This paragraph seems to say much.
A few points I can see that it makes.
An infinite length of line does not need to have far end termination. The line itself provides the termination.
A shorter line than infinite length needs to be terminated to allow it to mimic an infinite line.
A line chopped in half can never mimic an infinite line because it is missing the end termination.
A short line can never mimic an infinite line because it is missing the end termination.
Zo is the characteristic impedance of the line, not 1m of shortened line nor 1km of shortened line, nor any specified finite length of line. Infinite is implied in "the line".
If one chooses to use a shortened line, then as I started with, it must be terminated with a resistive load exactly equal to Z0.
BTW,
I know nothing about HF and transmission lines. I simply read what the Members put before my eyes.
And yet another interesting paper:
"Characteristic Impedance of Cables at High and Low Frequencies"
By the Engineering Department Belden
Characteristic Impedance of Cables at High and Low Frequencies
(Some of the figures are rather fuzzy. And the text font is very small.)
"Characteristic Impedance of Cables at High and Low Frequencies"
By the Engineering Department Belden
Characteristic Impedance of Cables at High and Low Frequencies
(Some of the figures are rather fuzzy. And the text font is very small.)
Sometimes it's better to be ignorant.😀
Speaker application is going to be more complicated I think. It seems the cable and load impedances are going to vary due to current going through these. Is this correct?
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I'm not clear what you are saying here. A short (i.e. non infinite) line must be terminated in Z0 if you want to see Z0 at the input. Otherwise, you get a different input impedance (but, of course, exactly the same characteristic impedance).Andrew T said:
I was not saying that a short line (whether chopped in half or not) can mimic (or not) an infinite line. I was merely saying that if you take a line and shorten it then it retains exactly the same characteristic impedance because this is a property of the line construction and frequency, not the length.
No. Cable impedance does not vary with current. Loudspeaker impedance might vary a little, as drive units are non-linear. Input impedance to a line will depend on load impedance, in a non-trivial way. Maybe this is what you were trying to say?soongsc said:
Yes, the characteristic impedance is of the infinite line.
A shortened line can only mimic the infinite line when it is correctly terminated.
I am not actually disagreeing with you. But you are swapping about terms that I think are confusing to those that read your version.
Whereas, JN's explanation seems clear to me. I see no ambiguity.
I'll put it another way.
A shortened line can only have a characteristic impedance when it is correctly terminated to mimic the infinite line.
I suspect the science behind my statement is ridiculous. But it allows me to clearly understand transmission lines that behave properly.
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If I cut an infinite line at one meter, then connect them properly, then send a signal down it, the one meter cable will have a characteristic impedance that matches that of the infinite line it is attached to. The one meter length of cable has just demonstrated that it has the exact same characteristic impedance as the infinite line. (expected) The one meter length Zo was not a result of it's length, but by construction.
By definition, Zo is for an infinite line. It can be confusing..
No. I fully understand it.
I did not attribute that statement to you. My apologies for the confusion.
I detailed the fact that I am analyzing a mismatched t-line. In order for you to "explain" how Shadowitz deals with this issue, you crossed the "line in the sand"...the quoted statement...The statement I posted was a quote from Shadowitz""
Quote from Shadowitz.."""throughout this chapter we will restrict ourselves to the usual high frequency case where Zo is a real quantity.."" end of quote.
So to "explain" to me how to deal with reflections, you now quote the chapter 16-2, where he states clearly that he is restricting the discussion to where Zo = Ro. And, I might add, where we all seem to agree on sqr(L/C)
Now, go back to my initial posts. From day one, I have been using this model as a best case analysis...
In fact, look at the pages I just photo'd...Shadowitz explains it quite adequately..
Had you not started your postings here in such a condescending manner...continuing with such grandiose gems as:
I would have directed you to the page where he details EXACTLY the analysis I have gone through using lengths and impedances typical of audio.
As it is, you completely passed it by. Missed it..Even though I spent a rather large amount of effort trying to move you in the right direction..As I stated early on, it's the journey, not the destination.
I have worked with and for approximately 200 physicists from every continent on this planet,(luckily, no travel to antarctica) and I have never, ever, found any of them to be condescending. So far, you appear to be one of two exceptions I know of. Please rethink the attitude..
I note that this one comment of yours may appear to be condescending, I wish to point out to all that I do not believe it to be.
""As a result, much of the innovation in engineering is actually done by physicists. ""
Ah, that is of course, my fault. You gave the author initials and I missed that.
Hopefully, this will be the last time I will need to explain how you've presented yourself. One can hope that in the future, you treat others as equals, but time will tell.
I note you mentioned typical speaker impedances incorrectly, so..speaker loads range from lows of 1 ohm up through high frequency unloading in the hundreds of ohms, resistive through wildly reactive in both directions, L and C. I've not extended my modelling to include reactive cases yet, but have limited it to pure resistive and best case settling..the use of slower waveforms will indeed require compensation for Zo variance as a result of frequency.Edit: To actually use audio frequency waveforms at current, and expect reasonably accurate test results given the di/dt, that is quite beyond normal expertise. I am not sure I could find low microsecond delays with a 1 ohm load and 500hz, the combination of external magfield trapping and physical inductance of the load resistor is a daunting challenge. 500 hz is essentially the lower breakpoint for human differential sensitivity, below that we localize mainly with amplitude differences..
Since modelling the system as I have been doing requires only a simple excel spreadsheet and simple math, not hyperbolics as you mention, I believe all can see now that my approach is indeed the easier one to use, perhaps they will also enjoy the "warm glow" even though they are mere mortals...
Remember, it's the journey..your expertise is refreshingly high level, please be nicer.
Cheers, John
Oh..ps. The fair use doctrine allows for the use of copyrighted materials for the use of teaching. I "invoke" that aspect of the clause for Shadowitz's work I have posted.
The content I am using is from:
The Electromagnetic Field, Albert Shadowitz, pages 560 through 567, Dover Publications, 1988.
Attachments
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No, the characteristic impedance is of that line type at that frequency.Andrew T said:
I am trying to correct JN's misunderstanding. I don't want to create further confusion!
No, a line of any length has its characteristic impedance. It will present this as the input impedance if it is terminated in the characteristic impedance too. I think you may be confusing input impedance and characteristic impedance.
Let me try again. If I buy a reel of 75ohm coaxial cable, then for all frequencies which are sufficiently high (so L and C dominate over R and G, typically a bit above the audio range) and sufficiently low (so only the TEM wave can propagate, typically below microwaves) the cable has a characteristic impedance of 75R. If I cut a meter or 10m of cable, or use the whole 100m drum, the characteristic impedance is 75R - because it is a property of that cable type so applies to any particular length of that cable.
If I try to measure the input impedance of a piece of that cable, then the value I get will depend on the length, the load impedance applied at the far end and the frequency. There is one exception: if I load the far end with Z0 (the characteristic impedance), then the input impedance I measure will always be Z0 too whatever the length of the cable and whatever frequency I use. If I load the far end with 2xZ0, then the input impedance can vary between 2xZ0 and Z0/2 and may not be a pure resistance but could have a capacitive or inductive element too. This is all for RF.
At audio frequencies exactly the same equations are true. The only difference is that Z0, the characteristic impedance, is no longer a pure resistance and it changes sharply with frequency.
I have explained things as clearly as I can, given that DIYaudio is not the right place to write a whole textbook chapter on transmission line theory! (And lots of other people have already written much better textbooks than I could write).
You're plain wrong with your assertions about Z0 only being a characteristic of infinite lines, and you implicitly acknowledge it...
It looks to me that anyone who disagrees with you comes under attack on a personal level. Quite frankly I am disappointed that someone with your reputation should resort to such tactics.
You need to take a long hard look at some of the things you have written.
Some of us mere mortals are getting a little tired of being reminded of our status by you immortals.
w
It looks to me that anyone who disagrees with you comes under attack on a personal level. Quite frankly I am disappointed that someone with your reputation should resort to such tactics.
You need to take a long hard look at some of the things you have written.
Some of us mere mortals are getting a little tired of being reminded of our status by you immortals.
w
No. That is just one definition of characteristic impedance. It is not confusing.jneutron said:
It is statements like that which caused me to believe that you have misunderstood transmission lines. When I tried to correct you your responses seemed to confirm my impression. I apologise if I am mistaken. You appeared to be confidently asserting error as truth, and I am afraid that is one of my 'hot buttons'. You appeared to be suggesting that you had a correct way of handlng audio in transmission lines, and everyone else was mistaken. I was merely trying to point at this is not the case. Do you accept that the standard theory, as I and others have tried to outline it, is correct?
I am sorry if I appear to be condescending. I try to understand why people seem to be confused about things, and in many cases I find that they were badly taught.
Um, actually I quoted Shadowitz..
Hmmm..Clearly you bring your animosity with you wherever you go. I had hoped that on another forum you'd behave. I was incorrect.
Calling stated and quoted sentences condescending is not condescending. You are confused.
Again, you are confused. The term "mere mortals" was used by DF96, not me.
I took exception to his statement.
As I asked you on the other forum, please read the posts slowly and more carefully. In your haste, you have made errors.
Cheers, John
Yes. As a matter of fact, to some extent the resistance of the cable will vary with current passing through it. I'me sure there are other issues as well.
I was giving the benefit of the doubt..
That was an assumption of yours. Not mine.
Actually, you have been, not "appeared". I'm confident a little feedback on that will assist you in understanding how you've come across.
I believe that enough has been said about that.
As I've stated, my analysis is entirely consistent with Shadowitz. The reason I've run this analysis is:
1. As Shadowitz pointed out, it can take microseconds for the cable to settle down to final value. Microseconds is actually within the realm of what humans can hear in ear to ear differentials.
2. It is a very easy model to do and understand for Rload </= to Zcable. As you also have said, easier is better..a typical acronym I follow is "KISS", keep it simple stupid..
3. Keeping the line model as strictly sqr(L/C) does indeed lose content, however..invoking only sqr(L/C) produces the fastest settling time, R will only slow the system response down.. Without cable R, a 2 ohm load still takes 6 uSec or so. The fastest possible pared down model shows that the effect does indeed fall within the range of human capability to discern. Had it been below 1.5 uSec, there would only have been two choices... a more complex model to accomodate the slower propagation and higher impedance of a more complex model, or abandonment of the simple model altogether..
4. It is far easier to use a 1 volt 250 pSec risetime to watch how a 10 foot zipline feeding a 1 ohm resistor from a zero ohm source settles...I cannot say the same for a 500 hz sinusoid, as the phase response of 1 to 100 ohm current viewing resistors is not consistent with the level of accuracy required. (yet)
5. My model allows for the voltage and current within the wire, which is consistent with the load of course given that audio is practically dc for a 10 foot length of wire..
Use of my model is consistent with what is written, it will produce the fastest settling time possible for the system (that would be using superconductors), and actual reality will be slower than that.
As can be clearly seen, the textbooks do not treat the particular subset of audio and load reflection consistent with what humans can discern, that of 1.5 uSec and up differential.. everybody, you included, has neglected those interaural as inconsequential, so any analysis in the texts disregards the possiblility. I note that the inverted bandwidth of 1.5 uSec is incredibly high, and far above human capabilities in terms of frequency.. but yet we are sensitive at that level despite 20khz..(not me, I'm way beyond that age..)
That was what I meant by the textbooks need updating. T-line theory is all fine and dandy...but everybody neglects it for specific audio applications. Shadowitz came the closest with the microseconds settling statement..
Cheers, John
Ps. As you may or may not have noted, I have presented my work consistently with an eye towards actual test. I've made sub nanohenry current viewing resistors which also do not trap flux via loops, and will soon create the 250-350 pico rise, zero ohm voltage source. (a mercury wetted reed from a very low Rs cap bank).
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Which is as it should be for domestic situations (recorded musical material, wire lengths <0.1% of wavelength of highest recorded frequency).
If you can demonstrate localization detection with left-right symmetrical delays of 4-5 us (even off center) using any recorded music, I'll be quite surprised. As I've pointed out repeatedly, this far exceeds the amplitude of normal unconscious head motions, yet with good speakers, recorded material, and rooms, the localization doesn't hop around unless it was recorded that way.
Sigh, there ya go with that wavelength in the wire thing...When ya gonna learn???😀
Hey, you need a 20/20uf, 450 volt new cap? I recently found one I purchased (then lost) for the repair of the Systron-Donner analog computer I had in my office. (hey df96, what did you think I used for modelling.. one them digital thingies?)
Me too. I've not the test/setup capability to do this. In fact, what recorded music controls differential? I'd not want to start with uncontrolled stuff..the test would be bad enough as it is.
I'd use one amp channel, two speakers, and swap out only one cable, with the subject looking for side shift of highs relative to lows..gets rid of level control issues..I'd use female vocal with sibilance..
Off center is the only possibility. On center is invariant to differential.
Cheers, John
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You are ignoring repeated explanations across several threads - the differential delay discrimination only requires in-band correlation between the two ears processed signal - there is no neuropsychological significance to the "inverted bandwidth of 1.5 uS"
Correlation based measurements can “trade” S/N, observation time for bandwidth
and you have phase/amplitude spatialization clues backwards in the earlier post, we do have absolute phase information at low frequencies since the hair cells fire only on positive pressure bending - but limited by the 4-8K/s max firing rate of most nerve fibers we lose the phase information for higher frequency sounds
high frequency localization is universally ascribed to using the head/pinnae shadowing/diffraction caused amplitude vs frequency differences
delays that are common to both channels, even fairly severe frequency variable group delays do not appear audible as long as they match in both channels
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AFAIR, studies in the past have shown that head motion does help in localisation.
Unfortunately i´ve lost some of these papers, so can only give references after restoration.
@ jneutron & DF96,
i´ve only glanced through your discussion, but somehow got the impression that you both do agree in most respects (see for example DF96´s conversation with AndrewT), could it be mainly a semantically based issue?
Despite the fact that there might be some disagreement on the audibility.
Sigh. Please re-read the context of the statement.
The context of my statement was to explain why, even though humans cannot hear beyond 20Khz or so, they have demonstrated the ability to discern inter-aural delays at the 1.5 uSec level. So you are preaching to the choir....again.
Again, you have missed context.
I do not have it "backwards". Differential sensitivity has been demonstrated up to 12 Khz, with reduced sensitivity as the frequency reduces in the 500 hz realm. Nordmark did that back in the 70's. Lots of other papers elaborate at length, but as far as I've seen, nobody has refuted his work.
Are you claiming that somebody else has refuted Nordmark?
Instead of bringing diversionary red herrrings up, perhaps you could provide content to add to the discussion?
Cheers, John
The context of my statement was to explain why, even though humans cannot hear beyond 20Khz or so, they have demonstrated the ability to discern inter-aural delays at the 1.5 uSec level. So you are preaching to the choir....again.
Again, you have missed context.
I do not have it "backwards". Differential sensitivity has been demonstrated up to 12 Khz, with reduced sensitivity as the frequency reduces in the 500 hz realm. Nordmark did that back in the 70's. Lots of other papers elaborate at length, but as far as I've seen, nobody has refuted his work.
Are you claiming that somebody else has refuted Nordmark?
Instead of bringing diversionary red herrrings up, perhaps you could provide content to add to the discussion?
Interesting..what research are you quoting this from?
Cheers, John
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