Oh well I lost all my stuff from last time this came up. I ran a large finite element T-line simulation as well as the bulk R/L/C one and as it HAS to be the little "teeth" from the full T-line behavior (multiple reflections) went right through the R/L/C one. That is the energy vs time delivered to the load is the same in both cases (in the real world there is enough low pass filtering that the reflections are difficult to impossible to actually observe).
If you can simulate reflections you are looking on a time scale waaaaay too short for audio. For speaker cables, perhaps 4 orders of magnitude too short to be audible. And besides, there's no stimulus in audio with a slew rate to be even vaguely interesting at VHF.........
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Note the impedance rises at lower frequency. As I've said all along, the rf analysis neglecting r provides the FASTEST settling time possible for the system. Inclusion of R actually SLOWS down the response. To wit, if a system analysis using T-line RF only says the settling time to 90% value is 20 microseconds, inclusion of the R only makes settling higher than 20 uSec.
Balking at T-line simply because it doesn't include R misses the point..T line shows that the settling delay exists. It provide very clear understanding of why it happens, and what can be done to mitigate it.
Actually, it's easy to see. The problem is risetime of the source, and inductance of the load. You should put the resistor I sent you at the end of 20 feet of zip, and toss a 1 nSec step pulse down it. You'll see the steps, and you'll see the exponential rise. That is real world.
Now, if you toss a step into the RLC equivalent, do you see the steps? No.
If you use an rlc model, you approximate real world. Most times, that is good enough.
When a load variation is one or two orders of magnitude, it will cause the step response to vary, and that settling time variation can fall into the human realm of ITD.
For a given line impedance, if the load matches it, there will be NO settling time, the load will be one transit delayed, or 10 to 20 nanoseconds. No bother.
If the load is two orders of magnitude below the line, there will be several hundred transits required until the load sees the current the amp is trying to deliver. Microseconds.
Can humans discern microseconds? Only via ITD, and only 2 plus micro.
Below a microsecond, I'd ignore it.
jn
You and me both. I have seen no maths and defiantly no deep understanding from System7 about electron herding.
Not the point, either analysis gives the SAME result so there is no argument.
Theres an elephant in the room, called a loudspeaker, and at worse, an amplifier misbehaving in a real-world load while its specs into a resistor state otherwise,. im too lazy to perform any kind of calculus into something i believe is insignifcant, crucify me if u will. fix the whuppy engine before fixing the warpdrive,
Regards,
Regards,
No chance in audio, for at least two excellent reasons. Firstly the rise time of audio program material is many orders of magnitude slower than the round trip of the cable, so there is no such effect. Secondly the load/source is inevitably lossy so there can't exist the 'convenient' several hundred reflections needed to stretch ITD toward the alleged threshold of audibility, even in the impossible event of a rise time fast enough to reveal it. In combination, this is very obvious with a decent BW scope/probe and an audioband spectrum limited 1kHz squarewave and a straightforward audio amp/cable/speaker. There is no settle distinct from lumped effects, no steps/teeth/whatevers in practice, no surprise.........
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Oh no, and there was me thinking someone was about to prove a need for S11 analysis for speaker interfaces 😛
Of course, if the speaker cable in some way manages to look like an antenna to RF nasties zipping around, and is able to deposit some of that back into the amplifier FB loop - then things start to look more interesting ..
An incompetent designer can make many things go wrong, but solutions are available to anyone with even basic google ability.
Luckily, as we all know, the designers of all audio equipment that one can readily buy are certified as being highly competent - there's probably a stamp on the stuff, somewhere, telling you that ...
I only care about the equipment in my system, where I have control over exactly what is connected.
Within specific limits, they do indeed provide the same result. So we both agree that the t-line model is accurate and viable, despite the protestations of others.
Both models have merits for specific reasons.
The LCR model, even a single stage, is far simpler to use for bog standard analysis via simulations. However, to approach the accuracy of reality, it requires many stages which increases the complexity beyond most to simply envision. However, the fewer the stages, the worse the high frequency accuracy becomes. A single LCR is a lowpass.
The t-line model provides immediate understanding of the frequency response at the load from dc to daylight. And, by inspection, the system settling delay can be seen. One can even use an excel spreadsheet to determine the settling time of the signal at the load. It is a simple matter to plug in the line and load values and use the reflection coefficients to examine the behaviour of the system.
The T-line also provides the concept of a "cusp" in settling time of the load. To wit, when the line matches the load, there is no settling time, so the load follows the load with a delay equal to the transit time of the signal in the wire, 2 nanoseconds per foot. Trivially small. BUT, when the load impedance is two orders of magnitude below the line impedance, the system requires many hundreds of transits before the system settles towards the final value.
The T-line model introduces to the user the concept of line/load mismatch and resultant settling time dependence. Settling time variations which reach into human discernment with respect to ITD.
The LCR model does NOT easily show that, one cannot figure out the settling time by inspection. One cannot, by inspection, see that a specific value of L and C per foot, lumped as one element, will provide a DC to daylight response with NO settling time variation.
If we were talking about a load which does NOT vary it's impedance with frequency, this discussion would be unimportant as all signal frequencies would have the same settling time.
Yes. See above.
The reflections and rise time are of no importance to the velocity of propagation of the load energy, they occur as a consequence of physics.
The fact that you cannot see it when the rise time exceeds the transit time does not alter physics. It remains there, even though the typical layman cannot see it. So your statement that there is no such effect is blatantly inaccurate, consistent with a lack of understanding.
One only needs use a reflection bridge to discern the reflections which occur at audio frequencies in a typical speaker run..this has been done, and it has been written up as an article.. I do not know if Cyril eventually published it.
Again, your understanding is incomplete. You need to research this more. The fact that you cannot see clear reflections does not mean they are not there. Your beliefs require superliminal velocities through the cable. You need to understand that your argument defies physics.
You need more research and understanding. Do you have access to the cyril bateman articles as a start?
jn
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Analogously, I could use a Schroedinger equation to compute the trajectory of a baseball. But why would I want to do that? Newton is far simpler and gives perfectly accurate results. Even without relativistic corrections. And then I don't have loony tunes telling me to plunge the baseball into a magnetic field first to align the spins.
When λ/d << 1, the lumped model works essentially perfectly.
As I said, the t-line provide a better understanding of the settling time dependence of the audio signal on the load variation of impedance.
At least we have progressed a bit here, no? Now, you and Scott at least agree with the validity of the t-line model. Just not whether or not that level of analysis is required.
Now my work with you guys is simply to get you to understand how the load variations can alter the settling time and hence delay for specific frequencies based on what the load does.
Eventually, all will understand that the best possible speaker run will be something that falls into the realm of the load impedance. How close certainly doesn't matter once the variations fall into the sub microsecond realm, waayy below human anything.. But two orders of magnitude above the load minima may be too much. For a load which can vary from 1 ohm to 40/50/60, a line at 20 or 30 lowers the spread quite a bit w/r to a line of 150.
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Nope. Stop with the RF approximations, they fall apart too quickly with mismatched lines. Sheesh, I larned that back in '74.
jn
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Problem is that experiment confirms that the lumped approximation works. See Greiner, for example.
Since a speaker's impedance generally varies by an order of magnitude in the audio range, it's a double fool's errand.
Since a speaker's impedance generally varies by an order of magnitude in the audio range, it's a double fool's errand.
You repeat what has already been stated. Scott and I have already finished that portion. The use of "they are close" to counter "they are close" serves no purpose. Does Greiner show settling time vs load impedance?
Generally..an interesting word, lacking specifics..
Kinda neglects resonance for one, as well as IdL/dt.
Approximations always need to be evaluated for validity.
jn
Grab a few random impedance curves off Stereophile's site. "Generally" means "vast majority."
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