Skin Effect

[DonH50]

No worries. I am trying to keep these "fundamental" threads very focused on a single topic. The idea of sonic signatures related to various cable geometries is interesting, just too much for this thread. I encourage you to start another thread, stating your observations and conclusions, as it would be interesting to look at it from a technical point of view and see what happens. I would also like to know if others have observed the same things. I admit it is something I have rarely considered, at least in the audio world. I am familiar with Litz wire, and woven cables (an ugly subset of Litz), but have not really thought about some of the new flat ribbon cable schemes. I have several ideas but would prefer to address the topic in another thread.

I am (so far) side-stepping speaker cables because (a) I think (suspect) they are more likely to interact with components (speakers and amps) and (b) I need a lot more work on my source and load models and have not had the time. Unlike line-level components, both amp output and speaker input impedances get pretty complicated. The frequency response and skin effect threads are precursors.

To put it another way, skin effect itself does not care if it's a line or speaker level signal, but the debate about it's consequences must include source and load impedances (among other things), and I prefer to put the debate in another thread.

A careful read of the text, plot, and table should show why skin effect is unlikely to impart a sonic signature but by no means rules it completely out. In my opinion, for most interconnect cables in most systems (with a reasonable range of source and load impedances), it is a non-issue. However, I have little insight into the construction of more esoteric cables, do not claim to know the impedances of every component out there, and as a rule try to avoid absolutes because there is almost always a counter-claim. (The sun will ALWAYS rise tomorrow, until it goes nova... )

HTH - Don

 

[DonH50]

I did a little further research into skin effect and different wire geometries. I used 12-gauge wire, breaking my rule to look at speaker wires this time around, mainly because I just don’t see skin effect being significant in interconnects due to the impedances involved. I started with standard round AWG 12, then the same gauge (as determined by cross-sectional area) but in the shape of a 1:3 (h:w) rectangle, and finally a 12-gauge litz wire made of 39, AWG 28 wires (remember the smaller wires must be insulated from each other). The table shows the resulting effective conductance area (based on T, the total carrier depth) and resistance at d.c. and 20 kHz.



A standard (round, circular cross-section) AWG 12 wire has 17.2 % higher resistance at 20 kHz compared to d.c. (0 Hz), though a ten-foot (about 3 meter) cable only goes from 0.016 ohms to 0.019 ohms. This is a relatively trivial change compared to typical amplifier and speaker impedances.

The rectangular wire’s resistance at 20 kHz is nearly 2.5 times the d.c. resistance, with a 10’ cable going from 0.016 ohms to 0.0395 ohms. Again, though the ratio is large, in practice the absolute numbers are still small.

The skin depth at 20 kHz still exceeds the diameter of a 28-gauge wire, so the cross-sectional area (and resistance) of the litz wire bundle is the same as at d.c. This is the reason litz wire was developed.

 

[garylkoh]

Hi Don, this is very interesting.

The very thing that some cable manufacturers claim - that a rectangular wire has less skin effects - when in reality the opposite is true! Is there a rectangular ratio beyond which the skin effect then goes the opposite direction? Then, Vince's assertion that a flat cable (which is rectangular with a very high width to height ratio) begins to make sense - and it will measure more like the Litz wire.

Given that music is not composed of sine waves, is there any way that you can model single transients? Say the leading edge of a square wave - what would be the equivalent ohms ratio. This would then lead to a calculation of rise time and slew rate that any conductor will limit in the musical signal that is totally uncorrelated to the steady state sine-wave frequency response.

 

[DonH50]

Hi Gary,

1. Well, yes, and the dimensions may not be so bad as you might think. If the conductor is flat enough the entire cross-sectional area will be used, so thinner, wider cables can be better for skin effect. Remember the carrier depth is 25 mils at 20 kHz. That is about the thickness of a 22 gauge wire so is not unreasonable. A cable that is 25 mils thick only need be 211 mils (0.211") wide to equal the cross-sectional area of a 12-gauge wire. That's about a 1:8.44 ratio. So, their claims may certainly be valid. That leaves open the question of how relevant it really is in practice. I suspect part of the advantage of flat cables lies in the fact that most of the ones I have seen (admittedly few) are pretty wide, and so are likely the equivalent of a much larger gauge. Another advantage is that capacitive coupling along the thin edges fairly widely separated is lower than for large round wires in close proximity (zip-cord) and some coaxial cables. Less capacitance means lower loading and wider frequency response. Again, not sure if we care if it goes from 500 kHz to 1 MHz, but the effect is real enough.

2. There are several ways, but I do not have a good way (i.e. easy for me to try, since I am lazy) at the moment. In a cable system, having distributed RLCG, skin effect can lead to dispersion. This means low frequencies arrive before high frequencies, and perhaps with different amplitude, leading to corruption of the pulse edge. This is a real effect, but again I am skeptical of it's audibility, at least for normal interconnects. For speaker cables, I need to think and do more model development, since the impedances are more complex and power levels much higher. I suspect it is still deep in the mud, but until I run the numbers I'll withhold judgment.

HTH - Don

 

[fas42]

The very thing that some cable manufacturers claim - that a rectangular wire has less skin effects - when in reality the opposite is true! Is there a rectangular ratio beyond which the skin effect then goes the opposite direction? Then, Vince's assertion that a flat cable (which is rectangular with a very high width to height ratio) begins to make sense - and it will measure more like the Litz wire.

Given that music is not composed of sine waves, is there any way that you can model single transients? Say the leading edge of a square wave - what would be the equivalent ohms ratio. This would then lead to a calculation of rise time and slew rate that any conductor will limit in the musical signal that is totally uncorrelated to the steady state sine-wave frequency response.

Gary, of possible interest to you and if you were not aware of it, Stan Curtis of Cambridge Audio fame is starting a series of articles investigating the correlation of cable parameters and sound quality in the subscription magazine HiFi Critic.

Frank