Talk:Electrical length

Merge proposal

Electrical length and electrical lengthening seem like one article too many on the same topic, but I don't have enough expertise on the subject to merge them myself.--Miniapolis (talk) 21:02, 29 October 2011 (UTC)

• All content from the Electrical lengthening article has been merged into this article. Northamerica1000^(talk) 10:54, 2 January 2012 (UTC)

Electrical length of an antenna

@Interferometrist: I am now very confused about which fact you think is dubious.[1] The electrical length of an antenna element is, in general, different from its physical length—and is very easily cited.[2]

@Interferometrist: Pinging again because I forgot to sign. SpinningSpark 18:38, 22 November 2014 (UTC)

Well I know this is very often mentioned, but it's a mistake. The only time the electrical length is different from the physical length (in either an antenna or transmission line) is when there is a dielectric (partly) surrounding it. The difference between the length of a half wave dipole and half wavelength is a separate issue, having to do with the solution of the Hallen integral equation, which specifies a difference in order to achieve resonance (X=0). Not surprising, since the voltage is not exactly a standing wave along the dipole element (as it WOULD be for an open transmission line) -- if it were then there would be zero voltage at the feedpoint! The full solution shows the offset for resonance depends on the diameter of the conductor. But again, this has nothing to do with a discrepancy in the velocity of wave propagation which is c/sqrt(epsilon) = c in most cases. That is why this is thrown around as a quantitative relationship but you will never never see an equation to that effect!

It is also wrong to say that the electrical length of an antenna arm at resonance is exactly 1/4 wave. But I'm not mainly tagging that because the page isn't about antennas (and it's approximately true). I can rewrite that after resolving the main issue I have cited. Interferometrist (talk) 19:03, 22 November 2014 (UTC)

The overwhelming majority of antennas nowadays are in mobile devices and are frequently in microstrip format so a dielectric most definitely is involved. There is also the issue of loading coils and stubs which are often explained in terms of adjusting the electrical length of the antenna. Even an element in air has a small (but insignifiacant) change in electrical length due to the relative permittivity of air not being quite exactly unity. SpinningSpark 20:08, 22 November 2014 (UTC)

Well great! It sounds like you (mostly) agree with me, not with the article. Before editing it I'll wait to see if anyone else tries to come up with a RS for the errors. I remember last time I dealt with this issue on WP I was shot down by those who were able to find (incorrect) material backing up the errors.

I also think "loading coils and stubs which are often explained in terms of adjusting the electrical length of the antenna" is using a crude term for impedance matching that isn't used in proper physics/engineering parlance and shouldn't be dignified in WP except to mention its (possibly) common linguistic usage. A short antenna that has been resonated with a loading coil or capacitive hat has a different resistive impedance and a slightly different radiation pattern than the 1/4 wave element (or from each other). The only thing they have in common with the resonant antenna is lack of reactance at the frequency of operation. So that's another issue. But mainly the article must point to "dielectrics" as the sole cause of v<c (and quantify it!) in transmission lines and in antennas (the majority of which nowadays, as you point out, are typically built on PCB in mobile phones and wifi equipment).Interferometrist (talk) 21:45, 22 November 2014 (UTC)

The terminology of electrical length is confusing because of the mixture of physical length and angular length (phase shift) measures. But I don't see any support in WP:RSs for your view that electrical length is the same as physical length: Interferometrist 1, p.451, 2, 3, 4, 5, 6, 7, 8. Where are your sources? --Chetvorno^TALK 06:19, 23 November 2014 (UTC)

Well this should be straightforward, so let me spell it out and you can identify where you find a discrepancy. First, I only said that electrical length (if that is a valid term) Lelec == Lphysical applies to conductors in a vacuum. As you imply, any meaning for Lelec in a transmission line (thus a straight wire w/r/t ground or wire pair) would require the phase delay of a wave along it phi = (2pi/lambda) Lelec = k Lphysical. The electrical energy transmitted by the line (although we usually think about current and voltage) is in the form of an EM wave, which has a propagation constant of k = 2pi / lambda in free space. If ALL of space were filled with a linear isotropic medium then k = 2pi n / lambda, where n = sqrt(epsilon_rel * mu_rel) or equivalently, v_p = 1/sqrt(espsilon*mu). In the case that only part of the space around the conductor is affected by the dielectric, then n_eff^2 = (1-f) + f*(epsilon_rel * mu_rel), where f is the fill factor (not really a property in itself but a factor due to the geometry of the dielectric which provides the correct answer to the wave's phase velocity according to that equation). In the case of coax filled with n between the conductors, f=1 (since ALL of the E and H fields are contained in that region). For stripline or twin line held together by a dielectric ribbon, f<1.

That clearly applies to a transmission line. With a finite length conductor (but not for coax) such as an antenna element, there is usually radiation produced by the current in the line, which adds a dissipative (imaginary) component to k, but doesn't affect the real part of k, at least to first order. Thus, for a dipole antenna in free space, as for an air filled transmission line, v_p = c and Lelec == Lphysical. Those are what the article should say (but also deprecating the term "electrical length" in the case of an antenna, where it doesn't have the clear significance it does in a transmission line where you can have a unidirectional wave and measure phase shift along it, and certainly deprecating the term "electrical lengthening" of an antenna for the reasons I stated above).

Now, am I missing something? Interferometrist (talk) 11:55, 23 November 2014 (UTC)

Sorry, but Wikipedia requires that all content be VERIFIABLE from RELIABLE SOURCES. It does not allow WP:ORIGINAL RESEARCH. Perhaps Wikibooks would be a better place for your ideas? They don't have a verifiability requirement. --Chetvorno^TALK 12:20, 23 November 2014 (UTC)

But wait a minute: none of the above is new research and all is verifiable, I am certain. The reason I mentioned it was to first agree on what we all know. And then for me to ask if there is another issue at work which might justify a definition of "electrical length" beyond L_physical/n_eff, as one might take away from reading the article. If so, then I would like to know about it, and if it's laid out in one of your references, perhaps you could point me right to that and I'll shut up. If not, then the page is based on popular mythology, not physics.Interferometrist (talk) 13:34, 23 November 2014 (UTC)

@Avid0g: Electrical length is certainly affected by the ratio of physical length to diameter. This is more significant at and above UHF, where structural factors and (skin) resistance may require a specific conductor diameter, even as length reaches microwave scales. At a l/d ratio of 10:1, the velocity factor is 0.90 At a l/d ratio of 1:1, the velocity factor is 0.80! Here I cite just ONE example: Antenna Toolkit [3] I hope this justifies my removing the "dubious" label. This book provides a graphical relationship, and should be cited in the article. — Preceding unsigned comment added by avid0g (talk • contribs) 21:39, 9 December 2014‎

@Avid0g: Yes, that would have justified removing {dubious} except that the reference is wrong in citing a "velocity factor". We've already looked at Carr among other good references which are mistaken in this regard. If you want to comment further on the issue please review the discussion on this page (above and below) first. The correct explanation for the shortening from 1/2 wavelength to obtain resonance has been written into Dipole antenna#Impedance of dipoles of various lengths (you may skip to the 4th paragraph).

Again, replies on a talk page should normally come at the bottom of the section, and end it with 4 tildes in order to generate a signature and date. Thanks, Interferometrist (talk) 21:13, 10 December 2014 (UTC)

In addition to avid0g's reference, the discussion Interferometrist refers to contains 4 additional references which support avid0g and my position that "velocity factor" and "electrical length" applies to antennas, and specifically l/d ratio. Interferometrist, you are the only one WP:PUSHing your personal view against consensus and a lot of WP:RSs. --Chetvorno^TALK 22:00, 10 December 2014 (UTC)

Well again, there are certainly more than four, but not a single one attempts to explain why there should be a "velocity factor" applying to an antenna in free space, nor how it would be calculated. But there are some good books which explain why an antenna should be shorter than 1/2 wavelength to achieve resonance and exactly how that is calculated, and I have calculated that myself and it is in the plot on the dipole page (where X=0 for each of the conductor diameters listed). Also those books specify that the current on the element goes according to sin(kx) (as a very good approximation when d/lambda<.01) where k=2pi/lambda, which contradicts any "velocity factor" which would have increased k. So the question is, do you want to accept the references which mention a word but don't explain it, or the ones that explain everything that is measureable but don't introduce such a word and in fact contradict such a concept in the course of analysis. If you disagree with what has been written on the basis of the latter, then you should attend to the text I edited on the dipole page.Interferometrist (talk) 22:20, 10 December 2014 (UTC)

@Chetvorno:Actually I did look at WP:PUSH and from that I can identify myself as a victim of the behaviour they list where persistance led to me giving up, last time this issue was considered a few years ago. Everyone, like you, was sure that there is such a velocity factor and wouldn't allow the non-existance of such a concept in sources by those who actually know how to calculate the shortening factor to question the beliefs promoted by secondary sources who copied the numbers from those actual sources but didn't understand where the numbers came from. So I gave up and allowed for Wikipedia to continue a myth, which gives the myth further life due to the prominence of wikipedia. So that realization and mentioning of editors who just gave up has strengthened my resolve to get it right this time.

I'm also looking at Wikipedia policy as spelled out in WP:VERIFY where it considers the types of sources available starting with: "If available, academic and peer-reviewed publications are usually the most reliable sources, such as in history, medicine, and science." That would appear to apply in this case, where the academic sources I've looked at (the ones that explain the shortening quantitatively) are consistent in not citing "velocity factor" and have currents as I=sin(kz) with k=2pi/lambda_0. So according to policy, those sources (in this case, Kai, Kraus, and especially Balanis who has over 30 pages just related to calculating feedpoint impedance) trump non-academic sources which repeat a popular myth (one that I once believed myself, by the way, also because "everyone knows it"). But even though I'm pretty certain about what I'll write according to the best sources, I'd rather do it with the cooperation of the other editors. So if you still think that I'm in error, I'm willing to discuss it further so we can reach consensus. Otherwise, I will just write an edit which you could either accept (as it will be properly sourced) or attempt to challenge (but I don't know how you would). Ok? Interferometrist (talk) 18:12, 11 December 2014 (UTC)

The policy position is that if two sets of sources give two different descriptions of antenna length, and they are both equally reliable then we should present both in our article. If there are no reliable sources saying that one description is misguided (and that appears to be the case at the moment) then we should present both without comment, leaving it to the reader to infer. Now we can say that one description is from more authoritative sources, and give them more weight than the other, but we need to be sure that they really are more authoritative. That a book gives more maths (although suggestive) is not sufficient evidence of authority. All kinds of fringe theories are stuffed full of clever looking maths. And it is certainly not more authoritative, as has been pointed out to you several times already, because it happens to agree with your reasoning. We would instead be looking for the author to be a recognised expert in the field (notability helps here) and/or that they are widely cited by other scholars.

Personally, I think that your reasoning on the diameter/length question makes a lot of sense. I am not so sure about the question of the effect of nearby objects. If I put a lump of metal near an antenna does that affect the wave velocity? What if I place six smaller lumps of metal, or ten, or a hundred? What if I completely fill the space around the antenna with microscopically small grains of metal (not touching)? Hmm... hasn't that filled the space with a material in which dipoles can be induced? That would be called a dielectric and we both agree that that would affect wave velocity. But it does not matter what I think, it is sources that count. It doesn't matter what you think either. It is pointless to continue to debate on this page; find sources that say what you want to say, then you can say it in the article. SpinningSpark 10:07, 12 December 2014 (UTC)

Again, no expert writing a comprehensive book laying out a subject from first principles is going to stoop to the level of "debating" an alternative theory of electromagnetism. In all of the good antenna books I've looked at, I've never seen the author specifically disagree with anyone else. That isn't how you write such a book. So please don't expect me to supply that anymore than an academic work on evolutionary biology will debate or even mention creationism. But "notability"? Please! John Kraus is surely the best known and respected name in the history of antenna theory, and (like Balanis and Kai who are less notable) explains the length of dipoles without ever needing to invoke this concept (in the cases where it doesn't apply).

@Spinningspark: Also, I'm wondering if what I'm writing gets read, but I not only admitted that its possible for a nearby conductor to influence the resonance of an antenna element but asserted that I would know how to do it in order to either raise or lower its resonance frequency. Neither one would change the velocity of electromagnetic waves in free space and I would be wrong to explain it in such a way.

And again, repeating myself for the umpteenth time, I have NOT been judging or picking sources on whether they agree with "me" (as if I have any personal views that I didn't learn directly in an antenna course before which I had also believed in a "velocity factor."). The thing I would most like to have found and cannot find and don't believe exists is a quantitative treatment of where such a velocity factor comes from. Or why it would be different for the same conductor diameter when considering different resonances. Because there is so much difference in the nature of the support for the actual theory and the folklore, the dictum to present "both sides of the debate" doesn't apply. There is no such debate within the academic field. If there were two competing theories then there would be, but there is only one theory (Maxwell's equations) and its solutions, and then there is vague conjecture. Interferometrist (talk) 11:52, 12 December 2014 (UTC)

I cannot agree that respectable authors never address common misunderstandings. The phrase "is a common misunderstanding" appears in thousands of books and there must be endless other ways of phrasing that. Same result for scholarly papers. So yes, you do need a source saying something is a misunderstanding or incorrect before you can write that in the article. I accept Kraus as an expert here (I never said he wasn't, I was only giving the general policy position), his 1988 work Antennas has a very respectable 3120 citations according to Scholar. SpinningSpark 12:14, 12 December 2014 (UTC)

Choosing one particular textbook to support a theory which is not supported by the rest is clearly WP:CHERRYPICKING. There are many perfectly adequate texts on antenna theory that cover this issue. Second, Interferometrist, just because an author doesn't happen to use the terms "electrical length" or "velocity factor" in his analysis of l/d ratio doesn't mean he disapproves of that use. That is WP:SYNTHESIS, inferring a conclusion not stated in the source, and a very tenuous synthesis at that. If you want the article to take the position that "electrical length" or "velocity factor" should not be applied to antennas, you are going to need a source that says that, not just infer it by omission. --Chetvorno^TALK 14:08, 12 December 2014 (UTC)

@Spinningspark, re your l/d remark above: Electrical length isn't a "fundamental" parameter that comes out of Maxwell's equations as Interferometrist is trying to claim. It is just an empirical catchall parameter that quantifies all the factors that cause the resonant frequency to depart from the "thin element" model, the same way as aperture efficiency is a catchall parameter that quantifies all the factors that cause an aperture antenna to fall short of a perfect energy-converting aperture. Isn't this the way it is used in mainstream sources? If a physical antenna has a measured resonant frequency of f it has an electrical wavelength of λ = c / f (see the 7 sources I gave above) There may be many factors, including l/d, that cause this to differ from the actual length of the antenna. In use these different factors are not usually distinguished. Including some and excluding others is not done in mainstream usage of the term. --Chetvorno^TALK 15:20, 12 December 2014 (UTC)

I don't have an issue with any of that. Where I was agreeing that Interferometrist may have a point (and possibly I was not very clear about this) is that velocity factor does not seem to refer to any real velocity change with l/d. But even that much does not currently have a source we can put in the article. Interferometrist, you might find Wikipedia: Righting Great Wrongs informative on our position here. SpinningSpark 15:37, 12 December 2014 (UTC)

I see, okay. Don't mean to beat on this, but I'd like to point out that whether or not there is an actual velocity change, you can define a "velocity factor" = λ_electrical/λ_physical; it just doesn't have the same interpretation as in a transmission line. That WP:Righting Great Wrongs essay is great. --Chetvorno^TALK 17:30, 12 December 2014 (UTC)

Rewrite is much improved

The latest edits of Chetvorno are quite an improvement so we can go further with this. I still have a few disagreements with regard to appropriate terminology, but for now I might make a few edits which avoid the issues of disagreement. My main remaining disagreement is with there being a meaningful entity as "electrical length" (other than Lphysical/n_eff) or "velocity factor (other than 1/n_eff) applying to antenna elements. (The terms do properly apply to transmission lines).

Since ‎Chetvorno went to the trouble of digging up 8 references, I did him the courtesy of looking at each one to see if or why it was wrong. In terms of their numbering above, I find that in terms of actual content but ignoring the terminology:

• 1 No problem, if his velocity factor = 1/n_eff (it isn't further specified).
• 2 Just a glossary, with the velocity factor ("Even in free space") claimed to be due to "end effects."
• 3 Again, a glossary entry, but nothing to disagree with.
• 4 No text available, but fiber optics is a waveguide, not controversial, velocity factor of a mode due to waveguide propagation constant, doesn't apply to present discussion
• 5 Does not explain velocity factor and author displays ignorance of the reason for the discrepancy (negligible for 80 meters, annoying at 2 meters) having to do with the conductor diameter / wavelength.
• 6 Ascribes discrepancy to "end effects".
• 7 Correctly talks about velocity factor of transmission lines, nothing about antennas.
• 8 Page 254 has exactly the curve I would have pointed to! He NEVER calls k the "velocity factor" (does talk about velocity factor of transmission line elsewhere).

So in summary, the ones which talk about "velocity factor" do not attempt to explain it in the least. Two of them, interestingly, talk about the discrepancy as an "end effect" which I neither agree nor disagree with. After all, to be an extra effect, it would have to modify an unaffected model, and I don't know what that original model is because the standing wave pattern along the antenna element is just a (good) approximation in lieu of solving (numerically) the Hallen integral equation which itself DOES predict the discrepancy. But let me just point out that the concept of a discrepancy due to an "end effect" and the concept of a slower than c "velocity factor" are rather disjoint, so both of them couldn't be "explanations" of the same phenomenon. Since they are not quantified in these sources, that's about all that I can say in judgement.

But here's my point: the best sources, including #8, do not invoke either of these concepts. I know that is true of my antenna coursebook which I looked through the last time this discussion came up. But moreover I found that you can now download the main work of John Kraus, a classic among proper (that is, physics based text, not a how-to manual) works, downloadable at [4]. Unfortunately its a scanned image so you can't search, but the places he discusses the length and reactance of a dipole/monopole element is on pages 227 and especially 420 where he supplies an actual solution good for L/diam > 100 which I had never seen before. Again, nowhere does he (as far as I can tell) talk about "electrical length" or "velocity factor." So what I am and have been saying, is that these terms in relation to antenna elements are not used in actual physics-engineering books (of the two I've consulted), and in the "practical engineering" works they are never explained in a quantitative way. I conclude that they are invalid from a scientific standpoint, but could be mentioned in wikipedia as misused terms.Interferometrist (talk) 16:59, 23 November 2014 (UTC)

My feeling is that, before going too deeply into the reasons electrical length is different from physical length, the article should explain better the elementary relations between electrical length, physical length, wavelength, phase shift, velocity factor, and frequency. Wikipedia is a general encyclopedia, and a lot of the readers of this page are going to be nontechnical people who want the simplest possible explanation. Some of the recent edits are a good start toward this end. That is the reason that velocity factor is used so much; it a convenient parameter that encapsulates the different factors that cause the waves' velocity to be slower in a medium than in free space. Re the above, I'm sure you understand that we cannot cherry pick sources. Again, keep in mind that, in order for it to stay, you will have to source the added content. --Chetvorno^TALK 21:35, 23 November 2014 (UTC)

One can (and even should) cherry pick sources if there is an objective rationale that the ones picked are the more authoritative. Regarding Interferometrist's comments, sources are not more authoritative just because they happen to agree with your thinking. I am also highly dubious on this idea that scientific sources must be more reliable than engineering sources. Pointing to a source that has an absence of what you consider to be wrongheaded thinking is not verification of such wrongheadedness. A source that explicitly states that the concept of electrical length applied to antennas is wrong would be much more convinving. SpinningSpark 02:32, 24 November 2014 (UTC)

Well editing this page is involving a high talk-to-editing ratio, especially for a page that isn't widely read and of great importance, and I find this rather frustrating. I think that was the reason I gave up on correcting this content last time I tried a few years ago. But this time I have really assembled enough material to properly finish the job, assuming that other editors are willing to place objective appraisal of the sources and arguments ahead of their preconceptions (BTW, I always had the same preconception about a "velocity factor" along an antenna element in free space before I took a course in antenna theory which explained the discrepancy with no reference to this fiction). Let me answer the specific points raised:

"I am also highly dubious on this idea that scientific sources must be more reliable than engineering sources." Perhaps I wasn't clear. There is no fundamental science involved in antenna engineering. Antenna theory is usually classified as "engineering" although one can term it "applied science". The ONLY basic science in antenna engineering is Maxwell's equations, period! The validity of EVERYTHING we are discussing boils down to whether the solutions satisfy Maxwell's equations. There is no further magic. So what I am saying, is that among sources that may look reliable (and may be reliable in almost all ways, such as shortening your dipole by 3% so it will resonate), one would prefer the ones that INCLUDE the mathematics showing how a result is obtained in a way which (perhaps indirectly) is shown to satisfy Maxwell's equations, over ones which do not show any math at all. In this respect I can point to one extremely telling fact: Of all the hundreds or thousands websites and even books which claim a "velocity factor" NOT ONE has an equation for it, let alone an explanation!! Yes, Chetvorno's ref 8 does plot k but doesn't call it (or imply it to be) a velocity factor. It is the CORRECT factor that Kraus and the other "good" (in the above respect) antenna books explain in more or less detail (but Kraus shows an actual calculation I hadn't seen before which is good for L/d>100). Surely, a source that introduces superfluous terms and doesn't explain their origin cannot stand up to one that explains it in detail as a consequence of Maxwells equations and never mentions those invalid constructs.

"A source that explicitly states that the concept of electrical length applied to antennas is wrong would be much more convinving." Yes, but that's a tall order! I have run across one radio amateur's antenna website which did very explicitely have an extensive discussion about why that was wrong (and he posted his objection to that on a couple other sites, which was how I found him, I believe). I don't know if you'd call him a RS and he would be "outvoted" by hundreds of other ham radio sites that do go along with the fictions even though they are good in other respects. I am quite sure that none of the "proper engineering" books (ones that show their math in this regard) would stoop to the level of repudiating popular mythology. Just like a serious astronomy book would say that the earth goes around the sun, and wouldn't even mention that once most people thought the opposite unless the book had a strong historical component, and even then it certainly wouldn't lay out all the evidence for the earth moving in orbit! Right? So none of my books even mention velocity factor let alone why it doesn't apply. BUT, I DO have equations in my books which show the current along a dipole (or monopole) element as being very well approximated by:

$I(z)=I_{max}sin(k(L-z))$

where k=ω/c. Rather than k= sqrt(ε) ω/c as it properly is for the current along an open coax stub with the velocity factor (correctly named) of 1/sqrt(ε). If there were any such velocity factor (not having to do with dielectrics in the proximity) then it would have been included in the expression for k. So I guess that does contradict the velocity factor idea as much as you could ask for, and I believe all 4 of the proper antenna books I have in front of me (and which I'll include as refs) include the above forms. BTW, in addition to book of Kraus (probably the most authoritative and recognizable name in antenna theory) which is downloadable at the URL I gave you, two others I have in electronic version, which I could share with you if you request by email.

Finally: "That is the reason that velocity factor is used so much; it a convenient parameter that encapsulates the different factors that cause the waves' velocity to be slower in a medium than in free space." Well I hope I have already answered that. There is only ONE factor that causes that in either an antenna element or transmission line: material permittivity (and/or permeability) in the vicinity. In the case of antennas, it still DOES need to be mentioned for the case of antennas where this applies, specifically stripline antennas. I don't have a good reference for that offhand (unfortunately the chapter on stripline antennas in one of my electronic books is in part 2 which I didn't get). I don't know enough about patch antennas to know if this concept applies or if you just base the design on the capacitance of a patch using a particular PCB.

I will start editing right now by making a few unrelated corrections to the page. In the meantime I would like the 2 editors (or others) to kindly acknowledge the invalidity of the antenna velocity factor so we can move on. I will include the references right away.Interferometrist (talk) 19:15, 25 November 2014 (UTC)

Also, I meant to say, that the .06% (actual) velocity factor correction for antennas in air rather than vacuum, really doesn't need to be mentioned. Every antenna paper I've seen uses free space as interchangeable with air, as this tiny factor is essentially unmeasureable in an antenna (unless you're doing a sensitive physics experiment) and small in comparison with other approximations invoked (such as a dipole's feedPOINT rather than a gap!).Interferometrist (talk) 19:22, 25 November 2014 (UTC)

I don't see why you feel this is such an important issue. Whether or not the "velocity" of waves on an antenna can be defined or not (I think you are arguing that it cannot be defined, right?) a "velocity factor" can obviously be defined for an antenna as $\scriptstyle v_{p}/c\;=\;\lambda _{\text{antenna}}/\lambda _{\text{free space}}$ In fact, since $\scriptstyle v_{p}\;=\;1/(\mu \epsilon )^{1/2}\;=\;1/(\mu \epsilon _{r}\epsilon _{0})^{1/2}$ Maxwell's equations can be written with a "velocity factor" in place of permittivity: $\scriptstyle \epsilon \;=\;\epsilon _{0}/(v_{p}/c)^{2}$ (assuming $\scriptstyle \mu \;=\;\mu _{0}$) where $\scriptstyle v_{p}(x)$ is regarded as a property of the medium. "Velocity factor" is just the reciprocal of the index of refraction: $\scriptstyle n\;=\;c/v_{p}$ It seems to me the only substantive issue is whether "velocity factor" is used in antenna design. If it is, we should include it in the Antenna section. It looks to me like it is 1, 2, 3. --Chetvorno^TALK 21:11, 25 November 2014 (UTC)

Well of course I agree with what you just said, which is what I was always saying. I was disagreeing with the text I believe you added yourself: "The electrical length of an antenna element is, in general, different from its physical length[2][3] For example, increasing the diameter of the conductor, or the presence of nearby metal objects, will decrease the velocity of the waves in the element, increasing the electrical length." That's wrong, as the 3 references I just added show. I will remove that and point out what you just said, and also point out the reason that antennas with different conductor diameters need different amounts of shortening in order to reach resonance, as that's related to the point of this page (and frequently misunderstood in terms of a non-existant velocity factor). But you're right, it isn't that important, but you have sure made it hard for me (see above entries) just to edit in correct content.Interferometrist (talk) 21:22, 25 November 2014 (UTC)

And by the way, of the references you just threw at me, two contain this common misunderstanding. They are wrong. The other one is about tower antennas with a very plausible geometric argument relating the current along the edge of the tower (at r,z) to the height (z). The fourth just talks about velocity factor of transmission lines (from what I can see).Interferometrist (talk) 21:29, 25 November 2014 (UTC)

Interferometrist's comments are quite lengthy and, however correct, Wikipedians are only convinced when they see a source stating them. We just can't take your statements that this and that book are wrong at face value. Therefore please refrain from using your own words and show us the sources. Mine are given below. Fgnievinski (talk) 22:45, 25 November 2014 (UTC)

1-12 VECTOR EFFECTIVE HEIGHT The vector effective height relates the open-circuit voltage response of an antenna to the incident electric field. Although we normally think of applying effective height to a line antenna, such as a transmitting tower, the concept can be applied to any antenna. For a transmitting tower, effective height is the physical height multiplied by the ratio of the average current to the peak current: Modern Antenna Design By Thomas A. Milligan [5]

"Beginning with the field approach, the receiving antenna converts the incident wave electric field Ei to an open-circuit voltage VA through the effective length h (also called effective height) of the receiving antenna that is defined as..." Antenna Theory and Design By Warren L. Stutzman, Gary A. Thiele [6]

You tuned in late. My references in this regard (which have not yet been applied to the article since I was trying to obtain the agreement of the other editors watching this page) have been temporarily added to the reference list of the page. They will become inline. The discussion of the relevance of these references is included in the long discussion above, which I'm not sure anyone has actually read through besides me. The page numbers point to the current standing wave following that of the vacuum wavelength.

This confusion came up recently and I answered it, but (I'm getting used to repeating myself these days....) the term antenna effective length is TOTALLY unrelated to phase or this entire discussion. It is a term that could be expressed in terms of the antenna gain and feedpoint impedance. I believe it is defined on the antenna page. Again, it's irrelevant to this discussion.Interferometrist (talk) 23:08, 25 November 2014 (UTC)

@Interferometrist I understand your argument. From a strict electromagnetics point of view, if the exact shape of the conductors was used in a calculation of the resonant frequency of an antenna, the "electrical length" would only differ from the "physical length" if there were a dielectric medium involved ($\scriptstyle \epsilon \;\neq \;\epsilon _{0}$). But the exact shape is not used. A lot of approximations are used in antenna engineering, and the most common is the "thin element" approximation, in which the wavelength and resonant frequency are calculated assuming the antenna elements are infinitely thin, perfect conductors. In antennas the "electrical length" (and "velocity factor") is used as a catchall parameter to account for all the factors which makes the actual resonant frequency of the antenna different from that calculated from the simple thin element approximation: (1) finite length/diameter ratio, (2) resistivity of the element material, (3) effect of nearby conductors, (4) presence of dielectrics like air or insulation (4) presence of loading coils or capacitors, and probably a lot of others. If Maxwell's equations had to be solved for the exact shape and resistivity, etc. of the elements to design an antenna, the radio industry would grind to a halt. Instead the "electrical length" needed is simply calculated from $\scriptstyle \lambda =c/f$ and corrections from handbooks for length/diameter ratio and the other factors are applied to get the "physical length". The references I've given above clearly show that "electrical length" is used with antennas in this way, and it would be misleading not to include it in the article. --Chetvorno^TALK 14:04, 28 November 2014 (UTC)

Thanks for the interaction. I will soon edit this, and provide sufficient references for what I write. I understand that there is sufficient literature (such as you have pointed me to) which refers to the "electrical length" of an antenna having a value (in meters) which is different from its physical length even when no dielectrics are involved. However those references are wrong. The diameter of the conductor absolutely does not reduce the velocity of propagation along it (nor does it in coax!). That is the reason that you will not find anywhere a formula for the supposed "velocity factor" or even an equation which would solve for it. It is a total misunderstanding. The one reference you gave me which has a good graph for the shortening required for a half wave dipole to become resonant calls it the "k factor" but nowhere talks about it having to do with the wave velocity along the antenna elements. Now, this isn't even the main point of the article, but I will add a word pointing out this misunderstanding and the actual reason a dipole has to be shortened in order to become resonant. BTW, the velocity factor page does not apply this term to antenna elements (or I'd be fixing that page too!).

Also, you said "A lot of approximations are used in antenna engineering, and the most common is the "thin element" approximation, in which the wavelength and resonant frequency are calculated assuming the antenna elements are infinitely thin, perfect conductors." Well no, that is not true of the antenna books I've been looking at. They all refer to the length/diameter ratio and its effects. They also do mention (but not dwell on) the finite conductivity of the elements, which causes loss, but does not slow down the waves (any more than it does in coax). The only approximation I've seen is the one which computes the k factor accurately only for L/d>100 (rather than solving the Hallen integral equation fully). It's plausible that "effect of nearby conductors" would change an element's resonance, and in fact I know enough about mutual impedance of elements to design something that would do just that! It would have to be near-resonant and very close. But this "effect" is never mentioned as a source of length discrepancy in and of itself. Even in Yagi design, this is not mentioned as a separate phenomenon but certainly is part of the calculation of the driving point impedance where the effect on the driving element from current induced in the parasitic elements certainly has a (small) effect. I'm pretty sure that I could engineer such an interaction to increase or decrease either the reactance or resistance seen at the feedpoint (by a small amount). I could probably engineer it so that someone who sticks to the term "velocity factor" would conclude a wave velocity faster than c! Whatever.....

I understand the term "electrical lengthening" for a short antenna to make it resonant, and I guess that is acceptable jargon if by the antenna you mean the antenna rod plus loading coil. Of course if you were sitting in between those, then you would just say the antenna has a very capacitive impedance and is being fed by a conjugate source (transmitter + impedance match). So this jargon requires seeing the coil as part of the antenna, which someone who just buys the antenna that way may be happy to do. It is further inexact because externally, someone observing the radiation pattern of the antenna will notice a certain difference from a full length dipole or monopole. And looking into the antenna system, you have a much smaller (but resistive) impedance than a full length antenna. In fact, the only way I can possibly think of an "electrically lengthened" antenna resembling a full sized resonant antenna is that there is no reactance seen at the terminals! So I, personally, consider it to be very crude terminology. Nevertheless, it is terminology that is widely in use, so it should be described as such.Interferometrist (talk) 17:55, 28 November 2014 (UTC)

Rewrote article

Completely rewrote the article along the lines of the consensus in the previous two Talk threads above. Pursuing this goal I deleted the confusing unsourced "Use of the term" section which implied that application of the term "electrical length" to antennas was improper or "inexact" "jargon"; this is not supported by references. Tried to explain the concepts at a more elementary level for nontechnical readers. Also added sections on "Scaling properties of antennas" and "Regimes of electromagnetics". It is not done yet; I need to add more sources, and hopefully diagrams. --Chetvorno^TALK 23:29, 24 December 2022 (UTC)