Talk:Transmission line

Input impedance of transmission line

In

$Z_{in}\left(l\right)={\frac {V(l)}{I(l)}}=Z_{0}{\frac {1+\Gamma _{L}e^{-2\gamma l}}{1-\Gamma _{L}e^{-2\gamma l}}}$

exponent 2 is due to back and forth reflection?

— Preceding unsigned comment added by 82.56.167.93 (talk) 07:48, 4 August 2014 (UTC)

Yes, $\scriptstyle {2l}$ is the distance from measurement point to the load and back again and so $\scriptstyle {e^{-2\gamma l}}$ is the phase delay for the round-trip, and $\scriptstyle {\Gamma _{L}e^{-2\gamma l}}$ is the voltage amplitude of the reflected wave relative to that of the incident wave. --catslash (talk) 17:52, 4 August 2014 (UTC)

Input impedance of transmission line: the reason(s) why $Z_{in}\neq Z_{0}$

In
"Since most transmission lines also have a reflected wave, the characteristic impedance is generally not the impedance that is measured on the line",
for completeness sake, shouldn't it be:
Since most transmission lines also have reflected waves and standing waves...?

I am not an expert but I am just reading here and there and it seems to me that those 2 are different phenomena:

• reflected waves are due to unmatched lines (terminations);
• standing waves may be generated by reflected waves, which thing usually happens;
  

don't both of them contribute to the reasons why $Z_{in}\neq Z_{0}$?

This way, the reasons why $Z_{in}\neq Z_{L}$ should be

• losses due to R and G of the line that we often neglect;
• reflected waves;
• standing waves;
  

— Preceding unsigned comment added by 95.237.220.142 (talk) 09:22, 6 August 2014 (UTC)

The standing wave is due to interference of the incident and reflected wave. It is not a separate phenomenon. The input impedance is a function of distance, ZL, Z0 and γ. The last two are functions of R and G amongst other things, but are not additional parameters needing to be taken into account—they are already included. SpinningSpark 14:24, 6 August 2014 (UTC)

Agree with Spinningspark: Reflected waves are the cause, standing waves are the effect. If you say that the measured impedance is affected by reflected waves, that already implicitly includes anything related to standing waves too. --Steve (talk) 14:53, 6 August 2014 (UTC)

"Schematic showing how a wave flows down a lossless transmission line" is wrong

Why has no-one noticed that the handy animated diagram at the top of the paper is wrong? Current maxima occur in parallel along the two wires. At the load the current must be at a maximum at both ends of the load simultaneously to satisfy charge conservation. I propose to delete it at a date at least 2 months from today. 77.96.212.249 (talk) 16:27, 24 October 2014 (UTC)

"Current maxima occur in parallel along the two wires" -- yes, when the electrons are moving most quickly leftward in the bottom wire, at the same moment directly above they are moving most quickly rightward in the top wire. That's what you're saying, right? I believe that this is true in the animation. For example, at the left edge, you can see the electrons entering the image on top at the same time as they exit the image on the bottom, and vice-versa.

The black dots represent electrons. So a violation of charge conservation would be black dots appearing out of nowhere, or disappearing. This does not happen in the animation. Do you agree?

I made the animation, so I'm biased. :-D But that also means I can easily correct it if I made a mistake. (But I don't think I did.) --Steve (talk) 16:38, 24 October 2014 (UTC)

I don't know what to make of the dots; it isn't intuitively obvious what electrons being bunched together has to do with current.

As for the voltage, the caption is unclear. Is a low voltage the most negative voltage, or does it mean low RMS voltage? Jc3s5h (talk) 17:06, 24 October 2014 (UTC)

Stare at just one of the dots, ignoring everything else. Watch as it moves back and forth. Is the dot moving left? That means there are electrons moving left, i.e. there is a current flow. Is the dot stationary? That means that the electrons are stationary, i.e. the current is zero at that location and time. Does that make sense?

I was assuming that most readers would find it intuitively obvious that when electrons move, it's a current. Is there any other way to think about current? That said, if you find it confusing then it's a safe bet that other people do too! So I hope you will help me understand where you're coming from. :-D

The color is instantaneous voltage, not RMS voltage. (RMS voltage does not oscillate :-P ) Do you think it would help if I changed the sentence from "Red color indicates high voltage, and blue indicates low voltage." to "Red color indicates a more positive voltage, and blue indicates a more negative voltage." ? Or is there another wording that would be better? --Steve (talk) 17:59, 24 October 2014 (UTC)

It would be much clearer if the load was electrically small instead of distributed over 5λ/16. If we assume the load is actually electrically small but simply not drawn to scale, then it should carry no current at all (because the upper and lower loops are each precisely λ/4 long, and therefore each present an infinite impedance in series with the load. --catslash (talk) 18:31, 24 October 2014 (UTC)

Diagrams are supposed to make the text easier to understand. If the reader has to ponder the drawing for 15 minutes to figure out what it means, it should probably be deleted. I especially object to complex drawings that move. If I'm having trouble understand something, I want it to stay still while I try to figure it out. Right now, it reminds me of a clay pigeon. The way to deal with those is to avoid thinking; just point and shoot. Jc3s5h (talk) 18:42, 24 October 2014 (UTC)

Catslash - This is a good point. I was imagining not only the load but also those thinner wires are electrically small (but not drawn to scale). Does that make sense? Now that you have pointed it out, I can see how that's very confusing!

Therefore I propose to erase the load altogether, and just have a simpler image with the two thick wires going straight through from one side of the image to the other. Basically I would crop off the right side of the image. Do you think that would help?

Another option is making an electrically small impedance-matched resistive load that is very small (drawn to scale), and with no weird leads. But I'm not sure how to fit it or what it could look like.

Jc3s5h: You are welcome to argue that the animation should be removed entirely. I disagree of course. We can see what other people think. But maybe you can also spend a minute thinking about how to improve the animation and/or caption (or as you might say: make it less bad)? For example, I proposed a small change to the caption text above, can you comment on it? Or suggest other changes that would make it easier to understand? --Steve (talk) 19:26, 24 October 2014 (UTC)

I like animations, but this one confuses me too. For me, it moves too fast to make sense of it. I think what might work better is a single pulse with some dead time before the next pulse.Constant314 (talk) 21:11, 24 October 2014 (UTC)

Yes, it's conventional is some contexts to draw transmission lines in bold and electrically small connections thinner as in your file:Smith_chart_explanation.svg diagram. However in mapping the current distribution, the actual size of the various parts is important, and so the change of scale is confusing. It's particularly unlucky that you chose 160 pixels for λ and 40 pixels for the loops! It's not necessary for the load to resemble a IEC-style resistor symbol, it could just be a small spot, maybe a small spot glowing red hot or even a small spot with a glow pulsing at the power harmonic.

There are a couple of other possible objections to the diagram as it presently stands. Firstly, the use of colour to show the 'voltage'; there is no well-defined electrical potential here as the E-field is far from conservative. In particular there is a potential gradient between the two conductors but not along them (assuming high conductivity), whereas in the diagram there is a prominent longitudinal colour gradient. It's more common to depict the E-field as arrows from one conductor to the other, bunched up where the field is strongest - but I don't know how you would animate that.

The second (lesser), objection is that the moving electrons should be on the surface facing the other conductor and not on the outer side. --catslash (talk) 21:25, 24 October 2014 (UTC)

Catslash - a highly conductive (or even infinitely conductive) wire can have an electric potential gradient along it [Update: Sorry, I was wrong here. I should have said "voltage drop down it, sorta".] ... if it's inductive! Which in this case it is! So, I agree that there are situations where there is no well-defined electric potential but I don't think this is one of them, luckily. The longitudinal color gradient is a correct representation of what's going on with the distributed inductance. Maybe the caption could even say this? "Voltage drops between the wires are related to capacitance, while voltage drops along the wires are related to inductance"...

Basic physics says that there is never a E-field component directed along the surface of a pure conductor. The E-field is the gradient of the potential only when a potential exists. The condition for a potential to exist is curl(E) = 0, which is not the case in the space round a transmission line where at every point curl E = dB/dt (one of Maxwell's equations). I'm not a fan of descriptive physics but one can think of the 'voltage' induced by a changing magnetic field linking a closed loop even though it's made from a perfect conductor, and this is a similar case where there is a potential across the ends of the loop even though there is no E-field (potential gradient) along the loop. 77.96.212.249 (talk) 12:33, 26 October 2014 (UTC)

The so called retarded potentials are always well defined except in impossible situations like inside a perfect conductor. Constant314 (talk) 20:54, 27 October 2014 (UTC)

Well, I'm going to try re-making the diagram with various changes: Make the waves move slower, make the wavelength longer, and throw out the terminal resistor altogether (notwithstanding Catslash's good suggestions to improve it). I think all these changes will make it easier to see what's going on. I will also put the electrons inside the wires, at the appropriate sides, assuming that it looks OK. Thanks again for the suggestions and feedback :-D --Steve (talk) 23:26, 24 October 2014 (UTC)

Look at the diagram: electrons bunched up means electrons changing direction - zero current. Electrons spaced out means electrons travelling quickly - maximum current. At the feed point, the diagram shows maximum current on one side coinciding with zero current on the other side, a breach of charge-conservation. 77.96.212.249 (talk) 16:07, 25 October 2014 (UTC)

Responding to _.249, The driver, if it is balanced, pulls electrons off one wire and puts them on the other wire. As a result a maximum of the electron density (electrons bunched up) is matched by a minimum of electron density (electrons spaced out) on the other wire as the signal travels down the transmission line. The minimum and the maximum meet at the load and cancel each other.Constant314 (talk) 23:14, 26 October 2014 (UTC)

77.96.212.249 - What Constant314 said, and also: The electrons at the center of a bunch are not stationary. On the contrary, an electron at the center of a bunch has the maximum possible rightward velocity. I hope this is easier to see in the new version -- take another look. :-D --Steve (talk) 14:37, 27 October 2014 (UTC)

Most people tend to think of a voltage signal traveling down a transmission line, but it is just as valid to think of it as current signal and they are related by the characteristic impedance. In the usual situation where the characteristic impedance is real, the peaks of voltage and the peaks or current are coincident. Constant314 (talk) 20:54, 27 October 2014 (UTC)

Yes, inductance must exist. A lossless, inductanceless line implies infinite wave velocities, which is impossible of course. Any geometry that gives rise to capacitance, must give rise to inductance through duality. SpinningSpark 00:12, 25 October 2014 (UTC)

Before re-making the diagrams you might want to review some field equations and reconsider your assertion that there is a longitudinal potential gradient (that is a longitudinal E-field and so not a TEM wave). There is of course inductance, but almost all of this is in the dielectric and hardly any in the metal (because the volume of the skin is very small compared with the volume of the dielectric). --catslash (talk) 00:24, 25 October 2014 (UTC)

It is easy to suppose that if there is a voltage drop straight across between the terminals of a coil of wire, then the same voltage drop must exist between the terminals following the path of the wire, but this is Kirchhoff-think and isn't so. The voltage drop for the round trip across the gap between the terminals and back along the path of the wire is equal to the rate of change of magnetic flux linking the path and is in general non-zero. If the wire is a (hypothetical) perfect conductor, then the voltage drop along the portion of the path following the wire is zero, while the voltage across the gap is non-zero. The same is true for the transmission line; the fact that the voltage between the two conductors is different at different points along the length does not require a counterbalancing voltage drop along the conductors. It can be very irritating when people presume to tell you what you think, so please forgive me if this wasn't your line of reasoning. --catslash (talk) 02:08, 25 October 2014 (UTC)

I think what happens is that there is an electric potential and a magnetic potential and that the E-fields produced by these potentials cancel each other. So there is an electric potential distribution along the wire but the E field tangent to the wire is zero. I have not run the numbers, but the directions of the E-fields produced by the two potentials are in opposite directions. Or it's too late at night for me to think straight. :) Constant314 (talk) 06:34, 25 October 2014 (UTC)

Yes, it is of course possible to define a vector potential $\scriptstyle {\mathbf {A} }$ and scalar potential $\scriptstyle {V}$ such that

$\mathbf {E} +{\frac {\partial \mathbf {A} }{\partial t}}=-\nabla V$

and

$\mathbf {B} =\nabla \times \mathbf {A}$

but many readers will not be sufficiently familiar with classical electromagnetism to understand the voltage in the animation in this way. --catslash (talk) 11:31, 25 October 2014 (UTC)

Yes, very few (I would guess less than 1%) would understand the role of the vector potential and I don’t suggest try to add it to the animation. I only mention it because it tends to validate the Steve’s animation which shows an electric potential that varies along the wire. The animation is, I believe, correct, even if the typical reader will not understand all its implications. That is the case with most of E&M.; it is complicated and it is difficult for the animator to get all the details into the animation. I think that, in this case, it would be sufficient to say that although there is a non-zero component of voltage gradient along the wire, there is no E-field component along the wire due to magnetic effects.

But, looking at it a different way, a voltage drop across the inductance is assumed in the derivation of the telegrapher’s equations. Constant314 (talk) 15:29, 25 October 2014 (UTC)

Your comments are very helpful! (Especially catslash's). Here is where I stand so far:

(1) If you naively look at the animation and compare it to the equation V=L*dI/dt, it works perfectly. This cannot just be a coincidence. It suggests that this plot of V reflects some kind of deep truth about how the transmission line works, even if it's not immediately obvious what the details are. :-D

(2) I definitely agree that there is no electric field along the wires (TEM wave).

(3) There is a question "What is the exact voltage distribution inside an inductor (the coil and core) and how is voltage defined there?" This question does not come up in normal circuit theory education because you only care about the effect of the inductor on the outside world (the rest of the circuit); and in the outside world there is always a well-defined V with ∇V=E. Unfortunately, this is not good enough for distributed inductance. :-P

(4) My #1 vote right now is not throwing out the colors but rather adding clarification / cautionary text to the caption. Maybe as simple as "Voltage drops between the wires are related to capacitance (Q=CV), while voltage drops along the wires are related to inductance (V=L*dI/dt)." At least that might get people in the mindset of thinking about lumped-component models (cf Telegrapher's equations) where "voltage drop" would be a literally correct description. --Steve (talk) 17:13, 25 October 2014 (UTC)

If you have a voltage drop along the wires, by duality you would have a current drop between the wires. Curent drop between the wires also shows up as part of the derivation of the telegrapher's equations. Constant314 (talk) 18:20, 25 October 2014 (UTC)

Here is a snap shot of a differential Gaussian pulse as I understand it:

A differential Gaussian pulse on a two-wire transmission line showing electron density, currents, electric potential, magnetic vector potential

Constant314 (talk) 18:20, 25 October 2014 (UTC)

HERE is a new version draft with just those minor changes I mentioned above.

It looks correct to me. Constant314 (talk) 22:36, 25 October 2014 (UTC)

As I said, I think it is correct, but it is visually difficult for me. I think that it is because the red and blue areas are propagating, but the electrons are oscillating about their rest position. All of which is correct. I have two ideas about. First, just make the electrons smaller so its easier to see the propagation. Visually, for me, the electron motion is dominant. The other possibility is to add another animation in the same picture, above the present transmission line that is the same except it has no electrons. That way you can see the propagation of the voltage clearly and then your eye can look down and see what the electrons are doing. But, good work. Constant314 (talk) 20:20, 27 October 2014 (UTC)

Constant314 - I agree with that. --Steve (talk) 22:18, 25 October 2014 (UTC)

Smaller electrons HERE (it's also smoother in general because I switched to subpixel-accurate rendering). But I'm not sure it helps much with the issue you mentioned (that it's not obvious that there is something moving right). So I also tried THIS, with a bit shorter wavelength, I think it's better but you're entitled to disagree. :-D --Steve (talk) 12:05, 28 October 2014 (UTC)

I liked them both better but prefer the second one. It's easy for me to think of things for you to do, but I think an animation of a pulse would be more elucidating. Constant314 (talk) 21:16, 28 October 2014 (UTC)

I like having an animation of the electron motion. It is such a common misconception that electrons travel at enormous speed down the wires. Animations like this help to dispel that misconception. But I do agree with Constant314 that a graphical representation of the voltage would be more intelligible than coloured voltages (if that is what he meant). I don't think it really matters whether it is sinusoid or pulsoid. There are two problems with the coloured voltages as I see it. One is that there is an implication that there is a definite voltage between each conductor and some external reference. This is not necessarily the case, a transformer coupled line is isolated from earth or any other external reference. The other problem is that information that relies on colour has accessibility issues. I also agree that it is easy to think of things for other people to do and I would be happy with the diagram staying as it now is. SpinningSpark 01:23, 29 October 2014 (UTC)

I tried making some pulses, for example SAMPLE PULSE. So far I don't find it any easier to "read" than the oscillation animation. But other people are welcome to disagree...

Thanks for the effort. After I study it, it makes more sense to me. But, why not have both?Constant314 (talk) 22:29, 5 November 2014 (UTC)

Arbitrary editing break

On voltages: If we want to say nothing at all about voltage, it is very easy to do: Just rewrite the caption to say "colors represent charge densities". Anyone can do this right now, without changing the animation.

So then the question is: Should we eliminate all mention of voltage in the caption? Personally, I would say no. I think that mentioning voltage (with very careful wording) creates more enlightenment than confusion. But that's mainly a judgment call related to pedagogy, and I could be wrong.

I have always understood the colors as representing relative voltages between the conductors.Constant314 (talk) 22:33, 5 November 2014 (UTC)

Spinningspark, I don't understand your position on this. You wrote "there is a [false] implication that there is a definite voltage between each conductor and some external reference", which suggests that you think we shouldn't mention voltage at all. But you also wrote, "a graphical representation of voltage would be more intelligible than coloured voltages", which suggests that you don't mind discussing voltage. Which is it? --Steve (talk) 21:38, 5 November 2014 (UTC)

I very much think we should be discussing voltage and I further think that it should be represented in any diagram aiming to give an understandable representation of what happens on a transmission line. My issue is that the colours do not, Constant314's comment notwithstanding, represent the differential voltage between conductors. It is only the differential voltage that is of any relevance here and at any one point along the line there can only be one differential voltage. However, each point along the line in the diagram is showing two voltages, a red and a blue (positive and negative?). This implies they are red and blue with respect to some external reference. One could argue, of course, that they are red and blue with respect to each other, but I would humbly suggest that that is totally confusing to the reader. That would mean you would be showing the same voltage twice, referenced to two different points in two different colours.

A possible way round this is to show one voltage, in one colour, between the two conductors. However, as I said in my original comment, I don't think this is the right way to display the voltage. It would be much clearer, and more understandable, to show it as a plot with distance colinear with the line. SpinningSpark 23:53, 5 November 2014 (UTC)

Can we fix it with a few words, such as saying the red and blue indicates voltage relative to the common mode voltage and if the common mode voltage happens to be zero, then the colors represent voltage with respect to ground. Of course if it were coax we would probably say the shield is ground and we might see both red and blue on the center conductor. Constant314 (talk) 01:27, 6 November 2014 (UTC)

It's always possible to talk yourself around it, but as I said, it is an unnecessary complication and detracts from the clarity that having a diagram is supposed to bring in the first place. It is also less than general as it does not properly represent a transformer isolated line. SpinningSpark 01:38, 6 November 2014 (UTC)

I'm coming around to your point of view. The colored area should be the dielectric. It should be blue when there is an excess of electrons at the top and red when the excess is at the bottom. Obviously the assignment of red or blue is arbitrary.Constant314 (talk) 04:49, 6 November 2014 (UTC)

Thanks everyone, this is very helpful, I think we are making progress.

How about if I get rid of all the colors and put little arrows between the wires, which point up or down based on the electric field? (A bit like the arrows here) --Steve (talk) 13:35, 6 November 2014 (UTC)

I like the arrows. You could have both and make them coloured. The diagram is surprisingly good at depicting a forward travelling wave, I wasn't expecting that. SpinningSpark 13:56, 6 November 2014 (UTC)

Arrows are what I see in most textbooks. That is, they focus on the fields instead for the voltages and currents. Regarding the pulse, I think it might be better if he pulse width were smaller and as a refinement perhaps pulses of alternating polarity so that is compatible with transformer coupling.Constant314 (talk) 14:08, 6 November 2014 (UTC)

E-field arrows, 1st draft, at http://sjbyrnes.com/anim602.gif. Feedback? :-D --Steve (talk) 14:27, 7 November 2014 (UTC)

The arrows are great. They really demonstrate that the voltage or E-field is sinusoidal. I am having trouble tracking the electrons relative to the voltage. It takes almost the full period for me to visually lock on a bunch of electrons. By the time I acquire a bunch, they are just about ready the move off of the end of the transmission line. Maybe if it was twice as long would be easier for me to follow because I would have be able to focus on a bunch of electrons for a longer time. But great work. Constant314 (talk) 15:29, 7 November 2014 (UTC)

I think it's fine. Constant, the electrons never move off the end of the line (except for those that are very close to the end to begin with, and then they only move off temporarily). They only shuffle back and forth around a reference position. Making the line longer won't make that any clearer. What might help you, is that I found it much easier to track individual electrons if I magnified the diagram. Anyway, it's certainly an accurate depiction. SpinningSpark 16:42, 7 November 2014 (UTC)

Spark, I know what the electrons do, but I see that my comment might suggest otherwise. I'm not actually watching the electrons; I'm watching peaks in the electron density wave. I am trying to see it as a person who doesn't know what the electrons are doing and I am trying to validate the animation by seeing if the current peaks where it should and is zero where it should be. I'm glad you can verify that the animation is accurate. I think it is accurate, but I cannot verify it. Usually there is no animation from a reliable secondary source to cite as justification for an animation. You would know more about that than I would. I suggest that an animation should be verified by at least two editors and I am trying to be the second one.Constant314 (talk) 17:13, 7 November 2014 (UTC)

Ah sorry about that. Actually, I was quite surprised that you were apparently having the difficulty I thought you were having. I should have known better. I would still recommend magnifying the diagram to get a better view. Windows magnifier works quite well if you have it. Perhaps Steve can make the native image larger so that it can be magnified within Wikimedia. SpinningSpark 17:47, 7 November 2014 (UTC)

Arrows are much better! --catslash (talk) 19:18, 7 November 2014 (UTC)

Constant314 -- In the version I uploaded, I made the wavelength slightly smaller so it's slightly more visually obvious where the high-electron-density regions are. Maybe that will help? I would increase the whole image size, but the manual of style frowns on images wider than 300px for some reason (I bet it's something to do with how the article looks on a smartphone.) --Steve (talk) 00:49, 10 November 2014 (UTC)

Yes, I can see the features quite well. It's been a pleasure collaborating with you.Constant314 (talk) 04:01, 10 November 2014 (UTC)

There is also this image in the article. SpinningSpark 02:03, 10 November 2014 (UTC)

Yes, I'm planning to redo the open+short image in the same style :-D --Steve (talk) 13:06, 10 November 2014 (UTC)

Finished: [1]. Then I also made one more, [2], at the suggestion of Constant314. I added the latter to the smith chart article, but I don't see a good place for it here. --Steve (talk) 15:18, 15 November 2014 (UTC)

Language version

I'm not sure that I can agree with marking this article as American English. The relevant passage of WP:RETAIN says;

When no English variety has been established and discussion cannot resolve the issue, the variety used in the first non-stub revision is considered the default. If no English variety was used consistently, the tie is broken by the first post-stub contributor to introduce text written in a particular English variety.

The version pointed to by user:Jc3s5h is undoubtedly a stub, being merely a semi-automated copy-paste from the glossary of Federal Standard 1037C, along with hundreds of other stubs created in the same way at that time. The first non-stub contribution is this edit by user:Heron. That contribution is unarguably written in British English. SpinningSpark 03:53, 12 May 2015 (UTC)

If you wish to change it, feel free. As you know, it's not that easy to spot which is the first non-stub version to use a national variety of English, what with all the wiki markup and author names that the spell-checker doesn't recognize. Jc3s5h (talk) 17:14, 12 May 2015 (UTC)

Thanks for replying. I'll leave it for a day or two to see if anyone else comments. SpinningSpark 19:19, 12 May 2015 (UTC)

• Use Oliver's English. Glrx (talk) 20:36, 12 May 2015 (UTC)

Telegrapher's equation: Figure transmission line element error

The figure of the transmission line element in the section of the Telegraphers equation is wrong. The conductance of the line is modelled as a resistance, therefore the value of the conductance should be (1/G)*dz. — Preceding unsigned comment added by Qvandenbrande (talk • contribs) 09:48, 5 August 2016 (UTC)

It is correct is shown. The symbol is a resister, but the text clearly states that G is the conductance per unit length. We can specify a resister by its resistance or its conductance, but we use the same symbol regardless of whether we are specifying resistance or conductance. Constant314 (talk) 14:01, 5 August 2016 (UTC)

ABCD parameters

I have just removed this addition to the article

I have a number of problems with this:

• Primarily, it is uncited, especially problematic is the numerical values of line length at which the various approximations apply. We definitely need a reference for that.
• The parameters Y, Z Y', Z' are all undefined.
• I might have been inclined to sort out the problems with the table formatting if that was the only problem, but as it stands, I though it best to remove it from the article.
• The addition opens with "we can also model..." The ABCD parameters are not an alternative to two-port modelling, but one specific instance of them among many. The AD-BC=1 requirement is a statement that the network is reciprocal and the A=D requirement is a statement that the network is symmetrical. Analogous requirements exist for other forms of two-port parameters. The requirements for reciprocity and symmetry could be stated more generally, and more clearly, without the need to invoke ABCD parameters. SpinningSpark 11:28, 23 November 2016 (UTC)

Transmission line approximations

This recent section seems to be specific to power transmission lines and the article is specifically not about power transmission lines. Certainly 10km is a long line for audio and its short approximation is RC. 1km is a long line for video. 100m is long for RF. Perhaps this information should to into an article about electric power transmission. Constant314 (talk) 23:13, 7 December 2016 (UTC)

I've just reverted it again, partly for the reason you give (@Clarksonchang:), widely spaced in air, chunky power transmission lines may well be dominated by series inductance, but typical telecomm cables are not. The lumped approximation we used to use for short audio lines (couple hundred metres) was series resistance and shunt capacitance. That worked pretty well. I also suspect this is a copyvio, probably from this book. The image in the "long line" section certainly is. Commons have already deleted it once, and seem about to delete it again. In any case, the "long line" section has exactly the same analysis as already in the article so is quite redundant.

On the wider question of whether power lines should be included on this page, I don't see any overriding reason why not. The theory and analysis is exactly the same, even if the numbers and approximations are different. We just need to be clear what is being presented. SpinningSpark 00:24, 8 December 2016 (UTC)

Currently the disambig sentence at the beginning essentially says that it's not about power lines. They really are two different meanings of "transmission line", even if they are technically unify-able. If they were in the same article, I think that terminology (2 meanings) would need to covered.North8000 (talk) 18:16, 30 January 2017 (UTC)

Single Wire Transmission line

I've noticed that in the examples there is a "Single-wire line" subsection. It points to unbalanced line, and also discribes the line as still being a two-line TL, just with the earth (or some other external thing) as the return. I feel that this should also mention single-wire transmission lines. Although one could argue that they are not truely transmission lines as they are more similar to dielectric waveguides (at least from what I understand), they should perhaps be mentioned as many authors cover them as "SWTs" or single wire transmission lines, and a reader could thus look them up and find them here, with an incorrect discription (For that specific type). There are a couple of IEEE references that could easily be pointed to, as well as perhaps a link to the article on the Goubau line? TheUnnamedNewbie (talk) 16:26, 30 January 2017 (UTC)

What is j? What is ɯ? The article doesn't tell me.

A interested layman asking. — Preceding unsigned comment added by Koitus~nlwiki (talk • contribs) 18:21, 21 November 2018 (UTC)

$j$ is the imaginary unit, $\omega$ is angular frequency, and the expression $j\omega$ is the imaginary part of complex frequency. You are right, the article could be a lot better at explaining its notation. --SpinningSpark 18:34, 21 November 2018 (UTC)

RF vs. Power transmission lines

@Spinningspark: I was trying to disambiguate RF transmission lines from power transmission lines. fgnievinski (talk) 03:49, 6 November 2019 (UTC)

Not sure that is necessary. They work on the same physics.Constant314 (talk) 04:05, 6 November 2019 (UTC)

I understood what you were trying to do, but we only add disambiguations to article names if another article, or a disambiguation page, already has the root title. I have no problem with you creating a disambiguation page, that is a good idea, but I don't think it should have the root name. I would argue that the current article is the overwhelming primary use and should thus have the primary title. It should be the disambiguation page that is disambiguated as Transmission line (disambiguation). SpinningSpark 11:31, 6 November 2019 (UTC)

I agree with Spinningspark's reversion because such a change should not be done without a discussion. I disagree that it is the "overwhelming primary use" and IMO in everyday discussion it is the opposite, so clarification between the two is important. But the current disambig (or whatever you call the thing at the beginning) takes care of that so IMO the current approach is fine. Sincerely, North8000 (talk) 14:02, 6 November 2019 (UTC)

Sorry for the bold renaming w/o discussion. I agree with North8000 that a layperson's transmission line is the one that conveys power or energy. I may agree partially with Spinningspark's comment, that a transmission line that conveys an information signal may be the most common one, for an electrical engineer. So which audience should we prioritize? Anyways, I've created the dab Transmission line (disambiguation) as suggested. My proposal now is to rename transmission line to radio-frequency transmission line, keep transmission line as a redirect here, and simplify the hatnote as follows: "'Transmission line' redirects here. For the movement of electrical energy, see Power transmission line." fgnievinski (talk) 14:31, 6 November 2019 (UTC)

My opinion is that a power transmission line is a specialization of transmission line. A power transmission line has a lot more subject matter (loss management, protection, regulatory, etc.) that would not be part of a general transmission line article, but there is almost nothing in a general transmission line article that would not apply to to a power transmission line. Constant314 (talk) 14:40, 6 November 2019 (UTC)

In RF calculations, as a rule of thumb, conductors less than 1/10 wavelength in length do not need to be treated as transmission lines. For a frequency of 60 Hz, this is 500 km. I never work with power transmission lines, but if this rule of thumb can be applied, then a large fraction of power transmission lines do not require consideration of characteristic impedance, reflections, and the like, as do RF transmission lines. Jc3s5h (talk) 15:24, 6 November 2019 (UTC)

They have different terms for similar things. Ferranti effect on power lines is just the voltage doubling phenomena you see on unterminated transmission lines. Surge impedance on power lines is just characteristic impedance. These are transmission line effects.Constant314 (talk) 15:31, 6 November 2019 (UTC)

IMO there are three meanings in play here, one of them uselessly vague:

1. The wires between poles outside that distribute power over longer distances
2. A method of engineering treatment of lines that are a significant fraction of a wavelength, and the name assigned to a line when it is receiving that treatment
3. Anything that carries electricity

Sincerely, North8000 (talk) 16:27, 6 November 2019 (UTC)

• In support of my claim that RF is the overwhelmingly primary usage, I offer this ngram. On the suggestion that transmission line should become a redirect to this article – no, it should not, that is entirely against our naming conventions. If no article takes the root usage then the disambiguation page should take that title, but as I have argued, that should not happen because we have a clear primary usage. SpinningSpark 16:48, 6 November 2019 (UTC)

I rebute SpinningSpark's first point with another ngram: [3]Furthermore, following WP:DETERMINEPRIMARY, I counted 989 daily page views for transmission line and 1225 for electric power transmission:

• [4]
• [5]

I also counted 1773 incoming links to transmission line and 1840 for electric power transmission:

• [6]
• [7]

Therefore, I conclude that either the primary topic is not RF transmission line or that there is no overwhelming primary topic. In any case, the article page can have a redirect, see WP:PRIMARYREDIRECT and WP:PARTIALDAB. fgnievinski (talk) 23:22, 6 November 2019 (UTC)

I fail to see how that ngram is meant to refute me. Rather it makes my point; "power transmission line" is a tiny proportion of all "transmission line" results, whereas "microstrip" by itself takes about half. Your comparison of article pageview statistics is not comparing like with like. The electric power transmission article is not solely, or even primarily, about transmission lines. SpinningSpark 15:45, 7 November 2019 (UTC)

It may not be relevant to the question at hand, but under meaning #2 above, "transmission line" is a term temporarily assigned to anything (e.g. a fence, a power transmission line) while it is being given "transmission line" mathematical treatment. North8000 (talk) 17:33, 6 November 2019 (UTC)

That topic would seem to be Electricity delivery. fgnievinski (talk) 23:22, 6 November 2019 (UTC)

I doubt that meaning 2 above, "A method of engineering treatment of lines that are a significant fraction of a wavelength, and the name assigned to a line when it is receiving that treatment", is mainly about electricity delivery. The phrase "significant fraction of a wavelength" indicates analysis of factors such as characteristic impedance, reflections, dielectric losses, and similar issues of interest in RF transmission lines. I presume such factors are also considered in the design of long-distance electricity delivery lines, but I believe many fewer designers are engaged in the design of long-distance electricity delivery lines compared to RF transmission lines. Jc3s5h (talk) 01:15, 7 November 2019 (UTC)

My main point just an observation without debating the main topic. And that "RF transmission" line is often just a "eye of the beholder" temporary designation when something is being analyzed by those methods. North8000 (talk) 16:13, 7 November 2019 (UTC)

Actually I think that this points to leaving the title as-is. The actual topic is not limited to transmission lines intended to be used for RF. For example if, today, somebody were applying multi-wavelength transmission line analysis to a power transmissions line (e.g. to analyze impulse response or 60Hz response over a 2,000 mile run), the power transmission line would temporarily be within the topic of this article. North8000 (talk) 12:26, 8 November 2019 (UTC)

I agree. Keep the title of this article as Transmission line. Constant314 (talk) 15:54, 8 November 2019 (UTC)

The title is good, but the text that limits the topic to RF seems wrong. The history (esp. Heaviside's work) comes from telegraphy and telephony, definitely not RF. And the principles of wave propagation along open-wire transmission lines apply as well to long-distance telephone lines. Dicklyon (talk) 17:09, 22 November 2020 (UTC)

Hello. I agree that the small signal and propagation aspects of those types of transmission line should be on topic. Surge impedance loading, Ferranti effect, dispersion limits in the early transatlantic telegraph should be on topic. There is a lot of overlap with Telegrapher's equations. I think the text tries to limit the article to RF is about avoiding other transmission lines like gas pipelines, the transmission line in a car, hollow waveguides, and also a plethora of topics about electric power lines such as the problem of starting fires in the woods, how many rings are on the insulator, health impacts, right of way issues, etc. The text could use some fine tuning. Constant314 (talk) 21:28, 22 November 2020 (UTC)

Yep, I wholeheartedly agree that this article should not be limited to RF. And in reality it is not so limited given its heavy emphasis on the telegrapher's equation. SpinningSpark 11:51, 23 November 2020 (UTC)

I disagree wuth removing RF completely from the definition. This is an example of a common problem in Wikipedia technical articles you could call "definition abstraction" or "definition overexpansion", in which the definition of the topic is expanded with extreme examples and uncommon special cases until it becomes incomprehensible to general readers. Excluding electric power distribution, the vast majority of things called "transmission lines" operate at radio frequencies, and engineers think of transmission lines as only necessary at RF. This info should be in the introduction, which is the only part of the article nontechnical readers will read. If we remove "radio frequency" from the lead sentence, we should add a sentence saying transmission lines are mainly used at RF.

A line carrying audio frequencies (20 kHz) must be treated as a transmission line when it is over 1.5 km, or about a mile. A line carrying voice frequencies (3 kHz) is a transmission line only when it is over 10 km (6 miles). The increasing cost of running long cables is making low bandwidth cables uneconomic. Virtually the only large use of "transmission lines" at subradio frequencies is in power transmission, already mentioned, and landline telephone local subscriber loops, which are being replaced by optical fiber. --Chetvorno^TALK 16:59, 23 November 2020 (UTC)

Well that's a bit of a strawman. No one has said remove RF completely, or even that the focus should not be on RF. SpinningSpark 17:20, 23 November 2020 (UTC)

Oh, okay, maybe I overreacted. It looked like it was heading in that direction. --Chetvorno^TALK 17:32, 23 November 2020 (UTC)

Since the ELF band goes down to 3Hz, I would suggest that RF is sufficiently inclusive that no change is needed to the article.Constant314 (talk) 18:58, 23 November 2020 (UTC)

I tweaked lead a bit in response to this discussion. To remove inference that it is only for RF & clarify that it includes cases where it requires such treatment. North8000 (talk) 19:22, 23 November 2020 (UTC)

I think the new version of the lead paragraph is much less understandable than the previous version. Specifically

• "...a transmission line is a specialized cable... designed to conduct electromagnetic waves..." is going to be very confusing to general readers who think of electromagnetic waves as traveling through space. All the transmission lines we are considering here have separate metal conductors and can be better described as "conducting high frequency alternating current", "...mainly at radio frequencies".
• "This applies especially to radio-frequency engineering because the short wavelengths means wave phenomena arise over very short distances (this can be as short as millimetres depending on frequency)." is confusing and still does not clearly tell readers that transmission lines are used at radio frequencies. Why not " Transmission line techniques must be used when the frequencies are high enough that the length of the line is a significant fraction of the wavelength of the waves".

WP:EXPLAINLEAD, WP:UPFRONT --Chetvorno^TALK 19:21, 24 November 2020 (UTC)

I think the new version is an improvement, but I also agree that waves is too technical/obscure and alternating current would be better and more meaningful to the general reader.Constant314 (talk) 19:30, 24 November 2020 (UTC)

Maybe replacing "alternating current" with "electromagnetic waves" was a bad idea and I wouldn't object if that was put back, but the former is also problematic imo, suggesting as it does a connection with power distribution. However, I don't agree that talking about waves is optional. On the contrary, this is the key concept, not frequency. The need for transmission lines is dependant on wavelength and this is not the same in two different lines even when operating at the same frequency. An extreme example is mechanical filters where transmission line considerations come in at many orders of magnitude lower frequency. SpinningSpark 10:44, 25 November 2020 (UTC)

According to this book, electromagnetic energy is the correct description and alternating current is positively wrong. SpinningSpark 18:22, 25 November 2020 (UTC)

Rightward ho

Schematic of a wave moving rightward down a lossless two-wire transmission line. Black dots represent electrons, and the arrows show the electric field.

If you fixate on the black dots, it's not so easy at first to discern the "rightward" propagation.

It might be useful to add the explanatory gloss that each arrow's magnitude follows the magnitude of the nearest arrow to the left a short interval later in time (globally uniform as illustrated, though you can build lines where the propagation velocity varies continuously).

Perhaps "moving rightward with uniform propagation velocity down a lossless two-wire line of uniform construction". — MaxEnt 17:40, 26 September 2020 (UTC)

Agree. --Chetvorno^TALK 18:22, 26 September 2020 (UTC)

A comment on wavelength in transmission lines

Length of RG58 Coaxial cable at 1/5 wavelength vs frequency

At frequencies below about 100 kHz, the phase velocity of signals in a transmission line with loss decreases. As a result, at low frequency, the electrical length can be significantly longer than the physical length. Because it amuses me, I plotted out the length of a typical polyethylene insulated RG58 Coaxial cable that would equal 1/5 of a wavelength (2/5 round trip). That is the point at which, I switch from lumped models to telegrapher's equations. Other people made use 1/4 or 1/3. It doesn't change the plot very mush, since it is on a log scale. So, you could run a voice line to the bottom of the deepest ocean trench without worry to much about reflections, etc., but not across Los Angeles the long way. Cheers. Constant314 (talk) 20:11, 23 November 2020 (UTC)

Wow! I had no idea. So a 1 Hz sine wave only travels through a coaxial cable at a rate of about 1000 miles/sec? It would take 3 SECONDS to travel across the United States from coast to coast. And a 10⁻⁶ Hz sine would only travel at a rate of about 1.8 MILES PER SECOND? Holy crap that is weird. --Chetvorno^TALK 21:09, 24 November 2020 (UTC)

In the low frequency regime velocity goes as $v={\sqrt {\frac {2\omega }{RC}}}$ so the velocity just keeps going down as the frequency goes down until, in the case, around a few microhertz. That is where G starts to dominate ωC. Constant314 (talk) 21:33, 24 November 2020 (UTC)

Tagged lead and related

I think that the tag on the lead is appropriate. And then we have two following sections (Overview and Applicability) which have the kind of material that is missing from the lead. I might try to tidy up unless someone else wants to. Sincerely, North8000 (talk) 13:08, 24 November 2020 (UTC)

Distributed circuit text removed

@North8000:. Why have you removed the material on distributed circuits? Your edit summary of pare matl;l that I copied in makes no sense. You did not copy in this passage. It was recently added by me. This is an important and widespread use of transmission lines. Very likely there are way more examples out there than simple connections of transmitters to antennae and other cabling applications. SpinningSpark 11:01, 25 November 2020 (UTC)

Well the reason why it seemed a minor thing was that I thought it was paring material that I had copied into the lead and thus material that is also in the body of the article. And the reason why I did it is because it looks too specialized for the lead. While I still think that the latter is true, between me being mistaken on the former and there being objection I just reverted my edit. Thanks for pointing this out. Sincerely, North8000 (talk) 12:56, 25 November 2020 (UTC)

Thanks for doing that. I'd be happy if some of it was moved out of the lead, but it definitely needs a mention, it's just too important and my text provides links to the relevant articles. There is already a section on stub filters which could be generalised out to the wider topic. Stub filters, by the way, are a rather out-of-date construction, mostly limited to the simple dc bias chokes role. They take up too much space in modern consumer devices. SpinningSpark 14:47, 25 November 2020 (UTC)

The article could benefit from more reorganization. How to do that would take some thought because it's structurally a bit complicated because it has two structurally different meanings:

1. Line designed to carry rf
2. Anything being analyzed by these techniques, at least during that analysis.

Sincerely, North8000 (talk) 16:19, 25 November 2020 (UTC)

In my opinion (and the opinion of the author of this book) the first of those is an incorrect definition of a transmission line. It is the signal being carried on the line, not the design of the line, that makes it a transmission line. SpinningSpark 18:17, 25 November 2020 (UTC)

Since the hollow waveguides are excluded, all the transmission lines that are part of this topic will have currents when they are carrying signals, it doesn’t seem wrong to say that the structure is designed to conduct currents. Also, a transmission line is a transmission line even when it is carrying no signals. Constant314 (talk) 19:21, 25 November 2020 (UTC)

@Spinningspark: We could add a hatnote at top saying for waveguide transmission lines see Waveguide. And/or insert a similar sentence after the lead, saying this definition doesn't include waveguide transmission lines. --Chetvorno^TALK 20:42, 25 November 2020 (UTC)

Another definition: "Electromagnetic waves... may be guided by transmission lines, waveguides, or optical fibers. [...] We take transmission lines to be two or more conductor lines. The term waveguide refers to hollow metallic guides. Optical fibers are actually dielectric waveguides, but we generally refer to them as fibers." 'Transmission line', The Froehlich/Kent Encyclopedia of Telecommunications, p.151 --Chetvorno^TALK 21:13, 25 November 2020 (UTC)

The second paragraph of the overview excludes hollow waveguides. I suppose that strictly speaking we are limiting the article structures that support the TEM mode and limiting the discussion to the TEM even though those structures usually support higher order modes. But, when you talk about TEM modes, you are talking at a post-graduate level, so I'm not sure what to say in the lede. But, at a lower level of understanding, the TEM transmission line is a complete circuit. There is always a return path for the current, which gets us back to talking about currents. In some older literature, I've seen them referred to as a "go and return" circuit. I suppose calling out the fact that there must be two or more conductors works at high school level and rules out more exotic wave guiding structures. Constant314 (talk) 21:41, 25 November 2020 (UTC)

I don't understand why waveguides have come to complicate this discussion. Our article plainly limits itself to conductors, and the book I linked to also does so:- "As the name implies, a transmission line is a set of conductors used for transmitting electrical signals." SpinningSpark 13:39, 26 November 2020 (UTC)

Further, in relation to my original reason for quoting the book:- "In general, every connection in an electrical circuit is a transmission line." That is, it is a transmission line whether or not it was designed specifically for that purpose. But as the book explains, it is not always necessary to take this into account. SpinningSpark 13:46, 26 November 2020 (UTC)

Okay, I misunderstood. I thought you meant the definition had to be expanded to include other types of transmission line besides two conductor, used at higher frequency. --Chetvorno^TALK 17:15, 26 November 2020 (UTC)

I still prefer to characterize the transmission line as a current guiding structure rather than a wave guiding structure, at least in the first sentence. Because: 1) everybody who understands waves also understands current, but many who understand current are mystified about waves, 2) almost all analysis and design of transmission lines focuses on the voltages and currents and ignores the fields, 3) the equations that govern the fields are such that knowledge of the currents and voltages is equivalent to knowledge of the fields, 4) the utility of the telegrapher’s equations is that they dispense with the fields and bring the analysis into the domain of currents and voltages. Constant314 (talk) 20:46, 26 November 2020 (UTC)

I also think that it's best to confine it to conductors. Then we stay within more of the meanings of the term. North8000 (talk) 17:18, 29 November 2020 (UTC)

Agree. --Chetvorno^TALK 22:13, 30 November 2020 (UTC)

@North8000: On the distinction you mentioned in your 16:19, 25 November 2020 post above between "lines designed to carry RF" and other electrical cables that have to be analyzed using transmission line techniques; I don't see this as too serious a problem for the article. I think the point is those other cables must be treated as transmission lines sometimes, but they are not called transmission lines. We can describe construction of standard RF transmission line types like coax, parallel line, stripline, etc. then have a paragraph explaining that any electrical cable which is not electrically short ($L\ll \lambda$) at the operating frequency must be treated as a transmission line to prevent reflections and distortion. And mention examples: long distance electric power transmission lines, landline telephone subscriber loops, and as frequencies increase into the microwave region PC board traces and circuit connecting wires all must be treated as transmission lines. --Chetvorno^TALK 22:13, 30 November 2020 (UTC)

Cool. I don't think that the "2 meanings" that I pointed out is a problem, just that it is something that we need to recognize. I brought it up mostly in the following context: I do think that the article needs some organization / tidying up. I did some work on the lead, but there's more to go. And the lead is supposed to be the overview but we have an overview section. Normally I'm pretty good at immediately seeing the path to do that but this time it sent my head spinning and I think that the main reason is the "two meanings". I think that to really tidy up the article we need to recognize the two meanings. A coax that is carrying radio waves is a transmission line even when we're not applying any math to it, that is a common meaning of the term. During the 5 minutes that I'm applying transmission line math to a piece of pipe, in that mathematical parlance the pipe is the transmission line. After that 5 minutes it's just a piece of pipe again. :-) North8000 (talk) 22:48, 30 November 2020 (UTC)

Sounds like we're pretty close together on the 2 meaning thing. My interest is in keeping the article comprehensible for general readers. This article is about products that are used in the electrical engineering industry. There are types of cable that are designed for use as transmission lines, that are called transmission lines, that have chapters in electromagnetics texts: coax, parallel line, stripline. Then there are all other cables and conductors, which are not designed solely as transmission lines and not normally called transmission lines. When these are used to transmit signals at frequencies at which their electrical length approaches or exceeds a wavelength, some transmission line concepts may have to be used in the design of these systems also. I think we should tell readers that. --Chetvorno^TALK 22:39, 1 December 2020 (UTC)

Duplicate section in lead

@Constant314: I don't think this edit was vandalism. The edit summary was "Removed duplicate section". The material removed from the lead is an almost exact copy of the "Overview" section. It was copied there by user:North8000 a couple of years ago who I think intended to then edit it down to a summary, but didn't actually edit out very much in the end. SpinningSpark 17:25, 17 June 2022 (UTC)

I reverted my revert. Still, the explanation was sparse. Constant314 (talk) 20:09, 17 June 2022 (UTC)

Thanks for the ping. Looks like I copied it into the lead and took out the reference in the lead copy. I have too few few wiki minutes at the moment to figure out what should be next. The lead should have that type of thing in it. I can circle back later or others should feel free to evolve / modify it. Sincerely, North8000 (talk) 18:59, 17 June 2022 (UTC)

I noticed that it got re-removed. In light of the unusual structure of this article (having the "overview" section, and the rest of the article consisting of a collection of specialized information and equations) I think it's probably best that way for now. North8000 (talk) 15:10, 18 June 2022 (UTC)