I have seen repeated references here and at AA to skin effect when explaining why esoteric wire and cables are sonically superior to regular copper wire. I have seen comments that larger diameter wire is inferior to smaller diameter wire for high frequency signals. I don't understand where these positions come from and would like someone who does to please explain how this could be so.
To start off, here is a well written explaination about skin effect (cribbed from a post from www.churchsoundcheck.com by Kenneth Reighard).
I understand this explaination and it makes sense that extremely large power bus links would be hollow because copper is expensive. Note that based on this a solid conductor of the same outside diameter would not be at a disadvantage compared to a hollow conducter as far as impedance or current carrying capacity is concerned, it would simply cost more to make.
The fact is that a larger diameter conductor is always going to have lower impedance than a smaller diameter conductor at any frequency.
Take the 20 KHz frequency for example: The skin depth is 0.5 mm (rounding off needless precision). Therefore a 1mm wire is the largest wire that will not exhibit skin effect at that frequency. A 1mm diameter wire will have a cross sectional area of PI*(0.5mm)^2 = 0.785mm^2.
A 2 mm wire will only use the outer 0.5mm of the wire to carry the 20KHz signal. This outer current carrying area's cross sectional area = PI*(1mm)^2 - PI*(0.5mm)^2 = 2.36mm^2
The ratio of current carrying cross sectional area of the two wires is 2.36/0.785 or almost exactly 3 to 1. This means that at 20 KHz the 2mm wire will have 1/3 the impedance of the 1mm wire. How could skin effect make the 1mm wire superior to the 2mm wire? The larger the wire size gets, the greater the advantage becomes for the larger wire.
Comments, rebuttals?
Phil
To start off, here is a well written explaination about skin effect (cribbed from a post from www.churchsoundcheck.com by Kenneth Reighard).
I understand this explaination and it makes sense that extremely large power bus links would be hollow because copper is expensive. Note that based on this a solid conductor of the same outside diameter would not be at a disadvantage compared to a hollow conducter as far as impedance or current carrying capacity is concerned, it would simply cost more to make.
The fact is that a larger diameter conductor is always going to have lower impedance than a smaller diameter conductor at any frequency.
Take the 20 KHz frequency for example: The skin depth is 0.5 mm (rounding off needless precision). Therefore a 1mm wire is the largest wire that will not exhibit skin effect at that frequency. A 1mm diameter wire will have a cross sectional area of PI*(0.5mm)^2 = 0.785mm^2.
A 2 mm wire will only use the outer 0.5mm of the wire to carry the 20KHz signal. This outer current carrying area's cross sectional area = PI*(1mm)^2 - PI*(0.5mm)^2 = 2.36mm^2
The ratio of current carrying cross sectional area of the two wires is 2.36/0.785 or almost exactly 3 to 1. This means that at 20 KHz the 2mm wire will have 1/3 the impedance of the 1mm wire. How could skin effect make the 1mm wire superior to the 2mm wire? The larger the wire size gets, the greater the advantage becomes for the larger wire.
Comments, rebuttals?
Phil
Power cords???
What I don't understand, and maybe this needs a seperate thread, is all the nonsense and hype surrounding these $200+ power cords and high grade wall power outlets
You have 20 miles of cheap wire between you and the power generating station and somehow 3 feet of magic wire is going to make a difference in the way your stereo sounds?
NOPE 'fraid not!
What I don't understand, and maybe this needs a seperate thread, is all the nonsense and hype surrounding these $200+ power cords and high grade wall power outlets
You have 20 miles of cheap wire between you and the power generating station and somehow 3 feet of magic wire is going to make a difference in the way your stereo sounds?
NOPE 'fraid not!
Konnichiwa,
Simple.The "skindepth" is defined as a "point" where a certain proportion of the "current" is forced towards the outside of the conductor. Yet at a lower frequencies there is still "cuurnt bunching" towards the outside of the conductor. If the outside is more oxidised (a reasonable assumption given the processes drawing wire) the this contamination becomes more relevant.
But admittedly the subject is much more complex.
But think of the "skindepth" the same way as you think about 55MPH on the freeway. There is a HUGE difference between 5.5MPH and 55MPH, but the highway patrol will only fine you if you are FASTER that 55. Yet surely you would not propose that (other than the fine) there is no difference between standing still and driving 54.9999999999999 MPH....
Sayonara
PS, all the "science" you quoted is factually correct, except it is being (deliberatly?) missapplied, with certain objectives and non of them the truth.
haldor said:
Simple.The "skindepth" is defined as a "point" where a certain proportion of the "current" is forced towards the outside of the conductor. Yet at a lower frequencies there is still "cuurnt bunching" towards the outside of the conductor. If the outside is more oxidised (a reasonable assumption given the processes drawing wire) the this contamination becomes more relevant.
But admittedly the subject is much more complex.
But think of the "skindepth" the same way as you think about 55MPH on the freeway. There is a HUGE difference between 5.5MPH and 55MPH, but the highway patrol will only fine you if you are FASTER that 55. Yet surely you would not propose that (other than the fine) there is no difference between standing still and driving 54.9999999999999 MPH....
Sayonara
PS, all the "science" you quoted is factually correct, except it is being (deliberatly?) missapplied, with certain objectives and non of them the truth.
I think the only "disadvantage" to the thicker wire is, as you said, you get less current capacity at 20kHz than you might have expected. Since this is a freqency-dependent resistance, I guess it is worth minimizing, but it can't have too large of an effect if the variables are kept within reason. Since it is X^(0.5) law the effect is actually decelerating with increasing frequency.
Yup, its true, and spectacular...
I 've seen this stuff first hand while working at the Robert Moses Power Plan in Niagara Falls. I spent a summer painting towers in the switchyard in between the two damns. The yard was divided into three voltages with step up/down transformers between them. I think the voltages were 115 KV, 260 KV and 345 KV.
The 345 KV bays I think had an operating potential of 2000 amps per leg. Circuit breakers were filled with dry nitrogen. The buss bars were big aluminum tubes about 4 inches outside diameter and like the guy says, 1/2 to 3/4 inch thick. The part that still gets me is that on hot days when they were running a lot of current through the buss would start to vibrate. To counter this effect and relieve some of the subsequent mechanical stress, they fitted the buss with additional runs of 1 1/4" stranded cable running up the center. I guess the idea was to add some mass and dampen the vibrations.
Corona was always a big issue. Standing next to a tower it was too easy to draw a continuous arc a few inches long. While climbing I always made sure that my fly didnt get too close to the metal. Never happened, but I wasn’t taking any chances.
The higher voltages were used for distance transmission. Niagara falls is part of the now infamous lake Erie loop on the NE power grid. A lot of the power generated there also goes down state to NYC, about 450 miles. I can imagine that in Malaysia you just might not need those high voltages. One of my co-workers grew up in Malaysia. He’s a good guy, I’m lucky to know him.
I 've seen this stuff first hand while working at the Robert Moses Power Plan in Niagara Falls. I spent a summer painting towers in the switchyard in between the two damns. The yard was divided into three voltages with step up/down transformers between them. I think the voltages were 115 KV, 260 KV and 345 KV.
The 345 KV bays I think had an operating potential of 2000 amps per leg. Circuit breakers were filled with dry nitrogen. The buss bars were big aluminum tubes about 4 inches outside diameter and like the guy says, 1/2 to 3/4 inch thick. The part that still gets me is that on hot days when they were running a lot of current through the buss would start to vibrate. To counter this effect and relieve some of the subsequent mechanical stress, they fitted the buss with additional runs of 1 1/4" stranded cable running up the center. I guess the idea was to add some mass and dampen the vibrations.
Corona was always a big issue. Standing next to a tower it was too easy to draw a continuous arc a few inches long. While climbing I always made sure that my fly didnt get too close to the metal. Never happened, but I wasn’t taking any chances.
The higher voltages were used for distance transmission. Niagara falls is part of the now infamous lake Erie loop on the NE power grid. A lot of the power generated there also goes down state to NYC, about 450 miles. I can imagine that in Malaysia you just might not need those high voltages. One of my co-workers grew up in Malaysia. He’s a good guy, I’m lucky to know him.
OK. skin effect is a real phenomena, but if it were a problem at audio frequencies then you would expect tweeters voice coils to be wound with Litz wire, would you not?
Also, I spend *all* day, *every* day in the design lab of the largest SMPS manufacturer in Australia and I get to see and play with all manner of HF transformers, large and small. Here, skin effect is something you have to take into account especially if you have turn-on edges of 10-15 nS. But if you are talking about audio with frequency components ~1000 times lower then I think it becomes one of those things that makes virtually no difference at all.
Spend you time and effort and money on things that make a measurable / audible difference first. If you already have, then is the time for skin effect stuff. But don't hold your breath.
*All and *every means 38 hour working week.
Also, I spend *all* day, *every* day in the design lab of the largest SMPS manufacturer in Australia and I get to see and play with all manner of HF transformers, large and small. Here, skin effect is something you have to take into account especially if you have turn-on edges of 10-15 nS. But if you are talking about audio with frequency components ~1000 times lower then I think it becomes one of those things that makes virtually no difference at all.
Spend you time and effort and money on things that make a measurable / audible difference first. If you already have, then is the time for skin effect stuff. But don't hold your breath.
*All and *every means 38 hour working week.
skin effect
I wouldn't worry about the resistive increase as a result of skinning in speaker cables..
I'd worry about the inductive change..the self inductance of a wire drops towards zero as the frequency goes up.
The stored energy in the wire is 1/2 L I squared, and if the inductance changes dynamically in response to current slew rate changes, how does the energy loss manifest?
I'm not sure that skinning is not an audio concern..
I wouldn't worry about the resistive increase as a result of skinning in speaker cables..
I'd worry about the inductive change..the self inductance of a wire drops towards zero as the frequency goes up.
The stored energy in the wire is 1/2 L I squared, and if the inductance changes dynamically in response to current slew rate changes, how does the energy loss manifest?
I'm not sure that skinning is not an audio concern..
Re: Re: Skin Effect in Wires.
Hi Thorsten,
You are the only one so far who has supported the idea that skin effect matters, so please explain to me what is being missapplied in what I said. The only characterstic of a conductor that I am aware of that is influenced by skin effect is the impedance of the conductor. So if the impedance of a larger wire is lower than that of a smaller wire even after taking into account skin effects then why does it matter?
I also don't see what your driving speed example has to do with the subject. Are you implying that as soon as the diameter of the wire exceeds twice the skin depth that some qualitative change is going to occur (the equivalent of getting a speeding ticket)?
P.S. The comment about hollow conducters being about lower cost is probably not accurate, I would image that the weight savings of using hollow bus links is more important that any possible cost advantages.
Phil
Kuei Yang Wang said:
Hi Thorsten,
You are the only one so far who has supported the idea that skin effect matters, so please explain to me what is being missapplied in what I said. The only characterstic of a conductor that I am aware of that is influenced by skin effect is the impedance of the conductor. So if the impedance of a larger wire is lower than that of a smaller wire even after taking into account skin effects then why does it matter?
I also don't see what your driving speed example has to do with the subject. Are you implying that as soon as the diameter of the wire exceeds twice the skin depth that some qualitative change is going to occur (the equivalent of getting a speeding ticket)?
P.S. The comment about hollow conducters being about lower cost is probably not accurate, I would image that the weight savings of using hollow bus links is more important that any possible cost advantages.
Phil
inductance/skin
The inductance equation for a parallel wire pair is:
L=.01016*length*{2.303*log(2*D/d)-(D/length)+(mu*delta)}
The last term is the skin effect term. delta is .25 at low frequency, and drops to zero at high frequencies.
The effect is reduced inductance at HF.
From Jackson, second edition, page 298:
"the hf inductance of circuit elements is somewhat smaller than the low freq inductance because of the expulsion of flux from the interior of the conductors."
The end result is at lf, the self inductance of any wire pair is .03 uHenries per foot, when fully skinning, self inductance is zero.
If a hf signal is added to a lf signal, what is the inductance of the wire pair? It would appear to be a time dependent function.
If the inductance changes, what happens to the stored energy of that inductance? It's gotta go somewhere.
Oh, BTW...Jackson seems to be talking about planar skin depth, not circular.
The inductance equation for a parallel wire pair is:
L=.01016*length*{2.303*log(2*D/d)-(D/length)+(mu*delta)}
The last term is the skin effect term. delta is .25 at low frequency, and drops to zero at high frequencies.
The effect is reduced inductance at HF.
From Jackson, second edition, page 298:
"the hf inductance of circuit elements is somewhat smaller than the low freq inductance because of the expulsion of flux from the interior of the conductors."
The end result is at lf, the self inductance of any wire pair is .03 uHenries per foot, when fully skinning, self inductance is zero.
If a hf signal is added to a lf signal, what is the inductance of the wire pair? It would appear to be a time dependent function.
If the inductance changes, what happens to the stored energy of that inductance? It's gotta go somewhere.
Oh, BTW...Jackson seems to be talking about planar skin depth, not circular.
SY said:
Near as I can find, the skin depth calculation is the same for a plane or a wire.
http://www.wikipedia.org/wiki/Skin_effect
This is discussed in greater depth here.
http://www.audioholics.com/techtips/audioprinciples/interconnects/ComponentVideoCables_2.php
The analysis of current carrying cross sectional area is valid independent of the actual skin depth of any particular frequency. Assume you start with a wire diameter that is exactly twice the skin depth (from what I have read this would be the ideal wire size for people who thinks this matters). Doubling the diameter of a wire increases it's cross sectional area by a factor of 4. Even after subtracting the diameter of the initial wire (which is the area deeper than 1 skin depth) you still end up with 3 times the current carrying cross sectional area. 3 times more copper means 1/3 the impedance.
Unless skin effect has some other influence beyond changing the AC impedance of a wire, I can't understand how this could be used to support claims that a larger wire is inferior to a smaller wire for carrying audio signals.
The comment about surface oxides is disingenuous. In order to make the impedance of the larger wire match that of the smaller wire, over half the volume of the larger wire would have to consist of copper oxide. I think you might notice if this was the case.
Phil
skin
Planar and round are not the same equation..Note in the wiki article, they specify it's good for D>>d.
A better desc. is in another link, I'm looking for it now.
Yes..I'm not talking about the AC impedance, but the self inductance..
All wires have the same dc self inductance, regardless of size.
Planar and round are not the same equation..Note in the wiki article, they specify it's good for D>>d.
A better desc. is in another link, I'm looking for it now.
Yes..I'm not talking about the AC impedance, but the self inductance..
All wires have the same dc self inductance, regardless of size.
Haldor, thanks for the links- the experimental data is exactly what would be expected. But the equations for skin depth are asserted, not derived. I'd like to know if there's a geometric factor when going from plane conductor to round, where the diameter is of the same order of magnitude as the skin depth.
Now, the audioholics paper asserts that the AC resistance formula is accurate to within a few percent. But the experimental data show AC resistance changes over the measurement bandwidth of a few percent, so...
I'm now terribly worried that I might also have a 0.047dB loss at 10 MHz. That's bound to reduce airiness and delicacy of the soundstage, and put a blanket over the subtleties of musical textures. Or something.
Now, the audioholics paper asserts that the AC resistance formula is accurate to within a few percent. But the experimental data show AC resistance changes over the measurement bandwidth of a few percent, so...
I'm now terribly worried that I might also have a 0.047dB loss at 10 MHz. That's bound to reduce airiness and delicacy of the soundstage, and put a blanket over the subtleties of musical textures. Or something.
skin
Here's a good link..He also talks of the round vs rect solution..
He says the bessel solutions get tough...(look at what he's written)...So he approximates..whew..
http://www.st-andrews.ac.uk/~www_pa/Scots_Guide/audio/skineffect/page1.html
The AC resistance don't mean squat, as you pointed out..
But the inductive stuff? I'm not sure.
Here's a good link..He also talks of the round vs rect solution..
He says the bessel solutions get tough...(look at what he's written)...So he approximates..whew..
http://www.st-andrews.ac.uk/~www_pa/Scots_Guide/audio/skineffect/page1.html
The AC resistance don't mean squat, as you pointed out..
But the inductive stuff? I'm not sure.
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