Calculating current distribution in a HF coaxial cable?

[Cedric Eveleigh]

Hello, I would like to calculate the current distribution in a coaxial cable where the skin effect is significant. I asked this question on stackexchange and I provided pictures and more details there:
http://electronics.stackexchange.com/questions/196617/how-to-calculate-the-current-density-distribution-in-a-high-frequency-transmissi?noredirect=1#comment410148_196617
So far no one has answered but I would really appreciate any help.

Thanks,
Cedric

 

[davenn]

Hello, I would like to calculate the current distribution in a coaxial cable where the skin effect is significant. I asked this question on stackexchange and I provided pictures and more details there:
http://electronics.stackexchange.com/questions/196617/how-to-calculate-the-current-density-distribution-in-a-high-frequency-transmissi?noredirect=1#comment410148_196617
So far no one has answered but I would really appreciate any help.

Thanks,
Cedric

Hi Cedric
welcome to PF

your last main comment on that other site was ...

@Li-aungYip The equation in the wikipedia page is specific to the skin depth of the second picture (regular AC wire) whereas I'm looking to determine the skin depth (or current distribution) in a transmission line for both the outer surface of the outer conductor and for either side of the dielectric layer (i.e. the inner surface of the outer conductor and the outer surface of the inner conductor). In terms of skin depth, this would be three different values.

in a correctly working coax system, there is NO current flowing on the outer conductor ( the braid) it should be at Earth potential
in fact, often measures are taken to ensure that RF current flow on the outer conductor doesn't happen by using BALUNS

So as a result the only conductor skin effect you have to worry about is the inner conductor and those questions were
answered for you with the wiki linksRegards
Dave

 

[Cedric Eveleigh]

Hi Cedric
welcome to PF

your last main comment on that other site was ...in a correctly working coax system, there is NO current flowing on the outer conductor ( the braid) it should be at Earth potential
in fact, often measures are taken to ensure that RF current flow on the outer conductor doesn't happen by using BALUNS

So as a result the only conductor skin effect you have to worry about is the inner conductor and those questions were
answered for you with the wiki linksRegards
Dave

Hi Dave,

If I'm not mistaken, as you can see in this gif of a transmission line's function, the current travels in opposite ways on both the inner and outer conductor and this is how the wire has no magnetic field outside of it (not affected by external EM):
https://commons.wikimedia.org/wiki/...#/media/File:Transmission_line_animation3.gif

Also, as you can see in this picture of the AC frequency in a coaxial being increased from left to right, the current accumulates on either side of the dielectric between the two conductors:
https://commons.wikimedia.org/wiki/File:Coax_and_Skin_Depth.svg#/media/File:Coax_and_Skin_Depth.svg

Because of this I don't think the equations on the Wikipedia page for the skin effect will be sufficient. Maybe I'm missing something?

Thanks,
Cedric

 

[davenn]

Hi,
Sorry, yeah I was going off on a bit of a tangent

I could find very little specific info on Skin effect on the inner surface of the outer conductor

If I'm not mistaken, as you can see in this gif of a transmission line's function, the current travels in opposite ways on both the inner and outer conductor and this is how the wire has no magnetic field outside of it (not affected by external EM):
https://commons.wikimedia.org/wiki/...#/media/File:Transmission_line_animation3.gif

Yes, that is correct for a solid outer conductor where it is a solid tube, or a thin metallic film wrap as used in many coax cables between the outer braid and the dielectric

but there are 2 situations where this situation fails and we get common mode currents flowing along the outside of the outer conductor
1) impedance mismatches between transmitter and transmission line or between transmission line and antenna ... and this is what I was really referring to when I was talking about the use of BALUNS and chokes to stop that current flow

2) a braided outer conductor outer conductor, because of its makeup allows RF currents to be present on the inside and outside surfaces
consider how the braid weaves over itself and at points it's inside and other points it's outside.
I suspect in such a case it would be difficult to study any inner surface skin effect, as the inner surface isn't continuous.

Here is a PDF article that does give some insight into skin effect on the inner surface of the outer conductor ...
http://iet-journals.org/archive/2012/dec_vol_2_no_12/7397481351593914.pdf

if I find anything else I will add it to the thread

The be all and end all of EM, transmissions lines etc is this guy ...
J.D. Kraus, he, in collaboration with others, has written pretty definitive publications on the subject

below is a link to a free copy of the 2nd edition

https://ia600703.us.archive.org/18/items/Electromagnetics_559/KrausCarver-Electromagnetics.pdf

there is at least a 5th edition, behind several different site paywalls

Regards
Dave

 

[Cedric Eveleigh]

Hi,
Sorry, yeah I was going off on a bit of a tangent

I could find very little specific info on Skin effect on the inner surface of the outer conductor
Yes, that is correct for a solid outer conductor where it is a solid tube, or a thin metallic film wrap as used in many coax cables between the outer braid and the dielectric

but there are 2 situations where this situation fails and we get common mode currents flowing along the outside of the outer conductor
1) impedance mismatches between transmitter and transmission line or between transmission line and antenna ... and this is what I was really referring to when I was talking about the use of BALUNS and chokes to stop that current flow

2) a braided outer conductor outer conductor, because of its makeup allows RF currents to be present on the inside and outside surfaces
consider how the braid weaves over itself and at points it's inside and other points it's outside.
I suspect in such a case it would be difficult to study any inner surface skin effect, as the inner surface isn't continuous.

Here is a PDF article that does give some insight into skin effect on the inner surface of the outer conductor ...
http://iet-journals.org/archive/2012/dec_vol_2_no_12/7397481351593914.pdf

if I find anything else I will add it to the thread

The be all and end all of EM, transmissions lines etc is this guy ...
J.D. Kraus, he, in collaboration with others, has written pretty definitive publications on the subject

below is a link to a free copy of the 2nd edition

https://ia600703.us.archive.org/18/items/Electromagnetics_559/KrausCarver-Electromagnetics.pdf

there is at least a 5th edition, behind several different site paywalls

Regards
Dave

The coax in question is impedance matched and the outer conductor is continuous (not braided).
Thanks for linking that paper. The problem is that I'm trying to calculate the current distribution and not the skin depth. In other words, I'd like to determine the current in function of radial distance. From this I could find things like the total maximum current anywhere in the coax.
I appreciate your effort to help.

Cheers,
Cedric

 

[jasonRF]

Cedric,
Are you looking to exactly solve this idealized coaxial cable, or is a simple approximation good enough? If the radius of curvature of the inner conductor is much larger than the skin depth then in both the inner and outer conductors the current will fall off approximately exponentially from the interior surface, just like it does (exactly) on a planar conductor.

Jason