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Re: Skin Effect At Audio Frequencies

Posted by Jon Risch (B) on September 23, 2003 at 14:56:07

In Reply to: Skin Effect At Audio Frequencies posted by MikeT on September 21, 2003 at 09:20:47:

Skin effect in audio cables has traditionally been dismissed due to very little difference in the transfer of signal amplitude at 20 kHz.

However, one of my contentions has been that sheer amplitude losses are not the only things that occur due to skin effect, and that the effects are occuring well below 20 kHz, and for wires much smaller than is traditionally thought.

As one example of what I am speaking about, lets consider the classic skin effect analysis. The skin depth for copper at 20 kHz is 0.463 mm (for silver it is 0.448 mm), and the usual way that this is related to wire gauge is to look at the diameter of the wire and say that any wire that has a radius that is smaller than the skin depth is free from skin effect issues. If we look at the diameter of various gauges of wires, we see that 19 ga. solid wire has a diameter of 0.912 mm, and a radius of 0.456 mm, which is less than the skin depth for copper at 20 kHz.

This might lead one to believe, that as long as we kept the wires smaller than 19 ga., we would not have to deal with skin effect issues at all, and that it was no longer a factor.

However, the skin depth is just a defined amount of penetration, in this case, a skin depth is defined as where the current density drops off to 37% of the value at the surface. The drop off is in the form of an exponential function. At two times the skin depth, the current density is aprox. 13.5% of the current flow at the surface. At three times the skin depth, the current density is approx. 5% of that at the surface, etc.

Now it might seem that if we had a 19 ga. copper wire, that since it's radius was less than the skin depth at 20 kHz, that there would be no significant losses or effects due to the skin effect. But note that there is still going to be a difference in the current density between the surface of the 19 ga. wire, and the center of the 19 ga. wire. Instead of being 37% down, it will be down say 35% (this is a guesstimate for the purposes of discussion, and not intended to be an absolute figure).

One might ask, if the signal amplitude losses at 20 kHz are not significant for copper wires larger than 19 ga., why worry about what is going on in a wire smaller than 19 ga.?

Because the skin effect is doing other things besides just causing simple amplitude losses at higher frequencies.

For one, it is definitely pushing the current flow out toward the surface of the wire, even at frequencies below 20 kHz, and for wires much smaller than the 12 ga. zip cords normally recommended by cable naysayers for use as speaker cables. This makes the surface of the wire, and what condition it is in, more of a factor than it would be otherwise. Platings, coatings, cracks or surface discontinuities, all of these now may be more of a factor in the sound, and how linearly the signal flows.

For another, skin effect seems to be the driving force for what has been referred to as "strand jumping".

See:
http://www.audioquest.com/
and go to main page, then Cable Theory, page 2 and 3.
(Note, this is just simpler than trying to describe it here uin gory detail).

The skin effect provides a force to cause the current to jump from strand to strand as the wire strands weave in and out of the wire bundle.

Note that at 20 kHz, a 12 ga. wire (diameter of approx. 2.4 mm) has 2.6 skin depths to it's center, and the current density at the center is down to less than 8% of the current density at the wires surface. The driving force to cause strand jumping is much higher for the 12 ga. stranded wire than for a 20 ga. stranded wire (diameter 0.914 mm), where there is only about one skin depth to the center of the wire (37% current density).

As a further example, the skin effect on a coaxial braid conductor layer is going to be very small, as the braid usually consists of 34 ga. wires, and the maximum thickness is then two wires on top of one another, which is 0.320 mm, or an effective radius of 0.160 mm. Very little difference in current density between the surface and the "center" of the braid.

If we analyze the situation even further, we would see that the braid has the only contact points between the two layers of wires at or near the center, where the current density is the lowest. We are only dealing with two layers or wires, as opposed to multiple layers for most commercial stranded wires.

Thus, we see that the braid in a coax (or a braided flat ribbon) is less likely to have as much force to drive strand jumping as most of the typical larger stranded wires.

In any event, the net result of the skin effect within the audio band is to cause the wire surface, and the purity and freedom from oxidation of stranded wires, to become more critical, and to make larger wires more susceptible to these problems.

Jon Risch

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