Voltage on a conductor due to skin depth

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  • #26
Baluncore
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Conductivity dominates skin depth discussion because, like frequency, it is an independent parameter.

“Electromagnetics”, Kraus and Carver, 1973, 2nd edition, sections 10-15 to 10-19. Summary attached;
 

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  • #27
meBigGuy
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Whilst this is strictly correct (and very interesting, too), it isn't the best thing to hit students with until they understand the real significance of what it really says.
I don't agree with the spoon-feed philosophy so often expressed here.
 
  • #28
nsaspook
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I don't agree with the spoon-feed philosophy so often expressed here.
Spoon-feeding to me is someone who says, "I don't want to do any hard work, just give me the answer (today)" with a positive response of just the answer. I don't see very much of that here. Taking small bites and sipping lets you savour and enjoy every small detail.
 
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  • #29
berkeman
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I'm getting a bit dizzy with all of this. Maybe we can all collaborate on a PF Library entry on "Electrical Skin Depth". We can address the different ways of visualizing/explaining it, and show at the core of it all what the EE equations are that determine it...
 
  • #31
sophiecentaur
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I don't agree with the spoon-feed philosophy so often expressed here.
Would you suggest hitting every student with everything at once, then? My suggestion is not spoon feeding, it is attempting to avoid confusion. Although the 'one wavelength' statement may be correct, it is not of as much practical use as the conventional description.
The article explaining the 'one wavelength' idea is surely not proposing that as a serious definition. The way I read it, it is just pointing out a quirky relationship. Students do not always appreciate quirky relationships when they want to get their ideas sorted out in a straightforward way. Quirky is something best left till they are familiar with the non quirky.
 
  • #32
meBigGuy
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lol. Read your sig
 
  • #33
davenn
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.....................
The article explaining the 'one wavelength' idea is surely not proposing that as a serious definition. The way I read it, it is just pointing out a quirky relationship. .............
and that was the confusing bit, cuz wavelength of a given freq is only slightly longer in a conductor than in free space when VF is taken into account. So I couldn't see how they could even use that definition in this context

Dave
 
  • #34
meBigGuy
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No, that is not true. You are thinking of the wavelength at the surface of the conductor where VF has meaning. That is what skin effect is about.
 
  • #35
Baluncore
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Davenn.
When an EM wave is being guided by a conductive surface in the presence of a dielectric, the velocity factor is primarily determined by the dielectric constant.

The minute proportion of energy that is coupled from the guided surface wave, deeper into the conductor, has a much lower velocity into the conductor than across the surface. See the equation for phase velocity in the table 10-5 from K&C, attached to my post #26.

K&C 1973, Table 10-4, shows the velocity into the body of copper as being 3.2 m/s at 60 Hz, at 1 MHz it is 410. m/s while at 30 GHz it is 7100. m/s. These are very much less than the speed of light or the velocities commonly found in transmission lines.

The refractive index of a good conductor is extremely high, so conductors make very good reflectors from RF through to UV. Energy not reflected, enters the body of the conductor and then travels with the very much lower velocity.
 
  • #36
berkeman
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This thread is now stickied because it is such a good debate about models and approaches to a real-world problem. Let's keep the debate technical -- I'm learning from it...
 
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  • #37
sophiecentaur
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No, that is not true. You are thinking of the wavelength at the surface of the conductor where VF has meaning. That is what skin effect is about.
It makes my point about "confusion" dunnit? (And Davenn wasn't born yesterday, either)
 
  • #38
meBigGuy
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Avoiding confusion is the enemy of understanding. You have an incomplete (maybe incorrect) perception (visualization?) of skin depth and accept it because it avoids confusion? What is really confusing is unlearning the oversimplifications.

<EDITED>
********************************************************
Moving on:
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BTW, I am not an expert in this field, and will never be. But, neglecting that trivial factor (lol):

The wikipedia page has a drawing with current loops that shows eddy currents flowing in every which way inside a wire. How do those "backwards" current flows happen without being related to the wavelength of the signal within the medium? My tendency was to just look at that picture and just accept it, not thinking any deeper about what it meant and what must be true for it to happen.

Then look at the animation in the http://fermi.la.asu.edu/w9cf/skin/skin.html paper. You see the positive and negative field relationships with respect to the skin-depth. Again, try to visualize how you get reversed fields in such short distances.

The electromagnetics to produce those is just beautiful.
 
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  • #39
sophiecentaur
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Avoiding confusion is the enemy of understanding. You have an incomplete (maybe incorrect) perception (visualization?) of skin depth and accept it because it avoids confusion? What is really confusing is unlearning the oversimplifications.

BTW, I am not an expert in this field, and will never be. But, neglecting that trivial factor (lol):

The wikipedia page has a drawing with current loops that shows eddy currents flowing in every which way inside a wire. How do those "backwards" current flows happen without being related to the wavelength of the signal within the medium? My tendency was to just look at that picture and just accept it, not thinking any deeper about what it meant and what must be true for it to happen.

Then look at the animation in the http://fermi.la.asu.edu/w9cf/skin/skin.html paper. You see the positive and negative field relationships with respect to the skin-depth. Again, try to visualize how you get reversed fields in such short distances.

The electromagnetics to produce those is just beautiful.
You seem to be assuming that this particular level of dealing with the subject involves no simplification and that it is some 'ultimate truth'. I think you imagine that I am 'knocking' the 'wavelength thing'. Quite the reverse.

I wonder whether you have ever done any teaching and I also wonder how many threads on PF you have read. There is absolutely no way that people can take everything on at once. Science (and personal knowledge of Science) is a constant process of realignment of theory to measured experience so there is little point in expecting not to be confused and not to expect to have to 'unlearn' some stuff on the way. This shows itself time after time when people want to leap into Physics half way through, instead of getting to it in an incremental way. They so often get hopelessly tied up and there are so many howlers, as a result. To my mind, and in my experience, it is a necessary process to start with crude models and to work towards better ones. There is little point in trying to leapfrog over Newton and Classical particle theory (over-simplifications, if you like) because they actually operate at a level that life is lived.

However correct (and fascinating) the idea of 'the wavelength thing' may be, it would be less useful to use that knowledge when deciding how thick to make the plating on the inside of a waveguide or the gauge to use in Litz wire strands.
 
  • #40
meBigGuy
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No, I didn't imagine you were knocking the wavelength thing. I went back and drew a line between my comment regarding confusion (the root of all learning) and the rest of my post. I really don't think this thread should address spoon-feeding/confusion anymore.
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The thing I still don't get intuitively is Baluncore's statement "It takes time for a surface current flow to soak into a conductor because it sees it's own reflection. " I don't understand the source of this reflection. Is reflection the right word? Or, is there a better way to say this?
 
  • #41
Baluncore
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Arguing over the curriculum is pointless at this stage. The approach should offer the “one cycle deep current” as a reward for understanding refractive index in conductors. Maybe, to separate the body wave from the surface wave situation, it could be called “wave depth” rather than “wave length”. The word “skin” might then be retired.

It will take careful planning to replace this WW2 artefact, a 70 year old multi-generational cul de sac, with a super highway.

This is a much deeper conceptual problem than has yet been admitted here on PF. Give it time.
 
  • #42
meBigGuy
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Baluncore:
Could you respond to my question in #40?
 
  • #43
Baluncore
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meBigGuy said:
Baluncore:
Could you respond to my question in #40?
Sorry about the overlap and delay in my reply but I am at the far end of a chain of busy radio links. I also have work to do here that must get priority over PF.
 
  • #44
Baluncore
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meBigGuy said:
The thing I still don't get intuitively is Baluncore's statement "It takes time for a surface current flow to soak into a conductor because it sees it's own reflection. " I don't understand the source of this reflection. Is reflection the right word? Or, is there a better way to say this?
When a wave travels at close to luminal speed along a conductor, the phase velocity equation demonstrates that it cannot be travelling inside the conductor.

A surface current on a conductor produces a magnetic field that in turn causes a reverse current to counter the majority of the initial current. That double application of the cross product can be called reflection. It guides EM energy as a wave, along the boundary interface, but travelling in the faster medium. We talk of that wave as an RF current, flowing at close to the speed of light, in the skin of the conductor. It is luminal only because it advances as an EM wave outside the conductor.

A good conductor leaves very little non-reflected energy to enter the body of the conductor at the much lower phase velocity. It represents an ohmic loss in the conductor.
 
  • #45
nsaspook
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The thing I still don't get intuitively is Baluncore's statement "It takes time for a surface current flow to soak into a conductor because it sees it's own reflection. " I don't understand the source of this reflection. Is reflection the right word? Or, is there a better way to say this?
Reflection is the right word. Penetration depth The 'effect' is caused by changing fields on the surface because (ironically) good conductors of electric current (charge) are poor conductors of 'electricity' (EM field energy).
 
  • #46
meBigGuy
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I'm still not quite getting it. The current density decreases continuously along the depth of the conductor. I'm trying to relate to that. That fits the description above: "(ironically) good conductors of electric current (charge) are poor conductors of 'electricity' (EM field energy) ". I can relate to the concept of reflection at the boundary, I just cannot associate the continuing decrease with reflection. But, perhaps the above is the key, not some sort of "continuous reflection".
 
  • #47
sophiecentaur
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I'm still not quite getting it. The current density decreases continuously along the depth of the conductor. I'm trying to relate to that. That fits the description above: "(ironically) good conductors of electric current (charge) are poor conductors of 'electricity' (EM field energy) ". I can relate to the concept of reflection at the boundary, I just cannot associate the continuing decrease with reflection. But, perhaps the above is the key, not some sort of "continuous reflection".
I see what you're getting at but I think you need to be careful here because the concept of 'poor conductivity' can imply energy loss and I think the evanescent fields are not totally in phase so little energy is actually lost. Compare the case of total internal reflection between two (ideal) dielectrics where the fields 'behind' the boundary actually carry no energy away from the surface. With a highly conductive metal, the skin effect phenomenon is at its strongest yet the actual loss is least.
Could it be an analogy too far?
 
  • #48
nsaspook
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I see what you're getting at but I think you need to be careful here because the concept of 'poor conductivity' can imply energy loss and I think the evanescent fields are not totally in phase so little energy is actually lost. Compare the case of total internal reflection between two (ideal) dielectrics where the fields 'behind' the boundary actually carry no energy away from the surface. With a highly conductive metal, the skin effect phenomenon is at its strongest yet the actual loss is least.
Could it be an analogy too far?
Yes, 'poor conductivity' here implies absorption, reflection and refraction instead of direct transmission in the media (highly conductive metal). The combination of the conductor and the space (with possible dielectric losses) near it combine to make the transmission medium, guide or line for EM energy.
 
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  • #49
meBigGuy
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I am having a difficult time intuitively relating to the phenomena that causes the electric field density to decrease continuously as the depth increases. Yes, that is the skin depth, but what is causing it. I'm not interested at the boundary but what happens after. Somehow the longitudinal current flow creates fields that limit the penetration depth at high frequencies and it relates to the short wavelength in metals. Baluncore referred to some sort of continuous reflection (I think), and "soaking". I'm just trying to get to the root of what that referred to.
 

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