[HN Gopher] Oliver Heaviside and the theory of transmission line...
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Oliver Heaviside and the theory of transmission lines (2021)
Author : xeonmc
Score : 214 points
Date : 2025-01-27 12:18 UTC (10 hours ago)
(HTM) web link (www.pa3fwm.nl)
(TXT) w3m dump (www.pa3fwm.nl)
| roelschroeven wrote:
| One of the diagrams has the text "40 sections elk 100 m long".
| "Elk" (or "elke", depending on grammatical gender) is Dutch for
| "each", so it looks like a small oversight in translation. It's
| not about deer that somehow got caught up in transmission line
| theory.
|
| Hope that clears up any confusion that might possibly arise.
| eldaisfish wrote:
| Elk is a type of transmission line conductor. Example -
| https://www.lzcable.com/acsr-elk-conductor/
|
| Others include moose and drake.
| cluckindan wrote:
| More info about the various types:
|
| https://www.electricaldesks.com/2022/09/Types-of-
| Conductors-...
| parsimo2010 wrote:
| In the context of this article, it seems clear to me that GP
| has the right translation. The other figures say "each" in
| the same position, and it looks like there was one word that
| didn't get translated from the figure. The fact that this is
| all on a .nl domain and the author says this is a translation
| from a Dutch magazine article lends even more weight to the
| idea that the author wasn't talking about a particular type
| of transmission line.
| eldaisfish wrote:
| i'm pretty confident both of you are correct. I know some
| Dutch and spotted that as well.
|
| I did find it an interesting overlap that in the field of
| transmission lines (electricity lines specifically) there
| is literally a conductor size names elk :)
|
| My original comment could do with an "also".
| parsimo2010 wrote:
| A very interesting explanation with history and math combined!
| I'm not sure if most of HN cares about rf things at this level
| but I was very happy to see a discussion of transmission lines,
| and a lot of the discussion of the trades of parameters to
| improve a Morse code transmission.
| scrlk wrote:
| RF is definitely interesting - it's the closest thing to black
| magic in electrical engineering (all went over my head during
| my degree...that's why I ended up in power systems :^) ).
| ninalanyon wrote:
| But you still have transmission lines, just at a much lower
| frequency!
| amelius wrote:
| Yes, especially since in power transmission the distances
| are large; if you turn on the power at point A, then point
| B will not immediately receive the power and this is quite
| measurable.
| mhh__ wrote:
| He's buried near where I grew up. Must pay him a visit at some
| point.
| bandrami wrote:
| For years and years I thought the "heavy side" function was 1 on
| one side of the origin and 0 on the other. I also thought the
| "pointing" vector pointed in the direction the wave was
| travelling.
| selecsosi wrote:
| Nominal Determinism at its finest
| idlewords wrote:
| Nominative determinism. There's also the pithy Latin phrase
| _nomen omen_.
| IndrekR wrote:
| And Li-ion batteries are good enough:
| https://en.wikipedia.org/wiki/John_B._Goodenough
| phreeza wrote:
| This exact theory is also used to model the electrical behavior
| of neurons in the brain, with some slight differences (no
| inductances, non-linear resistances), under the name "cable
| theory" https://en.wikipedia.org/wiki/Cable_theory
|
| I remember one professor mentioning the origin of this theory in
| undersea cable modeling at some point.
| brunohaid wrote:
| Tried skimming the page but couldn't find the answer: do we
| know if the neural connection impedance is perfectly matched?
| It looks quite organic in shape, with teardrop connections and
| so on, but curious how nature did that job?
| phreeza wrote:
| It is not always perfectly matched, because the mismatches
| can actually have a "computational" purpose, but e.g. the
| typical branching pattern of dendrites is pretty close to
| being matched . There is a chapter on this in the Dayan and
| Abbot textbook.
| brunohaid wrote:
| <3 awesome - this one https://boulderschool.yale.edu/sites/
| default/files/files/Day... ?
| phreeza wrote:
| Yes exactly. Chapter 6.3, though it is actually less
| detailed than I remembered.
| brunohaid wrote:
| Much appreciated! Maybe the impedance added some colorful
| garnish to your memory... :-)
| mattkrause wrote:
| If this is your thing, you might also want to check out
| Christof Koch's _Biophysics of Computation_. Cable theory
| is introduced in one of the first few chapters.
| mannykannot wrote:
| That's an interesting question. One follow-up question I
| would have is whether impedance matching is a relevant
| concept here, given that the model has no inductance (I'm
| guessing that's because the flow of charge is in the form of
| ions moving radially through the membrane. If neurons were
| more like transmission lines, would we be susceptible to
| interference from distant lightning?)
|
| I also skimmed the page and saw that equation 20 is not a
| wave equation (as the article says, it is a diffusion
| equation.) Again, I am not sufficiently knowledgeable to say
| whether that renders the question of impedance matching moot.
|
| Update: I see from the sibling thread and its excellent
| reference that the refractory period, where the sodium and
| potassium ions are being pumped back to their starting
| positions, suppresses reflection.
| brunohaid wrote:
| Sibling thread?
| mannykannot wrote:
| Sorry if that's not clear - I was referring to phreeza's
| reply to your question and the link you had posted below
| it, which is as far as the discussion had gone at that
| time. The refractory period, and its role in suppressing
| reflections, is mentioned in the reference you provided a
| link to.
| brunohaid wrote:
| Got it - haven't read it yet but, also thanks to your
| pointer, very much looking forward to!
| amelius wrote:
| This looks different, as there is a completely resistive path
| from source to destination, which is not the case for
| transmission lines (as that would mean an instantaneous
| response which isn't possible due to the speed of light limit).
| phreeza wrote:
| I think it's just a matter of scale, technically there is an
| inductance but the distances are so small and frequencies so
| low that they never really matter.
| amelius wrote:
| Yes, but then it is not a transmission line.
| CamperBob2 wrote:
| They're modeling delay with capacitance to 'ground', it
| seems. So there's capacitive reactance.
| amelius wrote:
| But that's not a complete model, as the output will start
| changing the moment the input changes. And a short burst
| will not appear so on the output.
| phreeza wrote:
| It will change instantaneously, but with a magnitude that
| decays exponentially with distance from the place the
| current is injected. The way signal propagation works is
| that you have "active" currents to ground that react to
| voltage changes in a nonlinear way. These lead to wave-
| like behavior in the transmission line, though it is
| quite nonlinear and harder to model than a straight up
| inductor.
| brunohaid wrote:
| Excellent post!
|
| Controlled impedance took me a long time to wrap my head around
| when starting PCB design, the moment when it finally clicked was
| watching this excellent AlphaPhoenix video
| https://www.youtube.com/watch?v=2AXv49dDQJw& asking and
| practically demonstrating the simple question:
|
| When you flip on a switch, to turn on anything, send data, morse
| something etc, how does the circuit know how much current the
| load at the other end needs?
|
| Spoiler: Given that information can't travel faster than light,
| the simple answer is: it doesn't. So it just guesses and adjusts,
| which you don't want as it gives you exactly the ringing etc
| Heaviside identified. The video is a nice complement, as it
| perfectly visualizes the issues at play.
|
| It's a pretty wild bit of understanding to have, even in simple
| situations like flipping on a light switch.
| thijson wrote:
| I remember reading about the first cable that was laid across
| the Atlantic.
|
| https://en.wikipedia.org/wiki/Transatlantic_telegraph_cable
|
| They didn't know much about transmission line theory, and even
| burned out the cable at one point. Heaviside was only about 8
| years old when the first cable was laid down.
| CharlesW wrote:
| That video (and channel, seemingly) is incredible, thank you
| for posting! I've never seen anything like the visualizations
| starting at ~10m.
| nyrikki wrote:
| That video is good for the water like wave explanation that is
| a very useful lens. If you want a more in-depth explanation,
| particularly how the field is in the dielectric and the
| wires/traces are simply the wave guide, this long presentation
| by Rick Hartley will help move to the next level.
|
| https://www.youtube.com/live/ySuUZEjARPY
|
| The dramatic shift in behavior above the audio frequency range
| is where the water wave lens starts to fall down IMHO.
|
| I was looking at my brothers memory card from a Cray 1a the
| other day and that video popped in my head. They had the timing
| traces snaking through several flat-pack chips legs. No wonder
| they had to move from parity to Hamming code even with
| exclusively using differential twisted pairs between modules.
| brunohaid wrote:
| That one's gold too, but for me it was the other way round -
| needed Hartley to fully grasp Alpha Phoenix.
|
| Understanding waves feels a bit like the bell curve meme for
| me: you start with the mental water model, and eventually end
| up with it again.
|
| Or Feynman: you hear him helpfully talk about bouncy rubber
| balls, then learn a bunch of stuff over the next decade, and
| randomly listen to the same lecture again, and suddenly all
| sorts of ,,aaaah, that's what he meant" lightbulbs go off.
| nyrikki wrote:
| I should also clarify something above, Oliver Heaviside did
| discover the energy flows through the dielectric, most
| explanations like that video use other lenses to
| communicate the very real need to consider voltage and
| current.
|
| The original link side stepped that as to be honest it is
| to complicated for the intended use case.
|
| All models are wrong, some are useful, and the water wave
| model is very useful for very real needs.
|
| I personally wasted a lot of time confusing the map for the
| territory, but yes everyones path will be different. I
| confused the "electron flow" and water wave model as being
| absolute _ground truth_ for way longer than I would like to
| admit.
| elteto wrote:
| Watching the Alpha Phoenix video I had a sort of
| realization that waves (as phenomena in general) are
| basically nature's calculator/probes. If nature doesn't
| "know" what will happen there's probably some wave involved
| to figure it out.
| rezmason wrote:
| There's a fascinating story about ego in science buried here.
|
| William Henry Preece was Engineer-In-Chief at the British Post
| Office in the late 19th Century (basically heading their
| telegraphy efforts) and controversially stuck to Thomson's model,
| or the "KR Law" as it was called back then, relying on poor
| quality experimental results to direct the organization.
|
| Oliver Heaviside publicly criticized Preece, who in turn blocked
| publication of Heaviside's writing to preserve his own reputation
| (according to Wikipedia). When Preece retired in 1899 and
| received a knighthood, Heaviside wrote in the preface of Volume
| II of "Electromagnetic Theory":
|
| "It is to be hoped and expected that the late important removals
| in the British Telegraph Department will lead to much improvement
| in the quality of official science."
|
| Writing by hand on his own copy, Heaviside suggested that the
| preface (and thus the book's publication) were "held back" so as
| to "allow W H Preece to make sure of his knighthood".
|
| https://outsideecho.com/DGT-BIO_files/PDFs/DGT13.pdf
|
| So! On the one hand, we have an esteemed engineer who ran the
| country's telegraphs and refused to admit he made a mistake,
| became a knight and faded somewhat from history; on the other
| hand, we have a self-taught physicist who made massive
| contributions to our understanding and analysis of
| electromagnetism, lived in "relative poverty" for fifty years
| while doing so, didn't shy away from calling out bad science, and
| he gets the analogue of heaven named after him in the musical
| "CATS".
| brunohaid wrote:
| Not a religious person, but there's something deeply spiritual
| about Katalin Kariko type characters, who throughout the ages
| stuck with their curiosities and craft for the craft's sake.
| myth2018 wrote:
| Thank you very much for sharing this. I've been trying to form a
| mental model of why reflection in transmission lines is a thing
| and never found a theoretical foundation that satisfied me. I've
| read a number of publications that just state that as fact,
| without further explanation. I'll spend some time sketching my
| own graphs and formulas to fully absorb the fine article.
|
| PS: he discusses the impossibility of moving signals faster than
| light. I'm in fact interested in moving them way slower than they
| do, since that could make it possible to build very short
| antennas. I'm surely not the first to think of this. Maybe that's
| not even possible and that theoretical model could help to
| demonstrate why (even though it applies to transmission lines
| while I'm concerned about antennas).
| jrmg wrote:
| Yes! I've dabbled in digital electronics and never managed to
| form an intuitive understanding on 'impedance' in signal wires
| despite reading quite a few 'basics' texts about it. I'd ended
| up accepting that I wouldn't really understand its basis
| without learning a lot more about analog electronics, but this
| explanation really worked for me.
| basementcat wrote:
| For me, an optics analogy appealed to my intuition. A
| transmission line is analogous to a periodic crystalline
| material, perhaps a form of quartz. Impedance is analogous to
| index of refraction; if two materials of differing index of
| refraction are juxtaposed, some of the light will reflect back.
| If the indices of refraction match ("impedance match") then
| there is no reflection and maximum energy transfer takes place.
|
| https://en.m.wikipedia.org/wiki/Refractive_index
| marcosdumay wrote:
| Yeah, that's easy to work with so it's a great working model.
| But as an explanation, it leaves a lot to be desired.
|
| In fact, I'd say it's easier to explain optical refraction
| with an electrical model than the other way around.
| myth2018 wrote:
| Thanks. I found experiments like this [0] helpful to
| visualize reflections and standing waves, but, like a sibling
| comment said, although these are similar phenomena and show
| what happens with the energy inside the wire, I couldn't see
| why these effects manifested at the electrical level.
|
| [0] - https://youtu.be/1PsGZq5sLrw
| DougMerritt wrote:
| > Impedance is analogous to index of refraction
|
| That's not just an analogy; impedance _is_ index of
| refraction, with the same body of modern theory, except that
| "impedance" derives from the history of analysis of low
| frequency ("radio") waves whereas "index of refraction"
| derives from the history of analysis of high frequency
| ("optical") waves.
| gzalo wrote:
| Indeed, if you search for "ceramic antennas" you'll see that
| they are already being used and smaller than equivalent PCB
| antennas. They rely on a dielectric material with high e_r,
| which implies that speed of light is slower there. Lots of
| portable devices use them nowadays!
| myth2018 wrote:
| I had never heard about them. Will do some research right
| away, thanks
| immibis wrote:
| It's the general theory of waves: whenever some value exists on
| a continuum, has a position and a velocity at each point, and
| the acceleration (change in velocity) brings each point towards
| the average of its neighbours.
|
| When someone waves a skipping rope at one end, they directly
| move the portion of the rope closest to them, which pulls on
| the portion next to it, which pulls on the portion next to it,
| and so on. Some wave-shapes happen to be are sustainable enough
| to travel along the whole rope with low distortion. (Like when
| you draw random pixels in Conway's Game of Life and run it, you
| usually end up with lots of gliders and a few spaceships
| travelling off in various directions, because those happen to
| be the simplest travelling patterns and the rest of your
| scribble died out or turned into things that don't travel.
| There aren't any non-travelling wave shapes.)
|
| In a rope, the usual wave packet is like a hump, and if the
| rope is infinitely long, the wave packet can travel forever, as
| sections at the front of the wave get raised up by the hump
| just behind them, and sections the hump passed through get
| pulled down by the rope in its default position behind them. If
| you now imagine the rope is cut in half and one end is tied to
| a wall, when the wave gets to this wall, the bit that is tied
| to the wall does NOT rise up because it's tied to the wall, so
| the bit just behind it gets pulled down more than it would be
| in an infinite rope, and after running the simulation for a
| short time, the net effect is that the back part of the wave
| doesn't just get pulled down to its equilibrium position like
| it would if the rope was infinite, but gets pulled down twice
| that, forming a negative copy of the original wave.
|
| And you can have in-between values, where some section of the
| rope is harder but not impossible to move, which causes the
| back part of the wave to be pulled down more than usual, but
| not twice as much, forming a smaller inverse copy, and the part
| that is harder to move is pulled up, but less than usual,
| forming a smaller non-inverse copy.
|
| You can also go the other way, and have a section of the rope
| that's easier to move than usual (or infinitely easy i.e. an
| open end), and when the wave gets to this point, the back part
| of the wave doesn't get pulled down as much as it normally
| would, leaving it still in the shape of the wave, i.e. a
| smaller non-inverse copy, instead of returning it fully to
| equilibrium.
|
| And if you can visualize this with ropes it works similarly for
| electricity - just replace position by voltage and velocity by
| current - or any other imaginable system where each piece of a
| continuum has a second derivative that tries to bring its value
| back to the average value of its neighbors.
| myth2018 wrote:
| Those are interesting insights, thanks for the extensive
| reply
| nereye wrote:
| Am partial to the following vintage video on transmission lines
| from Tektronix:
|
| https://www.youtube.com/watch?v=I9m2w4DgeVk
| Jun8 wrote:
| This guy was awesome! He innovated ways to solve DEs with Laplace
| operator for inputs with discontinuities eg, what is now called,
| the Dirac delta function. Years before the math for generalized
| functions was developed by mathematicians. When asked about the
| theory behind the method he happily announced that he doesn't k
| ow but that it just worked!
| smallmancontrov wrote:
| > Dirac delta function
|
| and the Heaviside Step function looks like Heaviside's head
| lol.
| dmd wrote:
| https://shot.3e.org/ss-20250127_095213.png
| gradschool wrote:
| Another Heaviside biography in addition to the one cited in the
| article is "Oliver Heaviside: The Life, Work, and Times of an
| Electrical Genius of the Victorian Age" by Paul J. Nahin. It's
| profusely illustrated and doesn't omit the math.
| DriftRegion wrote:
| I just finished reading this one. It was fantastic. I
| particularly enjoyed the spicy editorial excerpts from The
| Electrician ( https://en.m.wikipedia.org/wiki/The_Electrician
| ).
| vmilner wrote:
| Paul Nahins books are so good.
|
| See also The Science of Radio And the Mathematical Radio
| (Similar content but one more focussed at elec eng people and
| one more at math(s) people)
| B1FF_PSUVM wrote:
| > doesn't omit the math.
|
| "The best result of mathematics is to be able to do without
| it", he said, which seems strange but makes sense coming from
| the man who came up with functional operators.
|
| I knew this quotation in my undergrad school days; just now
| checked the net and there is a source:
| https://hsm.stackexchange.com/questions/7332/a-peculiar-quot...
| myself248 wrote:
| There's another really good explanation of transmission line
| theory over here:
|
| https://www.ibiblio.org/kuphaldt/electricCircuits/AC/AC_14.h...
|
| This is the one that finally made impedance "click" in my head.
|
| OP's, however, treats the subject of "loading coils", which I
| remember hearing about in the context of telephone lines but
| never really understood until just now.
| intalentive wrote:
| >One of Heaviside's achievements is that he converted Maxwell's
| twenty mathematical formulas into a more accessible set of just
| four, which nowadays are taught at all universities as "Maxwell's
| equations".
|
| Anyone know of an accessible guide to the translation of
| Maxwell's quaternions to Heaviside's vectors? Was Heaviside's
| compression of Maxwell's work -- lossless?
| BlueTemplar wrote:
| I doubt it, as pseudovectors are kind of a mess ?
|
| But you can also further compress those 4 equations into just a
| single one by using slightly more complicated geometry !
|
| http://www.av8n.com/physics/maxwell-ga.htm
| endoblast wrote:
| https://mathshistory.st-andrews.ac.uk/Biographies/Heaviside/
|
| >His neighbours related stories of Heaviside as a strange and
| embittered hermit who replaced his furniture with 'granite blocks
| which stood about in the bare rooms like the furnishings of some
| Neolithic giant. Through those fantastic rooms he wandered,
| growing dirtier and dirtier, and more and more unkempt - with one
| exception. His nails were always exquisitely manicured, and
| painted a glistening cherry pink'
|
| Genius confirmed.
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