4.3.1 Skin Depth & Litz Wire

Evidence Energy Flows Into a Wire From the Surrounding Fields

Jul 17, 2024

Advances in alternating current or AC electronics soon demonstrated the merits of Poynting’s and Heaviside’s counterintuitive perspective. The resistance of a wire increases with increasing frequency as current concentrates in a shallow layer within a “skin depth” of the wire’s surface.

The Poynting-Heaviside theory offers a natural explanation for how these resistive losses work: since energy predominantly flows outside the wire, whatever portion of the energy may be absorbed by the wire arrives from outside the surface of the wire and penetrates its way in. With high frequency AC, the electric fields of one polarity have less time to permeate into the conductors before the polarity reverses and the process starts over with fields of the opposite polarity. In Heaviside’s words:

It was discovered by mathematical reasoning that when an electric current is started in a wire, it begins entirely upon the skin, in fact upon the outside of its skin; and that, in consequence, sufficiently rapidly impressed fluctuations keep to the skin of the wire, and do not sensibly penetrate to its interior [[i]].

At the 60 cycles per second (or 60 Hertz) frequency of AC power in the U.S., the skin depth in copper or aluminum is about 10 millimeters (mm). High voltage power lines are often aluminum conducting strands (combining light weight and good conductivity) wrapped around a central steel cable for strength. Steel is a poor conductor, but because of the skin effect, virtually all the current remains in the outer aluminum portion of the wire. In certain high voltage lines, groups of three such strands are employed, because losses would be lower than combining the material into a single strand.

For commercial AM (amplitude modulation) radio at about a million cycles per second, the skin depth is about 0.1 mm. At the still higher frequency of a billion or more cycles per second (1 gigahertz or more), the skin depth is on the order of 0.001 mm or less. By comparison, the diameter of a human hair ranges between 0.017 mm to 0.180 mm.

Engineers use “litz” wire (from the German term “litzendraht,” or “braided”) comprising many fine strands. If the litz wire strands are so fine that their diameter is less than the skin depth, the fields can penetrate through the entire wire, and current can flow through the entire cross-sectional area. This lowers the effective resistance.

Figure 4.27 Current flows only in a narrow layer near the surface, so a bundle of smaller wires (right) offers more area for current to flow and presents a lower resistance than a single larger wire (left).

The skin depth (δ) at a particular frequency means current penetrates only a shallow distance into the solid conductor. This concentration of current into a relatively small cross-sectional area means high resistance. If we divide that same area of copper into many smaller strands whose diameter is the same as the skin depth, the overall bundle is a bit larger, given the gaps between strands, but now the entire cross-sectional area can carry current, significantly lowering the resistance compared to the single solid wire.

Figure 4.28 Three examples of litz wire architecture (courtesy, New England Wire Technologies–www.newenglandwire.com).

If a particular strand of litz wire remains near the interior of the bundle, it will tend to be shielded from the fields and will not support current flow. There is an art to braiding such a bundle so that individual strands are sometimes on the outside of the bundle, sometime inside. Figure 4.28 presents a few of the many possible examples.

Figure 4.29 Close up of the end of a litz wire, in this case, a bundle of 105 wires sized at 44 AWG (0.064 mm diameter). Scale is in millimeters (mm), grid in 0.1 mm (right).

The litz wire in the photo of Figure 4.29 has 105 strands of “44 gauge” wire. In the American Wire Gauge (AWG) 44 AWG wire has a diameter of 0.064 millimeters (mm). This litz wire bundle is roughly equivalent to a 26 AWG solid wire with a diameter of 0.45 mm. Engineers will select more fine strands to operate at higher frequencies. Difficulties in making the wire strands sufficiently narrow make it challenging to apply the technique in the High Frequency (HF) band, 3–30 million cycles per second (MHz) or above.

Litz wire offers a practical illustration of how skin effect works and how energy is carried by fields outside the wire, not within the wire itself. Minimizing resistance is not the only advantage of multistrand wire. There are also mechanical advantages. Power cords are braided so they can be flexible and suffer fewer fatigue failures than the equivalent solid wire.

Next time: 4.3.2 Inductive Telegraphy at a Distance: The First Wireless Technology

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References

[i] Heaviside, EMT vol. 1, p. 14.

Fields & Energy

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