# Is the skin effect a factor for low-current AC applications?

Another way to phrase the question might be, "Is the skin effect proportional to current flow?"

I am only vaguely familiar with the skin effect, so I read up on the subject to learn more about it, purely for academic reasons. (I don't currently have any projects where it is a concern.)

I understand that in order to determine conductor size for AC (or multiple conductors or waveguides, etc.), one must consider the frequency, the resistivity of the conductor, and the magnetic permeability. The Wikipedia article mentions:

"It is also important even at mains frequencies (50 – 60 Hz) in AC electrical power transmission and distribution systems."

This statement seems to imply it applies more to high power distribution rather than household mains.

I understand that the center of a conductor is utilized less as frequency increases, but I am not clear on how it relates to current flow.

Does the skin effect become more intense as current increases? A chart on the Wikipedia article shows that at 60Hz, the skin "depth" is 8470μm. If this is constant for that frequency, then am I correct in saying that the diameter of conductor should be based on that depth for the intended current flow? Or, put another way, is the center of the conductor beyond that depth effectively pointless, regardless of current?

• 8470μm is 8.47 mm which implies a conductor with diameter > 1.6 cm - which is quite a large conductor and not one encountered in most households. The 8470μm is the depth at which 63% of the current flows between the skin and the depth, so there is still appreciable current flowing in the core. Wikipedia suggests that tubular conductors can be used, which supports your final contention, but only for very large currents. I don't expect to see tubular conductors (or even litz wire) on iPhone chargers. Commented Jul 16, 2013 at 9:02
• @Redgr: Skin depth isn't a issue for iPhone chargers because the phone is charged with DC. DC current uses the whole crossection of the conductor equally. Commented Jul 16, 2013 at 16:33

Is the center of the conductor beyond that depth effectively pointless, regardless of current?

No, the centre isn't pointless because, as mentioned in a RedGrittyBrick comment, 63% of the current will flow in the skin (if the cable is big enough) and still leave 37% flowing closer to the conductor centre. For resistance critical applications this is significant in my book.

However, if the skin depth were only 0.1mm (as per 400kHz) the central region (say +/-0.25mm) of a 1mm diameter wire is a little pointless.

If you needed to pass large currents (tens of amps) you would make the wire bigger in diameter (enclosing more cross section at 2 or 3 skin depths) or make the wire hollow to save money.

It doesn't have to be massive current though. If you have a highly resonant tuned circuit, you want to keep series resistance to a minimum so you'd go for a wire that is unconventionally large to keep the Q of the circuit high.

I've seen a metal detector in a timber saw mill use standard copper pipe for its oscillator coil even though it was probably only passing a couple of amps at 100kHz oscillator frequency. They use MDs on timber in Canada to protect the saws from getting broken or blunt when cutting through timber that someone has been using for target practice!

For similar reasons I've used 750 strand litz wire to pass power from a resonant magnetic field to a small circuit located up to 40mm away. With 40mm distance the Q needed to be really high to create sufficient "depth" in the mag field at that distance.

The strands were spaced apart in three coils of 250 wires each because not only was I trying to avoid skin effect, but also proximity effect, another problem with high frequencies not utilizing the full conductor cross-section.

No, the skin effect is a function of frequency, not current. Basically, the skin effect makes the wire look like it has a higher resistance at high frequencies than it does at DC. That resistance is not a function of current.

This is somewhat of a aside, but note that lots of sources misleadingly give you a single skin depth value as a function of frequency. What they often fail to mention is that there is actually a smooth gradient of current density that falls off from the outside of the wire inwards. This function is exponential in nature, and usually the skin "depth" is quoted as one power of e down.