The characteristic impedance of a cable is Z=sqr(L/C).
The propagation velocity is V=1/sqr(LC), and also V=speed of light/sqr(epsilon times mu).
Massaging of the equations of a coaxial run provide us the relation: L times C = 1034 times the dielectric coefficient. The coaxial run is the most efficient use of the structure, anything else will not provide velocities as high..this is because the inductance of non coaxial runs is higher as a result of failure to confine the mag fields to within the structure.
It is useful to calculate the LC product, divide by 1034, to determine the EFFECTIVE dielectric coefficient of the wire system, as this is a direct measure of both the speed of propagation along the wire, and the actual line storage. Note that if that product is less than 1, the L and C data are in error...less than 1 indicates faster than light prop...a no no..
L in nH per foot, and C in pf per foot, of course..
As it turns out, the point of minimal line storage occurs when the characteristic impedance of the cable matches the load..so, in theory, an 8 ohm speaker would work best with an 8 ohm cable impedance..this of course, is not because of reflections per se, but rather, just simply from the calculations of inductive and capacitive storage...
E = 1/2 L I squared, and E= 1/2 C V squared. As it turns out, this energy storage is a lagging one for both the inductance and the capacitance..meaning, the energy delivered to the speaker will be slightly shifted lagging. At 10 Khz, this storage minima is actually about 4% of the delivered power. And, this 4% is delivered to the load 90 degrees out of phase with the primary signal current..
For audio, given the power slew rates at the output terminals and the wire lengths involved, reflections are of no concern.
One would be better off examining human localization capabilities with respect to wires, as 20 Khz isn't enough, one must look for time shifts on the order of 10 uSec, as that is well within our ability to hear...
Grain boundaries within the metal do not cause reflections...at any frequency..all they can do is add to the dissipation along the conductor. Since the mean free path of electrons is 3 times 10 (-8) meters (wish I could do exponents on this forum), adding a coupla more relatively speaking, does nothing to anything..can one hear say, 1000 more collisions on a meter of wire, when the electron collisions are 30 million per meter?..and the noise is entirely uncorrelated?
When the surface texture of the conductor approaches the wavelength of the signal, then problems arise..but at audio, nada..
As for dielectrics, the secondary parasitics within the insulations are very significant when one is hi-potting a large capacitance, or making a sample and hold circuit..but, for speaker wires, I'd have to see the parasitic numbers, to figure out energy balance, and level of effect..
As for listening..don't bother with the standard 20 to 20K JND numbers...unless of course, your intent is to establish differences with only one channel playing. For stereo, there is just a tad more at play here..
While I remain open to either possibility, I would insist on realistic scientific explanations...
Cheers, John
The propagation velocity is V=1/sqr(LC), and also V=speed of light/sqr(epsilon times mu).
Massaging of the equations of a coaxial run provide us the relation: L times C = 1034 times the dielectric coefficient. The coaxial run is the most efficient use of the structure, anything else will not provide velocities as high..this is because the inductance of non coaxial runs is higher as a result of failure to confine the mag fields to within the structure.
It is useful to calculate the LC product, divide by 1034, to determine the EFFECTIVE dielectric coefficient of the wire system, as this is a direct measure of both the speed of propagation along the wire, and the actual line storage. Note that if that product is less than 1, the L and C data are in error...less than 1 indicates faster than light prop...a no no..
L in nH per foot, and C in pf per foot, of course..
As it turns out, the point of minimal line storage occurs when the characteristic impedance of the cable matches the load..so, in theory, an 8 ohm speaker would work best with an 8 ohm cable impedance..this of course, is not because of reflections per se, but rather, just simply from the calculations of inductive and capacitive storage...
E = 1/2 L I squared, and E= 1/2 C V squared. As it turns out, this energy storage is a lagging one for both the inductance and the capacitance..meaning, the energy delivered to the speaker will be slightly shifted lagging. At 10 Khz, this storage minima is actually about 4% of the delivered power. And, this 4% is delivered to the load 90 degrees out of phase with the primary signal current..
For audio, given the power slew rates at the output terminals and the wire lengths involved, reflections are of no concern.
One would be better off examining human localization capabilities with respect to wires, as 20 Khz isn't enough, one must look for time shifts on the order of 10 uSec, as that is well within our ability to hear...
Grain boundaries within the metal do not cause reflections...at any frequency..all they can do is add to the dissipation along the conductor. Since the mean free path of electrons is 3 times 10 (-8) meters (wish I could do exponents on this forum), adding a coupla more relatively speaking, does nothing to anything..can one hear say, 1000 more collisions on a meter of wire, when the electron collisions are 30 million per meter?..and the noise is entirely uncorrelated?
When the surface texture of the conductor approaches the wavelength of the signal, then problems arise..but at audio, nada..
As for dielectrics, the secondary parasitics within the insulations are very significant when one is hi-potting a large capacitance, or making a sample and hold circuit..but, for speaker wires, I'd have to see the parasitic numbers, to figure out energy balance, and level of effect..
As for listening..don't bother with the standard 20 to 20K JND numbers...unless of course, your intent is to establish differences with only one channel playing. For stereo, there is just a tad more at play here..
While I remain open to either possibility, I would insist on realistic scientific explanations...
Cheers, John