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skin effect, bandwidth, etc.

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PG1995

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Hi

Q1: A copper wire is said to have the bandwidth of 1 MHz. I don't think it conveys the full information about bandwidth supported by a copper wire because bandwidth is highest frequency minus lowest frequency, therefore 1 MHz could be 13MHz-12MHz or it could be 21MHz-20MHz, etc. Do you see where I'm getting confused? Please help me. Thanks.



Q2: Previously, I used to think that a copper wire and a telephone wire are the same. But now I believe I was wrong because it is said that a telephone copper wire has bandwidth of 4 kHz which is enough to carry voice signals. Was I really having it all wrong? What does the term 'copper wire' exactly refer to?



Q3: In this thread you (assuming steveB is reading this) were telling me that a copper wire cannot support high frequencies because at high frequencies a copper wire is more like an antenna and moreover the resistive losses become too much. It looks like it all has to do with the skin effect. I hope I have it right. At high frequencies, the effective cross section will decrease to value that overall resistance becomes quite large and it explains the reason for increased resistive losses at high frequencies. But how a copper wire become a good antenna at high frequencies. I understand that at high frequencies most of current is pretty much flowing at the surface, but how does this phenomenon of current flowing at the surface boundary helps the wire to become a good antenna?

This is the reason which comes to my mind. An accelerating charge radiates energy in form of electromagnetic waves. Electric current is made up of many charges. As the frequency is increased, it means more cycles and hence more acceleration which results in more radiation and this makes it an antenna. Even at low frequency, there is an electromagnetic radiation but as, at low frequency, not much of the current is flowing around the outer edge therefore most of emitted radiation gets re-absorbed into the surrounding atoms. But at high frequency, most of the current flows near the outer edge therefore almost all the radiation goes into surrounding area and very little is re-absorbed. Thank you.


Regards
PG


Helpful Links:
1: https://www.electro-tech-online.com/mathematics-physics/135665-bandwidth-etc.html
2: https://www.electro-tech-online.com/threads/multiplexing-channel-etc.135748/
3: https://en.wikipedia.org/wiki/Skin_effect
4: **broken link removed**
5: https://whatis.techtarget.com/definition/skin-effect
6: https://docs.google.com/file/d/0B_XrsbDdR9NEZEZRRm9GZEwycWc/edit?usp=sharing (formulas for calculating power radiated by accelerating charge)
7: https://en.wikipedia.org/wiki/Larmor_formula
 

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You need to separate the properties of copper as a conductor in time varying fields from the properties of a transmission line. The bandwidth questions are mainly transmission line related as we can design lines that can handle Terahertz signals (confine their fields around or between) with nanoscale copper waveguides or Goubau/Sommerfeld mode surface waves.

Skin effect and antennas: https://vk1od.net/antenna/conductors/loss.htm
https://en.wikipedia.org/wiki/Surface_wave#Electromagnetic_waves
 
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Hi,

I can see part of that text in the first post here is outdated. Fiber now comes directly into the home from the pole. There could be multiple transceivers in the basement for multiple parties in the house, or all share one box.

The fiber that comes into my home comes straight from the pole. It comes into the house through a wall hole and runs directly to the Fios box on the wall. It plugs into a special socket that can interpret fiber optic signals of various frequencies.

The wall box then transmits and receives from the router, telephone, and TV set top box. The line from the wall box to the router is coax, to the TV is another coax, and to the phone is just regular phone cable. The router works with both the PC and the TV set top box providing digital content to the set top box as well as PC.

So things have changed a lot since that was written.

Back when i had DSL, we could only get it if we had what they called "copper" telephone cables, and we had to be close to the station which is still the same i believe, although the bandwidth was increased to 3Mb/s up from the text's quote of 1.5Mb/s, also showing it's age as that was several years ago.
 
Q1: A copper wire is said to have the bandwidth of 1 MHz. I don't think it conveys the full information about bandwidth supported by a copper wire because ...

Of course. You should never expect a simple statement to encompass the full realm of possibilities. There is no mention of geometry/configuration, noise, application, etc. so how can such a simple statement hold much water?

Q2: Previously, I used to think that a copper wire and a telephone wire are the same. But now I believe I was wrong because it is said that a telephone copper wire has bandwidth of 4 kHz which is enough to carry voice signals. Was I really having it all wrong? What does the term 'copper wire' exactly refer to?
Who knows? Your guess is as good as ours. With experience you learn to ignore this type of language. Things like this are meant to give a very rough feel for something, but you are trying to assign precise meaning to it.

Did you ever watch one of those TV documentaries where they are discussing a subject you happen to know very well? Notice how many poor statements and word choices are made? It can really drive you nuts if you let it. This is the difference between superficial learning and deep learning.


Q3: In this thread you (assuming steveB is reading this) were telling me that a copper wire cannot support high frequencies because at high frequencies a copper wire is more like an antenna and moreover the resistive losses become too much. It looks like it all has to do with the skin effect. I hope I have it right. At high frequencies, the effective cross section will decrease to value that overall resistance becomes quite large and it explains the reason for increased resistive losses at high frequencies.


Skin effect is an important effect and requires field theory to understand properly. Radiation is an important effect and also requires field theory to understand thoroughly. However, don't mix the two effects in the learning stage. There probably are cases where considering both effects is important, but for general understanding, you rarely need to mix the two separate effects.

But how a copper wire become a good antenna at high frequencies. I understand that at high frequencies most of current is pretty much flowing at the surface, but how does this phenomenon of current flowing at the surface boundary helps the wire to become a good antenna? This is the reason which comes to my mind. An accelerating charge radiates energy in form of electromagnetic waves. Electric current is made up of many charges. As the frequency is increased, it means more cycles and hence more acceleration which results in more radiation and this makes it an antenna. u.
Yes! This is the cause of radiation; the fundamental property that accelerating charges emit photons. That fact is a mystery of nature, but its truth is the basis of how electromagnetic radiation works. The skin effect is not relevant here. It's just a side effect.

Even at low frequency, there is an electromagnetic radiation but as, at low frequency, not much of the current is flowing around the outer edge therefore most of emitted radiation gets re-absorbed into the surrounding atoms. But at high frequency, most of the current flows near the outer edge therefore almost all the radiation goes into surrounding area and very little is re-absorbed.
No! When we do calculations for radiation, we assume a thin filamentary wire is the radiation source. Skin effect is not considered significant here. Yes, skin effect happens, but it does not significantly effect the radiation effects. The low frequency issue is related to rate of change (as you noted above) because a time derivative shows up in Maxwell's equations, and because at low frequency the antenna size need to be so very large, that we probably didn't make it large enough.
 
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Hi

Could you please help me with these queries? Thank you.

Regards
PG
 

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PG1995 said:
Hi

Q1: A copper wire is said to have the bandwidth of 1 MHz. I don't think it conveys the full information about bandwidth supported by a copper wire because bandwidth is highest frequency minus lowest frequency, therefore 1 MHz could be 13MHz-12MHz or it could be 21MHz-20MHz, etc. Do you see where I'm getting confused? Please help me. Thanks.

Disregard. This is advertising copy made up by some putz from the marketing dept who has NO idea what he's writing about. It's utter nonsense.

Q2: Previously, I used to think that a copper wire and a telephone wire are the same. But now I believe I was wrong because it is said that a telephone copper wire has bandwidth of 4 kHz which is enough to carry voice signals. Was I really having it all wrong? What does the term 'copper wire' exactly refer to?

This was the case back in the 19-oughts when telephone systems were purely passive. Back in those days, they actually installed loading coils at regular intervals to improve the characteristics for passive phone transmittions. Then common carrier systems began to come on-line in the 1920s, making it necessary to remove all those loading coils installed a decade earlier. The BW was limited to 4.0KHz so they could push more signals down the wire.

Q3: But how a copper wire become a good antenna at high frequencies. I understand that at high frequencies most of current is pretty much flowing at the surface, but how does this phenomenon of current flowing at the surface boundary helps the wire to become a good antenna?

It doesn't. As frequency increases, wavelength decreases. When the frequency becomes high enough, even a few inches can become a significant percentage of wavelength. If that happens, you get radiation whether you want it or not.

This is the reason which comes to my mind. An accelerating charge radiates energy in form of electromagnetic waves. Electric current is made up of many charges. As the frequency is increased, it means more cycles and hence more acceleration which results in more radiation and this makes it an antenna. Even at low frequency, there is an electromagnetic radiation but as, at low frequency, not much of the current is flowing around the outer edge therefore most of emitted radiation gets re-absorbed into the surrounding atoms. But at high frequency, most of the current flows near the outer edge therefore almost all the radiation goes into surrounding area and very little is re-absorbed. Thank you.

Has nothing to do with frequency. Consider: at 60Hz, the wavelength is 5.0E6 meters. A quarter wavelength of that is 1.25E6 meters. That's 776.71 miles. If you built a vertical antenna that tall (and satellites in LEOs didn't knock it down) it would radiate just as effectively as a 41 foot tall vertical operating at 6.0MHz. At 60Hz, any length of wire is going to have miniscule radiation resistance. It's only when considering cross-continent power lines that you have to begin to worry about radiative losses at power line frequencies.

That's the problem with low frequency work: everything gets big and very tall. Many a ham got knocked off the 160M and 80M bands by home owner associations that didn't appreciate the sight of an efficient vertical in the back yard. The high ends of the ham bands, VHF and UHF can be worked with less conspicuous antennae.
 
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Hi Steve

I believe I had it wrong in my previous post. I was thinking that a coaxial cable overcomes the limitations imposed by skin effect in addition to minimizing radiation effects (in other words, it doesn't become a good antenna). In short, it's not affected by the skin effect even though the signals it carries consist of very high frequencies.

Q1: Is this true that the configuration of a coaxial cable doesn't help with the skin effect? I would request you to re-read my question statements of Q1 and Q2 to see how I view the build-up of skin effect in a conductor, and question statement of Q3 to see how I thought that using a coaxial cable eliminates the skin effect. I was only after a basic intuitive explanation.

Q2: In physics, total energy and momentum of a system are always conserved. When the magnetic fields of inside and outside conductors cancel each other, where does the energy of the magnetic fields go? In my view, a coaxial cable helps to prevent the energy escaping the wire in form of magnetic fields, and further elimination of magnetic fields means no interference.

Thank you for the help.

Regards
PG
 

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For Q1, coaxial cable has no special ability to prevent skin effect. The current can only penetrate a certain depth into the conductors. However, special stranded wire, called Litz wire, can reduce the effects, or thin walled conductors (essentially tubes) can be used.

For Q2, remember that the energy in magnetic and electric fields is a potential energy. The energy does not need to go anywhere. The coaxial line supports a particular field pattern and as the voltages and currents create those fields, then energy is stored in that particular field configuration.

However, I understand the gist of your question, and there is a viewpoint you can consider to answer your question. Let's consider only the static case for either a magnetic field or an electric field. The magnetic field would be created by the currents in the conductors, and the electric field would be created by charges on those conductors. The latter case is basically a cylindrical capacitor.

For the magnetic field, consider the shield and the center wires separated by a large distance, but each having the correct current flow. Imagine the conductors are parallel and far apart. There will be a particular stored energy in the associated magnetic fields from these conductors. Now, consider the normal coaxial line with the same currents. The field configuration is different, and the stored energy is different. How do you now account for the difference in the field energies? Well, that is simple because parallel conductors with currents flowing will experience a force between them. Hence, in order to get from one configuration to the other, work must be done on the system, or the system must do work on something else, depending on the polarities of current and on which way you move.

For the electric field, you can do the same idea. The conductors can be charged with equal and opposite charges, and consider the coaxial line compared to the separated conductors. The electric fields are different in both cases and the potential energy is different in both cases. The difference in energy is equal to the work that must be done by forcing the conductors together, or forcing them apart.
 
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