http://g3ynh.info/zdocs/refs/NBS/Rosa1908.pdf
I'd like to see jn's comments (classic 1900's maths). It's not exactly backbreaking to measure the L of 1 meter of cable vs 10 meters, I not sure if the L of a single long wire in free space has much application to audio.
Even this java calculator shows this for a single wire in free space as soon as there is the return current included it ends, Wire Inductance | Electronics and Electrical Engineering Tools | EEWeb Community
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Ah, thanks. I woulda just said "grows faster than linear".
Seriously, I would have used "superlinear" as well, it's a really cool word..sounds very intellectual-like, and I can use that help...
Ah, looked it up. The derivation is good, but it does not relate to reality well. The very first statement of interest was "pay no attention to how the current actually got to the wire".. sigh, there goes any chance of using a meter..and the numbers have really nothing to do with reality as it were.
For real wire pairs, using infinite length numbers works very well because there is field cancellation of the bulk of the field and what remains is strictly linear with length. That linearity begins to fall down when the aspect ratio gets low. Terman covered that with the third term of his formula.
For the internal inductance, the author played fast and loose with the math, used A and B for ends, and B for flux..sloppy. The end result was a specific number, but the length of the wire attributed to that value was not mentioned.. like, this much inductance "per foot".
You cannot use a java app that was derived from a specific formula (they cited Grover as the source of the equations) to show that the source of the equations is correct or that they agree. That said, the math is correct but of no use in real world.
jn
They make some assumptions as to small physical dimensions and low frequencies, but from a quick look it appears there there is less inductance near the ends of an unterminated conductor with an axial displacement current because the magnetic energy in space at a length l from the end of the conductor has contributions from current flowing in conductor above and below the point of interest at l. Very near the lower end, there is little contribution from the short section of conductor below l, so the inductance is less there than if l were taken to be at a longer distance from the end.
Something like that. Probably I could have said it more properly if I thought about it more, but that's enough for now.
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Pavel, if you are referring to some of the conversation I was involved with, nothing personal was intended. I just thought a statement you made was incorrect and didn't want other people who might be reading the thread to take it as fact.
Trying to explain why it was incorrect to the satisfaction of various people here is where it got complicated.
As is often the case, when an explanation doesn't make sense to someone, there may sometimes be a tendency to jump to wrong conclusions rather than ask for clarification.
Somehow it seemed to end up being turned into a an angry political debate (at least on one side) rather than a disinterested scientific discussion. I was trying not to start lobbing insults, but not sure everyone was doing the same.
If there is something negative I am missing here about how my demeanor comes across in such situations, I don't know what it is. If somebody would like to tell me, it would probably be better for me to know than not know.
It was good. And clearly explains why it is superlinear (love it) at the dimensions discussed, as the part that is not contributing as much flux, the ends, is not what grows as the wire lengthens.
Note equation 14 and the text following. For the twisted pair, a real world example, he shows linearity with length with the caveat about aspect ratio.
jn
I thought I said that.
Right now I'm embroiled in a similar problem with the concept of free space capacitance so maybe my use of the word is not perfect. BTW you used to be able to go to Radio Shack and find books with Volta's electrophorus or Gilbert's versorium explained inside.Mark, I don't think there was any charged conversation going on, but it looked to me that you pretty well misrepresented Pavel's point. It wasn't wrong, even if you found it incomplete or disagreed with his opinion, which again you argued as if it were factually wrong. It is easy to add distortion back in. Likewise, you undermined your stance by attributing the limitations of emulation to the wrong thing, which have infinitely less to do with bandwidth than accurate modelling of the large signal behavior of the emulated amps and subsequent complex interactions with ones own playback transfer function. Sure there were some pokes and jabs at your expense, but I'd hardly call that malicious.
If you want to know what gets at my goat and probably others is that you conflate yourself as the arbiter of truth and morality, when in fact you are stating opinion. This is coupled with a quick jump to judgement that extends well past what can be adequately explained by the available evidence (oftentimes doubled with a clear misreading of what you're responding to). A lack of incredulity about your own experience (i.e. asking "am I full of it?") has gotten you into trouble as well. It doesn't help when you write before thinking and make simple sloppy mistakes and take offense when someone cuts down your argument by pointing out those faults in its foundation. Nor have such rebuffs seem to have affected your stance.
Now, am I guilty of many of these? I'm betting so, so perhaps figure out the very things you find frustrating in others and honestly ask yourself if you do that.
Patel's article from Y2009 uses modern notation and arrives at the same result
Sorry about the 3 different magnifications of the 3 different copy-and-pastes. My browser and my screen capture sw are not cooperating this morning. Click once to remove compression-distortion, and click on white X at lower left for full size imagery.
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Sorry about the 3 different magnifications of the 3 different copy-and-pastes. My browser and my screen capture sw are not cooperating this morning. Click once to remove compression-distortion, and click on white X at lower left for full size imagery.
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uuh. at high freq, where the Ls is lowest (surface)... is the flux density highest or lowest there?
THx-Richard
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for a parallel pair, the current keeps on squeezing in as frequency goes up, so definitely the flux density increases in the immediate vicinity of the current. Externally though, the field drops because the current centroids are closer together.
On the inner conductor of a coax, the core surface, the flux strength just outside the surface of the wire is independent of how the current is distributed within the cylinder, as long as circular symmetry is maintained. IOW, if you ran 1 ampere in the core wire and none on the shield, the flux on the outer surface of the shield would be "B". If you run 1 ampere on the shield and none on the core, the flux on the outer surface of the shield will still be "B. I would say that for a coax, there is no difference in the B field anywhere in the dielectric or outside the shield. Within the conductor, where the actual current resides, I would expect higher flux density but much lower area.
jn
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Reminded me of the many people over time which I have met which did great things in school but went on to do nothing with the knowledge. In talking to the man who painted the exterior of my house.... he had gone thru engineering program, got his degree and then got a job and there found out he didn't like engineering work. Liked the outdoors and being his own boss more. Been a house painter ever since and is a happy man. I wonder if he considered his many years in College a waste of his time?
I recently had visitors here for 3 days... ex Canadian diplomat and his wife. His wife is the daughter of my wife. She went to Duke and Harvard on her own... worked to get loans etc. no help from family.... got her PHD and MD. Lives in Georgetown- Wash DC. makes a lot of money. I never see her look happy and is close to burn out stage now. Stressed out to the max..... Trying to unravel her life and retire early.
And, I have seen some really happy people in science also. But for many a lot of years of ones only life wasted on work they don't like or just do it for the money.
THx-RNMarsh
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You probably also like 'superluminal'
I like words that are compact yet clear what they mean.
Jan
You probably also like 'superluminal'
That one got pretty popular when there was some rather famous timing errors.
Sorry to be off-topic, but I am reading a book by Ray Kurzweil where he details Einsteins thought-experiments that lead to his relativity stuff. I now better understand what it is what makes a genius a genius.
And yes, the superluminal concept (or lack of it) figures in it.
Jan
And yes, the superluminal concept (or lack of it) figures in it.
Jan
To piggyback on a Ph.D trajectory that was a short part of the conversation: Another tenure-track scientist bites the dust | Science | AAAS
The life sciences are the worst for sure, but other pure sciences are not far behind WRT funding and actually moving forward as an academic. With engineering, the majority already go into industry, so there's *less* but still soul crushing levels of competition for funds. While I just did get a Ph.D and am now a postdoc, it is very hard for me to recommend this track for anyone who cannot be convinced it's a terrible idea (and I'm ultimately leaning towards industry, but landed on an amazing opportunity that I couldn't refuse).
The life sciences are the worst for sure, but other pure sciences are not far behind WRT funding and actually moving forward as an academic. With engineering, the majority already go into industry, so there's *less* but still soul crushing levels of competition for funds. While I just did get a Ph.D and am now a postdoc, it is very hard for me to recommend this track for anyone who cannot be convinced it's a terrible idea (and I'm ultimately leaning towards industry, but landed on an amazing opportunity that I couldn't refuse).
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