire cross section of a wire.

When conducting AC current, the severity of Skin Effect is directly affected by both distance and frequency. Also, to a variable extent, Skin Effect is affected by capacitance, bending or coiling, and magnetic cores.

Douglas Krantz
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