Talk:Coaxial cable

RG-142

RG-142 often used in aircraft, not test configuration only.

References

TEM or TEM₀₀

I never see this written as TEM₀₀. My library is packed right now, but my recollection is that TM₀₀ = TE₀₀ = TEM. Also, do we need a citation for TEM being the dominant mode? Isn't this one of those cases where we know that that reliable source exists even if we do not cite it? Constant314 (talk) 15:37, 11 June 2022 (UTC)

I see the that is clarification needed instead of citation needed. It is my understanding that there is only one TEM mode, hence "the TEM mode." Constant314 (talk) 16:39, 11 June 2022 (UTC)

I am the person who added the clarification needed tag. I am only vaguely aware of different modes of propagation, and when I first read the sentence as I wrote it because when I visited the hyperlink transverse electric and magnetic mode when TEM was first mentioned in this page, I read:

"Modes in waveguides can be classified as follows:

• Transverse electromagnetic (TEM) modes"

Which is written as plural. And that made me confused about the use of the wording (in a previous revision) as a singular "The TEM mode". Above in this article it did specify the specific TEM00 mode "Power is transmitted through the radial electric field and the circumferential magnetic field in the TEM00 transverse mode" and I made that 00 a subscript. So I was a bit confused when I read this single-mode bullet point sentence without the 00.

If there is indeed only one TEM mode, then I suppose the usage of simply writing the singular "the TEM mode" is valid. But still in that case I would prefer something like "the fundamental TEM mode" here, like how the transverse mode section writes "In coaxial cable energy is normally transported in the fundamental TEM mode." Em3rgent0rdr (talk) 16:50, 11 June 2022 (UTC)

From what I can gather from google now, seems there is only one TEM mode for coaxial cables. Lasers it seems though can have higher TEM modes. So now I'm thinking that "the TEM00 transverse mode" in the sentence in "Signal propagation" section that "Power is transmitted through the radial electric field and the circumferential magnetic field in the TEM00 transverse mode" should be changed to just "the TEM mode" or "the transverse mode". Cause seems to be no need to distinguish from other TEM modes if there is only one. Em3rgent0rdr (talk) 18:29, 11 June 2022 (UTC)

I dug up the reference "Classical Electrodynamics" by Jackson on page 244 and find that it onnly talks about "the TEM mode" (singular) and it seems from what I can understand from that is there is only one TEM mode. That reference doesn't use TEM00 there, and from what I can tell elsewhere on internet, the TEM00 usage is found when talking about lasers, since lasers can have multiple TEM modes which need to be differentiated. So I've deleted the "00" from the TEM when it was first mentioned in this article and also here in the "Single-Mode Band" subsection. I've removed the clarification needed now that I get that there is only one TEM mode. Em3rgent0rdr (talk) 19:53, 11 June 2022 (UTC)

As far as I know, there can be more TEM modes, but there isn't much reason for them. The whole idea behind coaxial cables is that you can run modes with lower frequencies, down to DC, where hollow waveguides have a cut-off frequency. TEM, other than TEM00, would also have a cut-off frequency. I believe they would have radial nodes, and so wavelength much shorter than the radii difference. Also, at that frequency other modes could also propagate. So, in the case of coaxial cables it is implied that one wants TEM, and for that matter, TEM00. As well as I know, both are fine, so you should see what the usual WP:RS say as the WP:COMMONNAME. Gah4 (talk) 22:29, 11 June 2022 (UTC)

ah thanks. I'll leave it as plain "TEM" in the article for now in that case. But if someone who knows this stuff can briefly explain that (maybe in Coaxial_cable#Signal_propagation) that would be nice for others like me who stumble upon the article and wonder about higher TEM modes. Em3rgent0rdr (talk) 23:44, 11 June 2022 (UTC)

Well, actually, Waveguide_(radio_frequency) should probably explain them, along with all the other modes. It is a generalization of waveguide. Gah4 (talk) 02:06, 12 June 2022 (UTC)

Take a really big rigid straight coaxial cable with an air dielectric. Shine a laser through it. The laser light appears on the other side. Obviously, the coax can support all those many laser TEM modes. I know it sounds silly, but there is a continuous spectrum. And before dismising it, I got from reading Feynman. Those laser modes have a frequency much higher than the cutoff frequency of the cables next highest mode. No one would consider a coax for guiding those frequencies. So, we can say the TEM mode, confident that it is the only TEM mode that would ever be used with a coaxial cable. But there are cases where the lowest non-TEM mode is used. Constant314 (talk) 02:26, 12 June 2022 (UTC)

hmm...Waveguide (radio frequency) § Mathematical analysis only writes this on coax TEM:

> "This contrasts with two-conductor transmission lines used at lower frequencies; coaxial cable, parallel wire line and stripline, in which TEM mode is possible. Additionally, the propagating modes (i.e. TE and TM) inside the waveguide can be mathematically expressed as the superposition of two TEM waves." Em3rgent0rdr (talk) 02:28, 12 June 2022 (UTC)

I know that it says that, however, Wikipedia is not a reliable source. But be careful. He said the superposition of two TEM waves and not two TEM modes. It is easy enough to convince yourself that all TE modes in a rectangular waveguide can indeed be decomposed into the superposition of two plane waves, but those waves are not modes of the waveguide. Constant314 (talk) 02:38, 12 June 2022 (UTC)

History Section - Conflicting Information - First Transatlantic Coaxial Cable, 1858 or 1956?

The first entry in the history sections says:

"1858 — Coaxial cable used in first transatlantic cable."

The second to last entry in this section says:

"1956 — First transatlantic coaxial cable laid, TAT-1."

Only one of these can be true. Which one is it? 185.203.219.164 (talk) 19:50, 19 December 2022 (UTC)

1956 was the first telephone cable. the ones before were telegraph cables. Cheers. Constant314 (talk) 22:19, 19 December 2022 (UTC)

Attenuation vs. frequency

Searching the Internet for various graphs of attenuation vs. frequency, I can see that there is a simple relationship. To the first approximation, presumably when resistive and radiation losses are low, the square of attenuation (measured in decibels) is proportional to the frequency. This is important, because companies selling cable usually display attenuation at only one frequency, and it would be helpful to figure out what it is (roughly) at the frequency of interest.

Perhaps someone familiar with academic literature on the subject could post the correct formula, quoted from some relevant manual. I don't have access to one, unfortunately. The formula seems to be: $f_{h}/f_{l}=(a_{h}/a_{l})^{2}$ where $f$ is the frequency, and $a$ is the attenuation in decibels. Morycm (talk) 21:06, 10 February 2023 (UTC)

Here is a brief reply that is slightly WP:OR. There are nine possible frequency regimes (yes, nine) although typically we only concern ourselves with three of them which I will call low frequency (LF), intermediate frequency (IF) and high frequency (HF). LF includes the voice frequency range up until the point when skin effect is felt (perhaps 30 kHz). HF regime is where G/ωC << 1 and R/ωL << 1 or perhaps greater than 10 MHz. The IF regime is in-between. In the LF regime, attenuation (in dB) is approximately proportional to the square root of frequency. In the HF regime, attenuation is also approximately proportional to the square root of frequency, but with a higher proportionality constant than the LF regime. For the attenuation changes smoothly between the LF and HF regimes, it sometimes increases more rapidly than the square root of frequency. Finally, at a high enough frequency, dielectric loss may become dominant (not in an air core coax, of course) and you will see the attenuation increase proportionally to frequency.

Here is a representative plot based on published data and what I consider reasonable extrapolations at very low and very high frequencies. Note: I will collapse this figure to a thumb after the discussion is finished. At 1GHz, you can see the curve start to curve upward as dielectric loss starts to become significant. The transition points between the regimes depend on a number of things, so it is generally not reliable to extrapolate between low frequency attenuation and high frequency attenuation. However, the low frequency attenuation has a simple formula which is $\alpha ={\sqrt {\frac {\omega R_{\omega }C_{\omega }}{2}}}$ where $\alpha$ is the loss in nepers. In this regime $R_{\omega },C_{\omega }$ are roughly constant.

Typical Good Transmission Line Loss

Constant314 (talk) 22:06, 10 February 2023 (UTC)

On inductance of coax

@Constant314

My edit had the purpose of clarifying the specific assumption, used for formula derivation ${\frac {\ L\ }{\ell }}={\frac {\mu }{\ 2\pi \ }}\ \ln \left({\frac {\ D\ }{d}}\right)$

In this formula it's assumed that no magnetic field exists inside central conductor; which is the case for high frequency due to skin effect. However; if current distribution in the center conductor cross-section assumed even (low frequency range); the value of inductance changes to ${\frac {\ L\ }{\ell }}={\frac {\mu }{\ 2\pi \ }}\ \ln \left({\frac {1}{4}}+{\frac {\ D\ }{d}}\right)$ Brsbrs (talk) 17:04, 8 October 2023 (UTC)

Yes, I agree with you. I thought that I reverted my reversion. In general, at low frequency, L includes the internal inductance of the wire. However, that formula is the formula that applies at frequencies high enough for skin effect to be well developed. I was too fast on the revert button. So, my apologies for reverting your entirely reasonable edit. Constant314 (talk) 17:27, 8 October 2023 (UTC)

Actually, I think the formula for low frequency is ${\frac {\ L\ }{\ell }}={\frac {\mu }{\ 2\pi \ }}\left[\ \ln \left({\frac {\ D\ }{d}}\right)+{\frac {1}{4}}\right]$ Constant314 (talk) 17:50, 8 October 2023 (UTC)

Thanks! Yes, you are right, there was a typo in my formula. 1/4 should be outside of the logarithm Brsbrs (talk) 18:36, 8 October 2023 (UTC)

The inductance and capacitance per unit length should come out to give the right propagation velocity. But propagation velocity is only useful at higher frequencies. (Or extremely long cables.) Nice to get the low frequency limit right, but it doesn't come up all that often. Note also, that there are delay cables with a helical center conductor for increased inductance and lower velocity. Or you can figure how long it takes the signal to follow around the helix. Comes out pretty close that way, too. Gah4 (talk) 19:34, 8 October 2023 (UTC)