Talk:Telegrapher's equations

Merge with transmission line
These equations are all about transmission lines. On thier own they mean nothing but would greatly enhance the utility of the transmission line article. Does anyone object to the merge. If so, could you please state your reasons?--Light current 22:46, 12 September 2005 (UTC)

Ive copied all this matl over to transmission line. I'll leave it here also for a while to make sure of no objections, then we need to delete this page. I'm not sure how to do that.


 * I do have a possible objection. The telegrapher's equations are used for more than just transmission lines. For example, in the modeling of silver nanowires, the telegrapher's equations are used. Salsb 21:49, 26 September 2005 (UTC)

Not knowing about silver nano wires, can you briefly explain how the equations are used. Maybe we can use a redirect, rather than delete the page.--Light current 21:52, 26 September 2005 (UTC)


 * Just leave these. The partial differential equations are called that. But they don't 'belong' to any one application. Charles Matthews 22:00, 26 September 2005 (UTC)

Redirect to transmission lines s promised.--Light current 02:31, 10 November 2005 (UTC)

Equivalent Circuit Model
Is there any special reason, why the resistance between signal and ground is denoted by G in the equivalent circuit model? In the telegrapher's equations, G is used for the conductance between these two. Shouldn't one use 1/G as the value for the resistance instead? 89.49.148.145 (talk) 21:23, 1 May 2008 (UTC)

In the drawing what appears to be a resistance G is actually a conductance, as stated in the text. The telegrapher's equations are in fact dimensionally correct as they are. —Preceding unsigned comment added by 143.117.78.7 (talk) 17:06, 20 August 2008 (UTC)

The first contributor is quite correct. The diagram should show 1/G as the value of the shunt resistor element as its simply bizarre to have some resistors shown with symbols that are inconsistent, some needing to be reciprocals and others not. It's perfectly fine to use the symbol G in the text as it is defined in the text, just not next door to a resistance symbol. Can anyone fix the diagramCecilWard (talk) 14:27, 28 October 2009 (UTC)


 * I could change the diagram, but I am not convinced that would be the right thing to do. Transmission lines are pretty universally represented in my text books in the way shown, that is, with G not inverted. There is no separate graphic for a conductance.  Likewise, there are not separate graphic symbols for (admittedly much rarer) elastance and inverse inductance, the symbols for a capacitor and inductor, respectively, are used.  Sp in ni  ng  Spark  21:25, 30 October 2009 (UTC)

lossless lines
"Lossless transmission" should include the derivation at http://www.ivorcatt.org/digihwdesignp05.htm and http://www.ivorcatt.co.uk/4_1.htm. Ivor Catt —Preceding unsigned comment added by 62.245.72.207 (talk) 09:43, 5 June 2010 (UTC)

Frequency of Applicability
I'd like to propose changing "The theory applies to high-frequency transmission lines (such as telegraph wires and radio frequency conductors) but is also important for designing high-voltage energy transmission lines." in the first paragraph to "The theory applies to transmission lines of all frequencies including high-frequency (such as telegraph wires and radio frequency conductors), audio frequency (such as telephone lines), low frequency (such as power lines) and direct current."  I think there is general misconception that the telegrapher's equations and their solutions apply only at high frequency. In fact, there is no frequency assumption in the derivation and the results can be applied right down to DC. What is true is that the math is somewhat more tractable at high frequency. The characteristic impedance becomes complex and very large at zero frequency. This causes reflections at both ends of the wires. Each source end reflection demands more current from the source and each load end reflection supplies more current to the load. Once the reflections die out, we are left with the expected DC result.

Of course I am tacitly assuming the TEM mode. Even at frequencies high enough to excite waveguide modes, the equations still apply to the TEM mode, but there may be additional modes. Constant314 (talk) 14:08, 8 August 2010 (UTC)


 * The characteristic impedance becomes complex and very large at zero frequency. Don't think that is right, I believe that $$ \textstyle \lim_{\omega \rightarrow 0} Z_0 = \sqrt{\frac{R}{G}}$$, which might be large, but it aint complex. I agree that the equation certainly applies at all frequencies, but there is a diminishing need to use it at low frequencies because the phase delay is so much smaller, hence the effects of reflections are so much less noticeable.  A construction something like ...applies to all frequencies ... but is especially important to ... or something similar might be more appropriate.  Sp in ni  ng  Spark  15:03, 8 August 2010 (UTC)


 * The characteristic impedance becomes complex and very large at zero frequency. There is a piece of missing information and that is that G tends to become very small as the frequency becomes small. It is so small that usually sC >> G, at least into the sub hertz region. In that case  $$ \textstyle \lim_{\omega \rightarrow 0} Z_0 = \sqrt{\frac{R}{sC}}$$.    For example in Subscriber Loop Signaling and Transmission Handbook (Digital), by Reeve, Whitman, IEEE Press, 1995 appendix B, the characteristic impedance of 26 gauge PIC at 1 hertz is given as 20,562 - J20,551.    But yes, if Gdc > 0 then at a low enough frequency the characteristic impedance would become real.Constant314 (talk) 14:18, 3 October 2010 (UTC)


 * Regarding "there is a diminishing need to use it at low frequencies because the phase delay is so much smaller, hence the effects of reflections are so much less noticeable. " Even with pure dc, if the line is long, series resistance and shunt resistance are distributed.  You cannot merely use their lumped values.  Instead, you start with the solution from the Telegrapher's equations and take the limit as frequency approaches zero. Constant314 (talk) 22:04, 12 October 2010 (UTC) 15:02, 8 October 2010 (UTC)
 * Of course it's distributed, but that wasn't exactly the point. It is not necessary to invoke the Telegrapher's equation, to find the dc solution; there are much more straightforward methods.  Sp in ni ng  Spark  18:18, 8 October 2010 (UTC)
 * I'm never surprised to find that there is more than one way to solve a problem, but right now I cannot think of any way that would not amount to seting up telegrapher's equations without the L and C terms and solving them in the same way.Constant314 (talk) 22:33, 12 October 2010 (UTC)


 * Oh of course, I see what you mean. I should say "The characteristic impedance becomes complex and very large at low frequency." instead of "at zero frequency". Constant314 (talk) 22:41, 12 October 2010 (UTC)

Solutions of the Telegrapher's Equations as Circuit Components
I posted a simular schematic on the article "Transmission Lines" and I got a comment that I think is relevent to the schematic posted on "Telegrapher's Equtions" so I will repeat it and my response here.

Comment: Is this standard stuff? I've never heard of it before. Also, why would one want to represent a transmission line by an active circuit?


 * Regarding the question “why”
 * 1. You can insert it into your SPICE circuit simulator for robust simulation of the transmission line, its load, its source and all the other circuitry including equalizers, filters, pads, amplifiers and other signal conditioning.  It also lets you readily simulate such things as multiple bridge taps, gauge changes, splits, and corroded splices.  You can simulate complex structures such as customer wiring which might have bridge taps with bridge taps, on-hook telephones, off- hook telephones, etc.  If you can draw it as a circuit, then you can simulate it with SPICE.  Check out the link about SPICE simulation for more details.

http://www.eetimes.com/design/microwave-rf-design/4200760/SPICE-Simulation-of-Transmission-Lines-by-the-Telegrapher-s-Method-Part-1-of-3-
 * 2. Thanks to Linear Technology Corporation, SPICE is available to almost every one with a very general and free license at

http://www.linear.com/designtools/software/ltspice.jsp
 * 3. This is subjective, but I find this diagram to be highly intuitive. If the load side is open, it is obvious that the pulse voltage doubles and is reflected. If the load is shorted, the pulse current doubles and is reflected.  If the load is matched, then there is no reflection.  For a sanity check, assume that the line is lossless but has delay (T = pure delay) and then try various combinations of impedance at each end (infinite, matched, and zero) and verify that you get the expected behavior.


 * Regarding the question: “Is this standard stuff?”


 * The solutions to the Telegrapher's Equation are, of course, standard stuff.
 * Representing the transmission line as a two-port is also standard stuff.
 * Using the solutions of the Telegrapher’s equations to derive the two-port parameters is standard stuff.
 * Using circuits to implement equations is standard stuff.
 * The pararmeters of any of the standard two-ports can be derived from this circiut.


 * But, is this circuit new? The mathematical equations that the circuit implies have been around for decades.  So, is this standard stuff?  In my opinion, yes it is because it translates precisely to standard stuff (the Telegrapher’s equations).  But representing a transmission line as this circuit instead of a list of equations may be new.  Which is to say, I haven’t seen this particular circuit anywhere, although I recall seeing crude equivalent circuits buried in the back of very old (from the 90’s or older) SPICE manuals.  Constant314 (talk) 12:23, 21 October 2010 (UTC)


 * For now, I think it should be out. It's very non-standard, and fairly hard to understand, with all the complexity being hidden inside the little T(s) boxes in the "hybrid" arrangement; this form of T(s) transfer function is not itself something that's easy to describe and simulate in SPICE, I think.  If you want to describe the T(s), the transfer function to forward- and backward-propagating waves across a length x, that is published in reviewed articles (by me, for instance).  Dicklyon (talk) 18:20, 13 December 2012 (UTC)
 * I discussed this with an Admin before I posted it. His opinion was that an article published in EE Times met the criteria for a credible source.Constant314 (talk) 05:31, 14 December 2012 (UTC)
 * Somewhat later Paul Rako blogged about it on EDN: http://www.edn.com/electronics-blogs/anablog/4311804/Improved-Spice-model-of-a-transmission-line  and there was a round of comments http://www.edn.com/electronics-blogs/anablog/4311805/Ott-Gilbert-Sauer-Harvey-and-Fong-discuss-the-new-Spice-model-for-transmission-lines  You may recognize some of the names.  There is a wikipedia page on Barrie Gilbert.  Constant314 (talk) 05:40, 14 December 2012 (UTC)
 * I take it back about it not being easy to represent in SPICE. I see the Laplace object takes arbitrary formulas; this was probably added some time in the last 3 decades.  Dicklyon (talk) 18:45, 13 December 2012 (UTC)
 * Its a surprise that the Laplace objects work at all. Apparently they numerically calculate the impulse response and use that in the transient simulation.Constant314 (talk) 05:44, 14 December 2012 (UTC)
 * That would explain why they need to roll off at least 6 dB/octave at high frequencies to work well. For frequency response, of course, they're easy.  Dicklyon (talk) 07:03, 14 December 2012 (UTC)

Changing reference style to Harvard
I am going to switch all the references to Harvard style. I am the person that added all the references in first place.Constant314 (talk) 14:09, 19 November 2010 (UTC)

Using Kelvin or Celsius temperature scale.
In the article there are places where some temperatures are referenced in Fahrenheit. Because this scale is not the only one and also, the scale in SI is Kelvin's I propose using either Kelvins or degrees Celsius (because they have the same step of values). - A SI fan. — Preceding unsigned comment added by Nikolageneshki (talk • contribs) 14:34, 24 January 2012 (UTC)


 * Fahrenheit is still widely used in some countries, particularly the US. I suggest instead that you use the convert template.  Spinning  Spark  17:37, 24 January 2012 (UTC)
 * Presumably Fahrenheit is not used in science even in the US? More in everyday applications like room temperature and cooking? Billlion (talk) 17:12, 27 November 2012 (UTC)
 * Fahrenheit is still widely used in th US by industry, including the telecom providers. The data in the Values of primary parameters for telephone cable table is in Fahrenheit because the source used Fahrenheit. Constant314 (talk) 13:51, 14 December 2012 (UTC)

Skin Effect and Proximity Effect
The article says that The variation of R and L is mainly due to skin effect and proximity effect. Do these really affect L?  AlphaHelical (talk) 03:45, 14 June 2013 (UTC)
 * see the Skin effect article for a description of how skin effect reduces inductance and citations to Hayt's E&M text book. Howard Johnson's High Speed Digital Design: A Handbook of Black Magic describes how proximity effect changes the current distribution in the wires.  I don't recall what if anything he says about changing inductance, but it's plausible to me that if something changes the current configuration it would change the inductance too.Constant314 (talk) 04:53, 14 June 2013 (UTC)

Drift velocity and wave velocity
Why have you removed the explanation that it is the wave that is travelling at that speed, not the current carriers? This is a very common misconception (we get questions on it all the time on the refdesk. I understand your edit summary, and the text may be more appropriate in another part of the article, but not removed altogether.  Does a perfect (mathematically ideal) conductor not have current carriers by the way? I appreciate that drift velocity is intimately connected with resistance and is thus not applicable to an ideal conductor, but it is still the case, even in an ideal conductor, that the charge carriers are not moving at the speed of the propagated wave and this needs explaining.  Spinning  Spark  14:14, 15 May 2014 (UTC)


 * I did NOT remove it. If you look at the history page, you will see that Constant314 removed it.  If you are not happy about it, then put it back or discuss it with that person. First Harmonic (talk) 17:32, 15 May 2014 (UTC)
 * Beg your pardon. Let's wait to see what he says.  Spinning Spark  18:37, 15 May 2014 (UTC)
 * It was me that removed it. It seems like a comment from left field.  The article is doing a good job discussing the telegrapher’s equations and then suddenly there is this unrelated comment about drift velocity.  It's not a text book where the author may indeed warn the student about different kinds of velocity.  I don't think it belongs in an encyclopedia article about the telegrapher’s equations.  But I'm not going to war about it.  Regarding perfect conductors: in my opinion mathematically perfect conductors don't have charge carriers.  They don't have any internal structure at all.  The reason for invoking them is so you can concentrate on fields and ignore whatever is going on in the conductors.  I think imputing the existence of charge carriers and what they must be doing in perfect conductors borders on WP:SYN.  Also, I think drift velocity is a somewhat vague but complicated concept that should not be dropped casually into any article.  There are a lot of assumptions that go into calculating drift velocity and some of them are just convenient.  It comes down to this: drift velocity is just the average velocity of the electrons someone arbitrarily decides should go into the average.  You could average over all the electrons in the metal and get a really small number.  Or you can assume, as is commonly done, that it is one electron per atom and get a different number.  Or you can look at the Fermi ball and say that it is a whole lot less than one electron per atom that is available to contribute to the current so the drift velocity actually pretty big, though still less than the speed of light.  If you want to discuss velocities, it would be more appropriate to point out that transmission lines made of perfect conductors may have wave-guide modes that do propagate slower than the speed of light.  Bottom line: I think electron drift velocity is out of place in this article, but if someone wants to put it back, I won’t remove it again.Constant314 (talk) 02:53, 16 May 2014 (UTC)

Velocity: u or v?
I suggest that you go back to lower case v for velocity. Of the seven references for the section, four use lower case v, Sadaku and Metzger use lower case u and Marshall uses upper case U. Looking at other sources, Feynman, Griffiths, Johnson, Jordan/Balman, Ramo/Whinnery/van Duzer, Magnuson, Hilberg and Gupta all use lower case v. Constant314 (talk) 21:07, 17 May 2014 (UTC)
 * I'm not really bothered either way, but it bugs me when people arbitrarily change the format of anything to their preferred system without discussion. So just on that basis, I support going back to v.

Obtaining Telegrapher's Equation from Maxwell Equations
I'm really surprised this is not present in the article; we have to memorize it for exam, so apparently it's something "common".

Unfortunately I don't really understand this problematic nso can't add it to the article, but it's definitely missing! — Preceding unsigned comment added by 188.175.227.121 (talk) 00:28, 18 January 2015 (UTC)

Electrons do have inertia, don't they?
The sentence "The inductance L makes it look like the electrons have inertia" makes it sound like electrons don't *actually* have inertia. Electrons, like everything with mass, do in fact have inertia. Would it be more accurate to say "more inertia"? 67.188.28.229 (talk) 00:37, 17 June 2018 (UTC)


 * Yes, electrons have inertia.  It is an imperfect analogy.  In the plumbing model of circuits, the inertia of the water is analogous to inductance.  It might be better to say that the current acts like it has inertia.  I don't think that the language is particularly encyclopedic and there is no reference, so you are welcome to try to improve it.Constant314 (talk) 01:22, 17 June 2018 (UTC)


 * The actual inertia of electrons, related to the fact that the electron mass is more than zero, does indeed exist and is responsible for so-called "kinetic inductance". In this context, kinetic inductance is much smaller than normal (magnetic) inductance and can be ignored. Kinetic inductance is typically relevant at very high frequency (~1 petahertz = 1 million GHz, i.e. ultraviolet) and also in some superconducting circuits. I just added a link. Interestingly, magnetic fields have momentum too, and therefore they have inertia. I wonder whether magnetic inductance too can be explained as an actual mechanical inertia effect? I don't think I've seen that in any reference, it's just a fun thought. :-D --Steve (talk) 13:03, 17 June 2018 (UTC)
 * I think that perhaps kinetic inductance is a detail not needed in this article.Constant314 (talk) 22:58, 17 June 2018 (UTC)
 * Hmm, you're probably right, I just deleted it. --Steve (talk) 23:33, 17 June 2018 (UTC)

Beam me up
Hi people. Imma not el stupido, but this article is completely out of reach of the average person. Can one of you engineers try and explain this to your mother here? We need a Sarek, I guess, or Sagan or whomever. cheers 184.69.174.194 (talk) 05:46, 15 March 2019 (UTC)
 * Your complaint is too vague. Why don't you indicate the first paragraph that is confusing and tell us what makes you confused.Constant314 (talk) 06:10, 15 March 2019 (UTC)

Antennas section
I wonder if this section should be restricted to folded antennas. One of the references is entirely about folded antennas. I also find some mention in Balanis regarding transmission line modes on a folded dipole antenna. It makes sense, since the folded elements sort of look like transmission lines, but I have trouble imagining transmission line type analysis for general antennas. Constant314 (talk) 20:46, 30 October 2019 (UTC)


 * In short, the answer is ‘no’. There is no requirement for a second conductor, and folded dipoles do not illustrate a better-behaved system. If you sit down with a paper and pencil, you'll notice that the two currents in a folded antenna at a resonant frequency are flowing in the same direction, rather than opposite directions, like you'd expect of a transmission line. If you cut the shorted ends of the wires at the far end (the shorted, far end, is a current null = voltage peak) the RF performance is pretty much unchanged.


 * An honest-to-goodness (American style) telegraph line is a genuine single-conductor transmission line. If you like, you can either think of the return current coming back through the ground (telegraph) or reflecting off the open end (antenna) (both occur). Since American telegraph wires carried / carry a one-way DC current, it's easier to believe in the return via ground current, and hence its a good tutorial start-point for RF single-wire conductors.


 * There is also a single-conductor power line design. It was used in the early days of U.S. rural electrification (maybe elsewhere). The far end of the line, at the power delivery point, was attached to a transformer; the other end of the transformer was grounded. The AC return current (in principle) flows back through the ground (but in reality, the earth just serves as a local reservoir of electrons and electron holes). It is inefficient, but putting up just one wire greatly reduced the demand for copper, and allowed the first rural electrical lines to be put up quickly.


 * In the case of antennas, there is no ground reservoir that I know of; at RF there genuinely is an "invisible second wire". The fictitious second conducting wire is an image of the current in the wire seen in the ground-plane by the antenna wires dangling above it; in a salt-water marsh, there is no wire, but for more ordinary ground planes, the antenna-builder needs to put down a meshwork (chicken wire) or "star" network of grounding wires to give the "ground" better conductivity. (Actually, in passing, I should mention that getting neophyte antenna-users to pay attention to the ground currents that are dissipating their voltage without producing any radiation is something of an important lesson. So if the article included a § that explained single-conductor transmission lines, it might be usefully tutorial for antenna purposes.)


 * (None of the above discussion pertains to VHF / UHF single-wire wave-guides, that I know of. Those have the RF waves skimming above the outside of the conductor surface. There is indeed a smooth cross-over with frequency, from electrical waves conducted in the metal to radio waves surfing outside of, but near a conductor, but I'm not sure if Heaviside's $R′ L′ G′ C′$ model still applies at that point.)
 * 107.127.18.8 (talk) 19:21, 27 July 2021 (UTC)

A wave equation
The caption "In the presence of losses the solution of the Telegrapher's equation has both damping and dispersion, as visible when compared with the solution of a Wave equation.", doesn't make sense because the telegraph equation IS a wave equation. It should be qualified by what type of wave equation being compared to. — Preceding unsigned comment added by 128.163.239.235 (talk) 19:40, 11 October 2020 (UTC)


 * The "classical" wave equation is $$ \left[ \left(\frac{\partial}{\partial x}\right)^2 + \left(\frac{\partial}{\partial y}\right)^2 + \left(\frac{\partial}{\partial z}\right)^2 - \left(~\frac{\partial}{c\, \partial t}\right)^2 \right] W(x,y,z,t) = 0 ~.$$ Notice that there is no first-order term. The second-order-only form is what people typically mean when they refer to "the wave equation". Inserting first-order terms introduces energy loss: The waves die out. (Unless, of course, you get the sign wrong, in which case the waves grow.) (In mechanical systems and fluids, the first-order terms are usually fairly inaccurate approximations for the dissipative forces, although they are nearly perfect for electrical circuits, the only sticky issue being the mess that the $$\sqrt{f~}$$ factor from the skin effect makes.)
 * 107.127.18.8 (talk) 19:38, 27 July 2021 (UTC)

General solution for terminated lines of finite length
I have been looking for a WP:RS for this and haven't found any. I think I know why. It is a comprehensive result for a special case. It attempts to give the time domain solution for the volage everywhere inside the transmission line for the special case where the source impedance is zero. While I do not have any reason to believe it is incorrect, I do believe there are too many missing steps to accept it as verifiable (WP:V). So, I will remove it and replace it with something similar that does have a reliable source. Constant314 (talk) 01:46, 7 May 2023 (UTC)