This white paper is embarrassing in the level of errors, and erroneous conclusions.
The increasing rise in response above 400Hz is due to multiple reflections caused by the mismatchbetween the cable characteristic impedance, Zoand the impedance of the load. Note that the load impedance varies between 4 and 25ohms, which is an approximate match with the 18ohm cable.
Seriously?. This is not at all what is happening. If that was the case, the graphs would go up and down with frequency to match the impedance curve of the load as it mismatches with the cable like the peaks in impedance at 1.5KHz, and 10KHz, but they don’t. Why is that? I know why. The author? Not so much.
Now let’s have a good look at figure 12. The oscillations are 5 oscillations per usec. That’s 5MHz. No speaker puts that out. No human can hear it. Now how long is that cable? It’s 7 meters. * 2 = 14 meters. Waveform propagation speed is mainly related to dielectric, so let’s estimate speed at 0.6C = 180,000,000 meters per second. That’s about 13Mhz if due to transmission line reflections. Now what about the 18ohm impedance? Well it would also have transmission line reflections close to 13Mhz, but it appears to have oscillations close to 50 or 100MHz which if due to transmission line effects would require exceeding the speed of light.
For cable 6, Fig 3, with Zo 476ohms, driving the dummy speaker load with a step input from a square wave (the simplest transient) gives rise to severe ringing that has many oscillations.This is due to the transient reaching the mis-matched speaker load where only a small fraction of the signal is absorbed by the load. The remainder of the signal is reflected back to the source (the amplifier) where it is reflected back to the load. Again, only a small fraction of the now-diminished signal is absorbed by the speaker, with the remainder reflecting back to the source and so on. Over time, all the reflections will eventually be absorbed in the load.
Oh come on, really? That is not how characteristic impedance works at all. I sort of feel bad for the op putting this out. This is not going to go over well. Your simulation is highly flawed.
So, lets go back to the conclusion:
The results show that the principal factor determining the error of a cable is its geometry. Cables with very widely spaced conductors have the greatest error, closer-spaced conductor cables have less error, and very closely-spaced, flat conductor cables have the least, or near zero error.
No, this is not the principal factor at all, nor is it what your results indicate. Geometry (spacing) does play a roll in what is a determining factor and what all your results show.
Everything in your article points to 1 and only one 1 item. Inductance. Not characteristic impedance. Plain, simple inductance. Space conductors far apart, and the inductance is high. Space conductors close together and the inductance is low. Put two flat conductors really close and the inductance is very low (and the capacitance very high which can make some amplifiers unhappy).
The graphs in figure 3 - all inductance.
The oscillations in figure 12 - have nothing to do with transmission line effects, they are just a factor of the high or low source resistance in the simulation damping out the load oscillations slow or fast and impacting the frequency.
Reflections causing roll-off? They are at 13Mhz approximately. In your simulation they settle out completely after 10 microseconds (>100KHz bandwidth).
For low-level interconnect signal transmission, typical cables have an impedance of between 50 and 100ohmsanddrivea 10kilohm to 20 kilohm load. There are reflections from the load, but the source resistance is typically the same as the cable impedance, so the reflections will be absorbed in the source resistance and there will be no further reflections. This is known as “back matching”and usually occurs by default in audio and is de rigueur in video.
Source impedances in audio equipment single ended are typically 600-2000 ohms, some higher. That is not anywhere near 100 ohms or 50 ohms.
A high-loss dielectric distorts the electric field which has a second-order effect on the sound. The best practical insulators are air, PTFE and polyester. The worst is PVC.
Foamed polyethylene is better than basic PTFE which is why it is so common in high frequency cables. Reason PTFE is used in high frequency cables is dimensional stability. Polyester is not at all a good dielectric. It can be worse than PVC, or better, but never good.
