I can understand your skepticism, but I think you are responding to arm-waving with equal and opposite arm-waving. Coax specs list inductance, capacitance and resistance per meter. Are you saying those values change if the coax is 100' or longer? Or that they somehow start behaving less like LRC and more like something else? That could be true of course, but by how much is always the question. How much of a difference would you consider to be important?
I'm not disputing that a cable with enough inductance or enough resistance could change the sound of a system, that's well known.
What effects specifically, do you want to add to the model? LRC effects would potentially interact with the speaker, but skin effect and reflections wouldn't change circuit or speaker operation unless they caused the amplifier to oscillate.
The coax specs you refer to are reasonably accurate over a fairly wide range of frequencies. While there are not abrupt transitions from one mode to another, the specs probably good from around 100 kHz at the low end, up to somewhere in microwave frequencies at the high end. Below the low end, the effective current path is not exactly in the longitudinal direction of the cable, and that is due to the effect of eddy currents induced in the wire. Current ends up taking more of a spiral path through and along the wire.
At the other end of cable models, at very high frequencies eventually the dimensions of the wire start getting close to 1/4 wavelength of the signal frequency and waveguide propagation modes become increasingly significant. In addition, at very high frequencies dielectric constant becomes a complex number with an imaginary component. Again, the usual published equations become increasingly inaccurate.
Okay, we are only interested in the low frequency stuff here. As jneutron has pointed out, the standard equation for characteristic impedance of wire is based on some assumptions that are not valid at audio frequencies. Instead, a Bessel function solution to Maxwell's equations is much more accurate.
Anyway, I would agree that while transmission line effects and skin effect in audio cables can start having somewhat significant effects up around the top end of audio frequencies, they are far from the worst problems in accurately reproducing audio. And they are probably not worth worrying about too much in most DIYAudio situations. Especially so, since there is not a whole lot that can be done about it. It is very, very difficult to make a good transmission line at audio frequencies, and nobody actually does it. Expensive silver and oxygen-free cables don't help.
The only real practical solution I know of, if someone truly wants to avoid speaker wire-related phase shift and loss at high audio frequencies, is to use mono block amps and locate them in or immediately adjacent to speaker cabinets.
In addition, since most of the people around here seem to be old men who don't hear high frequencies all that well anymore, worrying about small-ish effects at 20kHz is probably a waste of time. That being said, there is probably no harm in trying to better understand the effects that do exist.
Last edited:
Mark, if you have something specific you want to see modeled, there's no reason we couldn't try it. Although complex dielectric constant sounds difficult. Maybe doable with ddi or ddt statements and laplace (although it seems to be slow in LTSpice).
As for skin effect, based on Jneutron's charts real skin effect is actually less at audio than the usual approximation, so we have even less to worry about. Even so, we can look at a particularly bad example of a transmission line - Romex. You can see the signs of skin effect here:
Just one thing about music - when it hits you feel no pain
Although admittedly that could be a lot of things in addition to skin effect. I guess it would be fun to swap our speaker cables with Romex and have a listen?
Henry Ott seems to use the figure of 1/20 wavelength for safe proximity from reflections and interference. That means our cable should be no longer than the wavelength of 400KHz. That is a 750 meter cable. Even remote feedback is a difficult solution in this scenario because the absolute delay of the transmission line makes a lot of feedback impossible.
As for skin effect, based on Jneutron's charts real skin effect is actually less at audio than the usual approximation, so we have even less to worry about. Even so, we can look at a particularly bad example of a transmission line - Romex. You can see the signs of skin effect here:
Just one thing about music - when it hits you feel no pain
Although admittedly that could be a lot of things in addition to skin effect. I guess it would be fun to swap our speaker cables with Romex and have a listen?
Henry Ott seems to use the figure of 1/20 wavelength for safe proximity from reflections and interference. That means our cable should be no longer than the wavelength of 400KHz. That is a 750 meter cable. Even remote feedback is a difficult solution in this scenario because the absolute delay of the transmission line makes a lot of feedback impossible.
From what I recall of jneutron's comments, as little as 6 or 12 feet of speaker cable can have non-negligible effects at 20kHz. That may have been more in reference to phase shift than skin effect losses. I would have to go back and take reread some of those threads to remind myself of some of the details of those discussions.
The 1/20 wavelength figure you mention is a reasonable approximation when a cable is behaving as a typical RF transmission line. Attached below is an illustration of the EM fields relative to the direction of propagation. In that mode, the 1/20 rule of thumb could be used. However, that's not what happens in the cable at very high or very low frequencies, and the rule is not accurate in those cases. At low frequencies, eddy currents in the conductors cause current flow to spiral around, rather than flow directly along the direction of the cable length. At very high frequencies different things happen, but we don't need to worry about those for audio purposes.
Regarding complex dielectric modeling, no need. I only mentioned that effect at very high frequencies to illustrate that coax cable specifications are mostly meant for general purpose RF use, and are most accurate when used not too high nor too low in frequency.
Anyway, since jneutron said cables much shorter than 750 meters would have significant effects, I wonder how close we could come to accurately modeling what actually happens. Unfortunately however, bessel solutions to transmission lines are complicated to calculate.
The 1/20 wavelength figure you mention is a reasonable approximation when a cable is behaving as a typical RF transmission line. Attached below is an illustration of the EM fields relative to the direction of propagation. In that mode, the 1/20 rule of thumb could be used. However, that's not what happens in the cable at very high or very low frequencies, and the rule is not accurate in those cases. At low frequencies, eddy currents in the conductors cause current flow to spiral around, rather than flow directly along the direction of the cable length. At very high frequencies different things happen, but we don't need to worry about those for audio purposes.
Regarding complex dielectric modeling, no need. I only mentioned that effect at very high frequencies to illustrate that coax cable specifications are mostly meant for general purpose RF use, and are most accurate when used not too high nor too low in frequency.
Anyway, since jneutron said cables much shorter than 750 meters would have significant effects, I wonder how close we could come to accurately modeling what actually happens. Unfortunately however, bessel solutions to transmission lines are complicated to calculate.
Attachments
- Status
- This old topic is closed. If you want to reopen this topic, contact a moderator using the "Report Post" button.