Skin Effect and shape of conductor

[likephysics]

Let's say we have 2 different conductors - one a round wire, another a round wire but with hollow core.
The wire with the hollow core has higher resistance. But for the sake of argument, let's assume that it has the same resistance and the round wire.
Will the skin effect be less for the hollow wire?

 

[phinds]

Been a long time since I did fundamental electronics, but as I recall, when operating at high skin effect frequencies, it doesn't matter if there is a core since none of the current is in it.

 

[yungman]

I can't speculate about different resistance of the two wires you described. But in general , under high frequency, the hollow core wire should conduct better as it has two surface area...inside and outside. Solid core only has the outer surface.

 

[marcusl]

I can't speculate about different resistance of the two wires you described. But in general , under high frequency, the hollow core wire should conduct better as it has two surface area...inside and outside. Solid core only has the outer surface.

I never heard this before. Do you have references?

 

[yungman]

I never heard this before. Do you have references?

What reference? I am just talking about hollow wire has two surface, the inner and outer surface and both carry current. So for the same diameter wire, you have almost double the surface area ( or width) for conducting current. Nothing more than that.
Just a very general comment without getting into the specific conductance and all.

 

[phinds]

What reference? I am just talking about hollow wire has two surface, the inner and outer surface and both carry current. So for the same diameter wire, you have almost double the surface area ( or width) for conducting current. Nothing more than that.
Just a very general comment without getting into the specific conductance and all.

It was my impression that the skin effect drives all the current to the outer surface, so an inner surface would be irrelevant. Do you know otherwise, as you stated?

 

[yungman]

It was my impression that the skin effect drives all the current to the outer surface, so an inner surface would be irrelevant. Do you know otherwise, as you stated?

Thats a good question! My understanding is as long as you have a surface, you have the current. You connect the wire at two ends, the current start to flow, then the field developed and all current goes to the surface.

It is like the litz wire, it does not matter the particular wire is in the middle of the bundle, you start the current from one end, it goes equally to each wire, then because of the E field attenuation, the current stay on the surface of each wire. That should works for the inner surface of the hollow wire here.

If the logic of the inner surface of the hollow wire don't carry current, that means the only the outer strands of the bundle of litz wires at the connector wire interface conduct current, the strands that are in the middle never get the current.

Itn't inner surface the same as output surface? it's a surface and surface current flows?

I don't know, just my logical deduction. I am no expert, let me know, I love to learn.

 

[marcusl]

My understanding is as long as you have a surface, you have the current.

Yungman, I wish you'd be a little more careful with answers in areas where you are not expert. The skin effect is exactly as phinds said: at high frequencies all current flows on the outer skin of the conductor, which is why hollow conductors can be used without increased loss. So-called "semirigid" coax for microwave use is an example. It often uses a steel center wire--which is a terrible conductor, but is inexpensive and strong--coated with a few microns of expensive silver, which has the highest conductivity of any metal, on its outer surface. All the current flows in the silver due to the skin effect.

 

[Bob S]

See picture of skin depth in http://www.rfcafe.com/references/electrical/skin-depth.htm
It varies as 1/f^1/2.
At high frequencies it is a few microns. See table of skin depths at
http://www.rfcafe.com/references/electrical/cond-high-freq.htm

 

[yungman]

Yungman, I wish you'd be a little more careful with answers in areas where you are not expert. The skin effect is exactly as phinds said: at high frequencies all current flows on the outer skin of the conductor, which is why hollow conductors can be used without increased loss. So-called "semirigid" coax for microwave use is an example. It often uses a steel center wire--which is a terrible conductor, but is inexpensive and strong--coated with a few microns of expensive silver, which has the highest conductivity of any metal, on its outer surface. All the current flows in the silver due to the skin effect.

I know skin effect on the surface. OP is talking about a hollow wire, why is the inner surface of a hollow conductor wire not conducting current? Is it because there is no field inside the hollow wire?

 

[jim hardy]

i though your mention of Litz wire was right on.

In my utility scale generator(20Kiloamps) the conductors were long hollow rectangular tubes maybe five by ten inches made of square strands (perhaps 1/4 inch) stacked together and insulated like giant Litz wire.
The strands were intertwined so they did not run full length, about forty feet, in same location but ran partway near inner surface and partway near outer surface.
Cooling gas was forced down the center passageway.

So the inner surface of that rectangular tube conductor certainly had current. But it was only 60hz.

 

[Bob S]

Yungman, I wish you'd be a little more careful with answers in areas where you are not expert. The skin effect is exactly as phinds said: at high frequencies all current flows on the outer skin of the conductor, which is why hollow conductors can be used without increased loss. So-called "semirigid" coax for microwave use is an example. It often uses a steel center wire--which is a terrible conductor, but is inexpensive and strong--coated with a few microns of expensive silver, which has the highest conductivity of any metal, on its outer surface. All the current flows in the silver due to the skin effect.

I fully concur. The skin effect completely shields the inside of the conductors from carrying ang RF current. It is just a form of Lenz's Law. See Equation (4) in http://www.ultracad.com/articles/skin%20effect.pdf

 

[marcusl]

I know skin effect on the surface. OP is talking about a hollow wire, why is the inner surface of a hollow conductor wire not conducting current? Is it because there is no field inside the hollow wire?

No. The concentration of current to the outside of the conductor is related to flux linkage between fields generated by currents at different radii, and to Lenz's law.

i though your mention of Litz wire was right on.

In my utility scale generator(20Kiloamps) the conductors were long hollow rectangular tubes maybe five by ten inches made of square strands (perhaps 1/4 inch) stacked together and insulated like giant Litz wire.
The strands were intertwined so they did not run full length, about forty feet, in same location but ran partway near inner surface and partway near outer surface.
Cooling gas was forced down the center passageway.

So the inner surface of that rectangular tube conductor certainly had current. But it was only 60hz.

Litz wire is not relevant to the original question about solid conductors, Jim. It is, furthermore, useful only at low frequencies where capacitive coupling between turns is small. Strands located near the center of Litz wire still want to carry little current, requiring the strands to be woven so as to alternate between center and exterior of bundle, as Jim said, in order to create some reasonable average current flow. The original question was about solid conductors, however, and there's still no escaping the skin effect there--the interior carries no current at sufficiently high frequencies, allowing it to be eliminated without affecting the AC resistance. All current then flows on the exterior in a thin skin. If some current is still flowing on the interior surface, then the frequency is too low for the skin effect to be in full play.

 

[yungman]

No. The concentration of current to the outside of the conductor is related to flux linkage between fields generated by currents at different radii, and to Lenz's law.
Litz wire is not relevant to the original question about solid conductors, Jim. It is, furthermore, useful only at low frequencies where capacitive coupling between turns is small. Strands located near the center of Litz wire still want to carry little current, requiring the strands to be woven so as to alternate between center and exterior of bundle, as Jim said, in order to create some reasonable average current flow. The original question was about solid conductors, however, and there's still no escaping the skin effect there--the interior carries no current at sufficiently high frequencies, allowing it to be eliminated without affecting the AC resistance. All current then flows on the exterior in a thin skin. If some current is still flowing on the interior surface, then the frequency is too low for the skin effect to be in full play.

I think I find the answer, in a closed cavity inside the conductor, there is no field, so there is no current in the inner surface of the hollow conductor.

Can you provide reference on why the inner strands of Litz wire don't conduct? I do not see any explanation in EM books.

 

[marcusl]

I think I find the answer, in a closed cavity inside the conductor, there is no field, so there is no current in the inner surface of the hollow conductor.

No that is not the reason. If the thickness of the annular conductor is less than the skin depth, then the inside surface carries some current even though B=0 in the hole. The reason is due to flux linkage.

Can you provide reference on why the inner strands of Litz wire don't conduct? I do not see any explanation in EM books.

To clarify my earlier statement on Litz wire: A small strand at the center of a uniform bundle of strands would find itself with flux linkage analogous to the solid case, reducing its current flow. The key to Litz wire, however, is the weave that brings each strand from center to outside and back as you move down the wire's length. Each strand ends up as an average of inner and outer, so all strands carry the same current. You can find the skin effect in round conductors discussed in most E&M texts, but I have no references to Litz wire.

 

[yungman]

I am still digging up notes. My understanding is all signals travel as EM wave. PCB trace, coax, even a wire is really a guided structure for EM wave to propagate. Signal voltage and current are the consequence of boundary condition of E and B. True current in form of electrons CANNOT travel in any speed as given by $v_p=μ\vec E \hbox { where μ is the mobility.}$. It is only EM wave propagation that give the speed we see in circuit.

I am still having a hard time relating Lentz Law, flux linkage to EM propagation. The books I have derive skin depth and attenuation constant using EM wave, not with magnetics.

 

[marcusl]

Yes, we derive the skin effect mathematically with Maxwell's equations and vector calculus. Did you get a good mental picture of why the skin effect occurs by looking at the modified Bessel functions, or ber and bei functions? It's not easy to gain intuition that way. Faraday thought in terms of "flux tube" linkage, which I mentioned because it can provide an intuitive picture of how the effect works. Magnetic field lines (or tubes, as Faraday called them) from current at the wire center link with those flowing in thin shells at greater radii to produce an emf that opposes the current at the center and reinforces it at the surface.

 

[marcusl]

I found this picture and description online that may be helpful in visualizing the skin effect, although I think that the transverse currents shown are a little misleading.
http://books.google.com/books?id=t2TgU-uuNQ0C&pg=PA98&lpg=PA98&dq=skin+effect+round&source=bl&ots=omfhwH8azH&sig=lTO13HAMM7ZpV6dO4vl8hHDP8Jw&hl=en&sa=X&ei=-tSMT4PmAYei8QTAwODNCQ&ved=0CEQQ6AEwBQ#v=onepage&q=skin%20effect%20round&f=false
The view I've been discussing is found in the last paragraph of section 3.4. The full mathematical solution follows in sections 3.5-3.9.

 

[yungman]

I know the flux line is much easier to understand. But from working with RF, I have been more looking at EM point of view. I started working on some guitar pickup circuits lately where people use magnetics instead. I am currently asking questions in the Classical Physics sub forum in how I relate EM with flux circuit and magnetic circuits etc. I am going through my notes again and see what did I forget. If you have any suggestion, I'll be really appreciated.

Simple thing like Faraday's Law $EMF=-\frac{\partial \Phi}{\partial t}\;$ is giving me problem. For air coil, it is easy as varying B pass through the closed area of the coil induce EMF. But what if the middle of the coil is a alnico magnet that is good conductor? Aside from distorting the magnetic field, I have issue looking at it in EM point of view that all field disappeared inside a good conductor. Instead the boundary condition give rise to surface current and charge. How is that relate to magnetic circuit that the flux $\Phi\;$ is continuous through the good conductor core?

Further more, how is eddy current form in the point of view of EM? Bob S answer one part of this question and I still not clear whether this relate to free current density due to boundary condition or there is another mechanism of producing free current in a good conductor.

I know, this is out of this subject, but I have been going around and around on this. Any suggestion will be really appreciated.

Thanks

Alan

 

[yungman]

I found this picture and description online that may be helpful in visualizing the skin effect, although I think that the transverse currents shown are a little misleading.
http://books.google.com/books?id=t2TgU-uuNQ0C&pg=PA98&lpg=PA98&dq=skin+effect+round&source=bl&ots=omfhwH8azH&sig=lTO13HAMM7ZpV6dO4vl8hHDP8Jw&hl=en&sa=X&ei=-tSMT4PmAYei8QTAwODNCQ&ved=0CEQQ6AEwBQ#v=onepage&q=skin%20effect%20round&f=false
The view I've been discussing is found in the last paragraph of section 3.4. The full mathematical solution follows in sections 3.5-3.9.

Is this a good book? I don't mind buying it if it is good. Most of the EM books don't spend a lot of time in magnetics. So far, I have been using Griffiths and Cheng where Cheng is mainly on field and wave and tx lines.

 

[marcusl]

Please ask your questions about Faraday's law in a new thread. This one concerns the OP's question about round and hollow conductors.

I am unfamiliar with the book other than finding it online and reading the two paragraphs on skin effect, which I think are pretty clear.

 

[Born2bwire]

I know skin effect on the surface. OP is talking about a hollow wire, why is the inner surface of a hollow conductor wire not conducting current? Is it because there is no field inside the hollow wire?

The easiest reason is that the electromagnetic wave will never penetrate to the inner surface. The wires are acting as waveguides with the waves traveling between the two wires (if we assume something like a twisted pair). Because of the short electrical length of higher frequencies, the waves will not penetrate into the wires, hence the skin effect. As marcusl pointed out, Litz wire is a different case because it intertwines the outer and inner surfaces.

 

[yungman]

I have been thinking why there is no current on the inner surface in terms of EM wave. This is what I come up with:

I believe the reason is the inner surface is shielded by the hollow conductor. It cannot set up a guided structure even though it has a surface.

In order to form a guided structure, you have to have the forward and return path( unless it is a wave guide). They have to go in pairs to form a guided structure for EM wave to propagate along. Even a single wire in this case, the return path has to be either a wire, a ground plane, or even the Earth ground. But the inner surface of the hollow tube do not "see' a return path and cannot form a guided structure for EM wave to propagate, therefore there will not be current.

Of cause if the hollow is design so the inner circumference is λ/2 type and become a wave guide itself, but this is another can of worm.

Tell me whether this make sense. In higher frequency with skin effect, I would prefer to understand in terms of EM propagation instead of flux.

 

[yungman]

The easiest reason is that the electromagnetic wave will never penetrate to the inner surface. The wires are acting as waveguides with the waves traveling between the two wires (if we assume something like a twisted pair). Because of the short electrical length of higher frequencies, the waves will not penetrate into the wires, hence the skin effect. As marcusl pointed out, Litz wire is a different case because it intertwines the outer and inner surfaces.

For lower frequency, the EM wave can actually penetrate through the hollow tube.

I still don't see why Litz wire loss the advantage at high frequency. Each individual wire is shielded, each wire can form a guided structure with the return path. This is unlike the hollow tube that the inner surface is shielded.

I believe Poynting Theorem and normal TEM wave show that the E point inward to the center of the wire and not radiate out. Why is the outer wire shield the inner wire?

Anyone has article talk about why Litz wire don't work at high frequency?