Talk:Propagation constant

Phase constant
can anyone tell me how to find the phase constant?
 * It's the imaginary part of Propagation constant (gamma) Zebov 22:43, 30 March 2006 (UTC)

root ZY
It is also equal to the square root of Yl* Zl myclob 22:45, 13 April 2007 (UTC)
 * Well you might need to define what you mean by Y1 and Z1. That is true of the transmission line if you mean the distributed series Z and shunt Y per metre but it is not true of circuits in general.  Usually there will be a log, trig or hyperbolic trig function involved depending on exactly how you define everything.  See for instance image impedance.  Sp in ni  ng  Spark  14:12, 3 June 2008 (UTC)

Merger proposal
I am proposing merging into this article attenuation constant and phase constant. All three articles are likely to remain stubs as there is little more to say on any of them. They only stand a chance of being a decent article when taken together. There is also a very large number of alternative names for these quantities, it would be good if all the redirects where to point to the same place.  Sp in ni ng  Spark  14:11, 3 June 2008 (UTC)

Proposal wording change in Copper Lines
In the “Copper Lines” section,in the clause: there are some decidedly non-linear effects I would like to suggest changing the phrase some decidedly non-linear effects to frequency dependant effects. The reason is that non-linear often means that there is a non-linear interaction of the signals leading to harmonic distortion and intermodulation distortion and I don't think that is what is meant. Constant314 (talk) 02:36, 26 May 2010 (UTC)


 * I agree with that, the meaning is non-constant rather than non-linear.  Sp in ni ng  Spark  08:08, 29 May 2010 (UTC)

Proposal to discuss propagation constant in three frequency ranges
I want to propose that the ‘’Copper lines’’ section be expanded to include a discussion of the propagation constant and characteristic impedance in the three frequency ranges. That would be high, intermediate and very low frequency including dc. High frequency is when ωC >> G and ωL >> R. Intermediate is when ωC >> G and R >> ωL. Low is when G >> ωC and R >> ωL. Constant314 (talk) 12:53, 27 May 2010 (UTC)


 * You might want to consider instead linking to Primary line constants where this is already discussed.  Sp in ni ng  Spark  08:13, 29 May 2010 (UTC)


 * Thanks, I had not seen that article before. I did not see where it covered the dc case. There is considerable overlap with "telegrapher's equations" and "propagation constant".  I would propose merging them, but it would be more than I would want to bite off. Constant314 (talk) 13:05, 29 May 2010 (UTC)

Attenuation constant, confusing language
it says "Losses in the dielectric depend on the loss tangent (tanδ) of the material, which depends inversely on the wavelength of the signal and is directly proportional to the frequency"

So, does the loss tangent depend inversely on the wavelength, which is what I think the language says and is wrong, I think,

or does the Losses in the dielectric depend inversely on the wavelength, which is what the following equation seems to say, and would be true if the loss tangent were more or less independent of frequency?Constant314 (talk) 21:30, 12 November 2010 (UTC)

Attenuation constant
In the alternative names for Attenuation constant, I have placed "attenuation" in front of "coefficient" since I intend to merge Attenuation coefficient into this page. At present Absorption coefficient is merged into Attenuation coefficient, which is wrong. I will unmerge that first. In general, Absorption does not equal Attenuation. — Preceding unsigned comment added by Abmcdonald (talk • contribs) 10:48, 20 January 2013 (UTC)


 * Following further investigations I no longer plan to merge Attenuation coefficient into this page. A B McDonald (talk) —Preceding undated comment added 15:29, 22 January 2013 (UTC)

Phase constant
In

"It represents the change in phase per metre along the path travelled by the wave at any instant and is equal to real part of the angular wavenumber of the wave."

is the wavenumber a complex number?


 * Yes, or it can be. If we can speak of complex frequency, it follows that wavenumber can also be complex.  See this book. SpinningSpark 12:30, 6 August 2014 (UTC)

Phase constant and wave number
I am not seeing any sources that define wave number as ω/c as claimed in this edit which I have reverted. I agree that the dispersion formula,


 * $$\ \left ( {\omega \over c} \right )^2 = \beta^2 + k_c^2 $$

is correct, but sources usually treat as synonymous phase constant β and wave number k, as in this book for instance. ω/c is the "free space" wave number, or k0, so we could write the dispersion formula as,


 * $$\ k_0^2 = k^2 + k_c^2 $$

The only source I found after a quick search that does not treat them as synonymous was this book which has wave number synonymous with propagation constant instead of phase constant, but that is still not the same as the claim put in the article. SpinningSpark 22:25, 23 February 2016 (UTC)

Inconsistency in the section "Phase constant"
Near the start of the section, it says


 * ''...the phase constant... is the imaginary component of the propagation constant for a plane wave. It represents the change in phase per unit length along the path travelled by the wave at any instant and is equal to real part of the angular wavenumber of the wave. It is represented by the symbol β and is measured in units of radians per unit length."

This implies that in the present context, "angular wave number" refers to the complex wave number. So far, so good.

But in the next line, we have


 * ''From the definition of (angular) wavenumber:


 * $$k = \frac{2\pi}{\lambda} = \beta.$$

The way the sentence is expressed, it suggests that k is the "angular wave number". This would imply that k can be complex and β = Re(k). Yet the formula forces k to be real, because the other two terms are real.

I fixed this, but maybe there is a better fix. 178.39.122.125 (talk) 16:47, 9 February 2017 (UTC)
 * k is normally a real value. In casual use, it is  a real value.  However, sometimes it is some times convenient to let it be a complex value.  This is usually done when the medium is lossy.  The imaginary part of k represents the loss. So β = Re(k) is correct but overly complicated most of the time. You find both versions in the literature, but in the introductory level text books, k is usually real. Constant314 (talk) 17:18, 9 February 2017 (UTC)


 * I agree with these statements. For many applications, the symbol k is a wave number that can only be real, whereas for many others, it has to be complex because that captures something important about the problem.


 * What is confusing in the present text is that a) First the complex version is mentioned under the name "angular wavenumber", b) then k is implicitly called the "angular wavenumber", c) then k appears in an equation that forces it to be real.


 * It would help if someone would write a verbal characterization (definition) of k, of the form "where k is..." It's a good general practice to do this for every variable that's introduced. In the case at hand, it would force the writer either


 * 1) To say that k is the real part of the "angular wavenumber". This has the advantage that we don't have to restrict to the lossless case. (But the complex version is often called k, so this could be confusing.)


 * 2) To make an explicit assumption that we are in the lossless case (or nearly so), and perhaps point out that for many applications the difference doesn't matter.


 * My suggestion (alternative 1) was reverted, it would be great if someone could fix it or make another suggestion. 178.39.122.125 (talk) 18:39, 9 February 2017 (UTC)

Another inconsistency in the section "Phase constant"
Later in the section it says:


 * ''In particular, the phase constant $$ \beta $$ is not always equivalent to the wavenumber  $$k$$. Generally speaking, the following relation


 * $$ \beta=k $$


 * ''is tenable to the TEM wave...

The problem here is twofold:

1) Earlier in the section, the relation $$ \beta=k $$ is stated unconditionally, without mentioning that there will later be a restriction.

2) Furthermore, this relation is presented as the definition of $$\beta$$, i.e. the phase constant is synonymous with the (real) wavenumber of plane waves in the medium. The relation is not presented as a theorem, approximation, or observation. So it's hard to see how they could ever be different, or what criteria a person could apply to determine that they are different.

Of course, there is a difference: the wave number is a property of a wave, whereas the propagation constant is a property of a medium. But I don't see how this can be used to drive a wedge between them. 178.39.122.125 (talk) 17:20, 9 February 2017 (UTC)


 * The apparent contradiction arose, I think, because the article orginally only discussed transmission lines (ie conducting lines). In those kinds of transmission the mode of transmission is always TEM, the same as plane waves in free space.  However, another editor later added a piece pointing out that waveguides support non-TEM modes.  In a waveguide the guide wavelength (λg, someone needs to write that article) is always longer (how much depends on mode) than the wavelength (λ) of the same transmission in free space (or in a dielectric filled waveguide, in an unrestricted medium).  Comparing the equation the editor provided with the equation for guide wavelength in Waveguide filter it is clear that the editor is using the definitions k=2π/λ and β=2π/λg. SpinningSpark 19:19, 9 February 2017 (UTC)


 * I think the wave guide example may be incorrect. In the wavenumber article it states $$k = \frac{2\pi}{\lambda} = \frac{2\pi\nu}{v_\mathrm{p}}=\frac{\omega}{v_\mathrm{p}}$$  which I believe is correct.  In this article it states $$k=\frac{\omega}{c} $$ which I think is incorrect. The cases that I am familiar with where $$ \beta=k $$ is not true is when k is complex.  The advantage of a complex k, especially when dealing with waves in 3 dimensional lossy media is that k can be a vector that handles propagation in 3 dimensions while accounting for phase and attenuation.  So, we have all that complication also.  But, this article is about the propagation constant and not the wave number. Maybe this is not the place for a detailed discussion of the wavenumber. Constant314 (talk) 22:19, 9 February 2017 (UTC)


 * This is all very interesting! I am starting to grasp the myriad of situations that have to be covered. If an expert would express the scope and assumptions of the various assertions more clearly, and in the right places, it would improve the clarity of the section. There are a number of points where this could profitably be done.


 * The first paragraph of the section ought to give a fully general definition of β, but it appears to do so only for the case of a plane wave, not a wave guide, without warning the reader that the scope will be widened later.


 * It seems to present the equation $$ \beta=k $$ as if it were the definition, rather than a statement that only works for plane waves (or maybe TEM waves).


 * Here is a possible fix for the later paragraph where $$ \beta=k $$ breaks down:


 * ''In the broader setting of periodic waves that are not plane waves, such as a waveguide, the phase constant $$ \beta $$ is not always equivalent to the unconstrained wavenumber  $$k$$.


 * ''Generally speaking, the relation $$ \beta=k $$ holds for a TEM wave (transverse electromagnetic wave) in free space or in TEM-devices such as the coaxial cable and two parallel transmission lines. Nevertheless, it is invalid for a TE wave (transverse electric wave) and TM wave (transverse magnetic wave). For example, in a hollow waveguide where a TEM wave cannot exist but TE and TM waves can propagate, we have


 * $$\beta=k\sqrt{1-\frac{\omega_c^2}{\omega^2}}$$


 * ''where $$k=\omega/c$$ is the wavenumber for the same frequency transmission in free space.


 * Presumably β still has same definition as in the case of plane waves, namely the wavenumber along the direction of propagation, but it's been computed for the finite-width waveguide. (But k is for a free space wave. Actually, this seems inconsistent with the earlier k, for plane waves, which at least took the medium into account.)


 * Unfortunately I don't have enough expertise to know if it's all true...


 * 129.132.208.37 (talk) 23:44, 9 February 2017 (UTC)


 * I pulled out my copy of Time Harmonic Electromagnetic Fields by Harrington. He  gives k as the "intrinsic phase constant" of the (lossless) dielectric and β as the phase constant of the mode.  So if the dielectric is vaccuum, then $$k=\omega/c$$ is correct. Constant314 (talk) 00:28, 10 February 2017 (UTC)


 * (after edit conflict) It's only a matter of definitions. The waveguide literature is littered with these kind of confusions.  For instance, one often sees the formula 1/λg2 = 1/λ2 − 1/λc2.  Now λc here has to be read as the wavelength a wave at the cutoff frequency would have if it were in free space for the formula to work.  Of course that is just a  convenient nonsense to make the formula simple: The wave in free space will not have a cutoff, and in the guide its wavelength will be the guide wavelength, not the free space wavelength.  Something similar is going on with k = ω/c.  The k (or better, β0) here could better be described as the free space phase coefficient/wave number and β (or βg) as the guide phase coefficient/wave number rather than try to make a distinction between k and β.  That would be clearer to my mind, but I don't know whether that is ever done in the literature.  If someone finds a source we could write it that way.  Constant314, there is an unstated assumption by the waveguide editor that the waveguide is air filled making k = ω/c correct under that assumption and with the implied definitions he used.  I agree the waveguide passage has been shoehorned into the article in a rather inelegant way, this is the original series of edits that did it for reference. SpinningSpark 00:39, 10 February 2017 (UTC)


 * Another point on notation, I prefer to define wavenumber as k=1/λ (ie, the original meaning of wavenumber: the number of cycles per metre) and phase change coefficient as β=2π/λ (radians per metre) but I accept that that is not the most common definition. <b style="background:#FAFAD2;color:#C08000">Spinning</b><b style="color:#4840A0">Spark</b> 15:05, 10 February 2017 (UTC)

Red herring in the section "Phase constant" ?
The following paragraph from the section "Phase constant" seems to be "generalities" from quantum mechanics that are almost out of place here. Why is it relevant to mention the momentum of a photon at this point? It doesn't seem to tie into anything else.


 * ''The phase constant is also an important concept in quantum mechanics because the momentum $$ p$$ of a quantum is directly proportional to it,  i.e.


 * $$ p= \hbar \beta$$


 * where $ħ$ is called the reduced Planck constant (pronounced "h-bar").  It is equal to the Planck constant divided by $2π$.

I also wonder if this is even true.

Everyone knows the relation $$ p= \hbar k$$, where k is the wavenumber of a "free" photon or one that has explicit interactions with quantum particles -- in any case, at a very fundamental, atomwise level. On the other hand, β takes into account the material properties of the medium in a kind of summarized way, like Maxwell's equation in a medium.

Can we even mix these two levels? Looking at the two references, it appears that the relationship with β is not standard at all, but is being speculatively proposed by the authors of the two papers. Yet it is hidden here in the Wikipedia article behind a fairly bland presentation, which does not brag about the two papers.

Can an expert sort this out? 129.132.208.37 (talk) 23:15, 9 February 2017 (UTC)


 * I came upon this Topic from my edits on Matter wave.
 * I read the Tremblay paper cite on the questioned link. Very interesting proposal to connect heuristic Planck's QM of a blackbody to electromagnetic modes of a closed box. I found nothing there to connected the sentence above and the article does not seem to have been peer reviewed.
 * The ZY Wang article is not available online. I can well imagine from the abstract that it does indeed support the sentence. However, this article has no impact in the physics community. 6 citations and none related the the sentence.
 * It's my conclusion that the claim of the sentence is not sufficiently supported. Johnjbarton (talk) 01:28, 22 May 2023 (UTC)