Jneutron
You seem to be a little too easy to get upset about some things so it's going to be hard to please you. I'll do my best.
Zero capacitance? Sure, my perfect conductor example was just that. You can't do anything in that cables example let alone the capacitance. Not sure why you got so excited about it. Yes, a dielectric constant of 1.0 is a give away to the fact that capacitance can't be zero in THIS world, but I wasn't limiting the perfection to the real world but the "perfect" world where things do go infinitely fast, have no resistance, ETC. I see no sense in making a "perfect" wire half-in one world and then the other. So, I put it all in ONE world.
And yes, you're right, I do not have a source for very low frequency skin effect. Nor does it seem anyone else! As long as the numbers are "close" and you use a wire size that is smaller than the calculation, and use the number of wire to meet DCR things should get into the reasonable range.
As far as transmission line effects well, the source impedance sure is small at less than 0.05-ohms on average of an amplifier's output stage. The cable impedance is small (looking at the real component of the cable) compared to the speaker's varying input impedance so it is hard to imagine the speaker cable as a classic transmission line (matched source, line and load impedance’s). Not to mention the wavelength are WAY long to even begin to couple between the source and the load. A reflection bridge certainly can show reflections but to say this is a transmission line?
If I shove my amplifier up to the speaker terminals where is all the power dissipation going? the speaker. If I stick a cable in there, the power is still going almost all into the speaker and not the cable. The L and C energy eventually goes into the load but is lagging one way or the other. Probably not a good thing.
True, the "impedance" of the cable can be complex in nature and a higher vector magnitude per low frequency equations (mostly capacitive, as the resistive load value is so small in the cable). But at such a low frequency it's really hard to see this as a transmission line, or impedance values near the speakers input impedance.
How do we negate the effects of the LONG wavelengths relative to the line length at audio? Even worse, go lower than 20KHz.
I'm all ears on your low frequency transmission line model (pun intended)and impedance matching. The Z=SQRT(L/C) is only good above 1 MHz.
The ability to design to metrics that are repeatable would be a great benefit to designers who want to use the best of what's really capable in design without "faith" based engineering. But, I'd rather try to do the right thing with a few bumps in the road than do the wrong thing perfectly. Too little risk can limit the outcome as bad as anything else. Yes, we lose a few that insist on only what they perceive and hear. That's fine, but for right now I want to concentrate on the "knowns" (yes, even the one's I don't know!) to look for in a nice, and reasonable, cable. Design elements that are always beneficial to sound.
Bridges go up and fall down, space shuttles go up and explode... all these things have "experts" at the wheel and still failed. People may be experts, but the ones that do their jobs can overreach even their understanding(s).
So, as far as being the second one, I sure didn't know I was competing with the first. Sorry about that. If I only stick with what I know today, what benefits do I achieve tomorrow?
Looking at cable, you can't see a common design thread across the lot of them that indicates forward thinking to a known set of conditions. I can even see a few, not hundreds, of designs for a specific set of amp (SS or VALVE)/speaker (dynamic or electrostatic) combinations.
I listen to cable with the same R, L and C and am amazed at how different they sound. I am not even close to shutting down my ears. That’s what got me in this mess! How do you recognize correctly made audio speaker cables.
I did look back at some of your post so as NOT to pester you, and yes, the main things my ears hear is much improved openness, imaging stability, precise location of the image and debth in good speaker cords.
I can't say I grasp speaker cable impedance at such low frequencies as they "rise" as the frequency drops, making consistent low impedances at audio seem implausible, at least to my way of thinking about the measurements. My guess is if you look at the cable like a T-line, the impedance is the same at any cable length. Of course, the low pass nature of the cable changes too.
With your respone Jneutron, I close comments in this post. I've bugged you all enough.
You seem to be a little too easy to get upset about some things so it's going to be hard to please you. I'll do my best.
Zero capacitance? Sure, my perfect conductor example was just that. You can't do anything in that cables example let alone the capacitance. Not sure why you got so excited about it. Yes, a dielectric constant of 1.0 is a give away to the fact that capacitance can't be zero in THIS world, but I wasn't limiting the perfection to the real world but the "perfect" world where things do go infinitely fast, have no resistance, ETC. I see no sense in making a "perfect" wire half-in one world and then the other. So, I put it all in ONE world.
And yes, you're right, I do not have a source for very low frequency skin effect. Nor does it seem anyone else! As long as the numbers are "close" and you use a wire size that is smaller than the calculation, and use the number of wire to meet DCR things should get into the reasonable range.
As far as transmission line effects well, the source impedance sure is small at less than 0.05-ohms on average of an amplifier's output stage. The cable impedance is small (looking at the real component of the cable) compared to the speaker's varying input impedance so it is hard to imagine the speaker cable as a classic transmission line (matched source, line and load impedance’s). Not to mention the wavelength are WAY long to even begin to couple between the source and the load. A reflection bridge certainly can show reflections but to say this is a transmission line?
If I shove my amplifier up to the speaker terminals where is all the power dissipation going? the speaker. If I stick a cable in there, the power is still going almost all into the speaker and not the cable. The L and C energy eventually goes into the load but is lagging one way or the other. Probably not a good thing.
True, the "impedance" of the cable can be complex in nature and a higher vector magnitude per low frequency equations (mostly capacitive, as the resistive load value is so small in the cable). But at such a low frequency it's really hard to see this as a transmission line, or impedance values near the speakers input impedance.
How do we negate the effects of the LONG wavelengths relative to the line length at audio? Even worse, go lower than 20KHz.
I'm all ears on your low frequency transmission line model (pun intended)and impedance matching. The Z=SQRT(L/C) is only good above 1 MHz.
The ability to design to metrics that are repeatable would be a great benefit to designers who want to use the best of what's really capable in design without "faith" based engineering. But, I'd rather try to do the right thing with a few bumps in the road than do the wrong thing perfectly. Too little risk can limit the outcome as bad as anything else. Yes, we lose a few that insist on only what they perceive and hear. That's fine, but for right now I want to concentrate on the "knowns" (yes, even the one's I don't know!) to look for in a nice, and reasonable, cable. Design elements that are always beneficial to sound.
Bridges go up and fall down, space shuttles go up and explode... all these things have "experts" at the wheel and still failed. People may be experts, but the ones that do their jobs can overreach even their understanding(s).
So, as far as being the second one, I sure didn't know I was competing with the first. Sorry about that. If I only stick with what I know today, what benefits do I achieve tomorrow?
Looking at cable, you can't see a common design thread across the lot of them that indicates forward thinking to a known set of conditions. I can even see a few, not hundreds, of designs for a specific set of amp (SS or VALVE)/speaker (dynamic or electrostatic) combinations.
I listen to cable with the same R, L and C and am amazed at how different they sound. I am not even close to shutting down my ears. That’s what got me in this mess! How do you recognize correctly made audio speaker cables.
I did look back at some of your post so as NOT to pester you, and yes, the main things my ears hear is much improved openness, imaging stability, precise location of the image and debth in good speaker cords.
I can't say I grasp speaker cable impedance at such low frequencies as they "rise" as the frequency drops, making consistent low impedances at audio seem implausible, at least to my way of thinking about the measurements. My guess is if you look at the cable like a T-line, the impedance is the same at any cable length. Of course, the low pass nature of the cable changes too.
With your respone Jneutron, I close comments in this post. I've bugged you all enough.