Bubblepuppy wrote on Fri, 01 September 2006 07:21 |
Here is another point of view on your conclusion
Attenuation causes
Okay, if the cable's varying length didn't cause the attenuation to change, what did?
To understand this, we have to understand what causes attenuation in the first place (for more on this, see pages 386-389 in Modern Cable Television Technology, by Ciciora, Farmer and Large). There are four fundamental reasons why cable has attenuation: signal leakage out of the cable because of less-than-ideal shielding; resistive losses in the cable's metallic conductors; signal absorption in the dielectric; and signal reflections caused by impedance mismatches.
Without getting too deep, the majority of attenuation comes from resistive losses in the cable's metallic conductors. What's of interest here is the conductors' resistivity, which is temperature-dependent. Resistivity is a "bulk property of material describing how well that material inhibits current flow. This is slightly different from resistance, which is not a physical property. If one considers current flowing through a unit cube of material (say, a solid metal cube that measures 1 meter on each side), resistivity is defined as the voltage measured across the unit cube length (V/m) divided by the current flowing through the unit cube's cross sectional area (I/m2). This results in units of Ohm m2/m or Ohm-m." [University of British Columbia Geophysical Inversion Facility]
In case you were wondering, the resistivity of copper is 1.673-8 Ohm-m, and aluminum is 2.650-8 Ohm-m, both at 68 degrees F. Each of these metals has a temperature coefficient of resistivity of about 0.22 percent/ degrees F. Conductor resistance varies as the square root of resistivity, so the resistance of the center conductor and shield (and the attenuation) changes about 0.11 percent / degrees F.
Yeah, but why?
Colliding electrons
Well, it's because the electrical resistance of a conductor such as copper or aluminum is dependent upon collisional processes within the metallic conductor. A closer look at conductivity shows it to be proportional to the mean free path between collisions (d). For temperatures above about 15K (that's kelvin...), d is limited by thermal vibration of atoms.
Huh?
Let's look at electrical conductivity (s = 1/r, where s is conductivity and r is resistivity--see, all this stuff is related!). Many metals make good conductors because they have lots of free charges--usually electrons--in them. When a voltage difference exists between two points in a metal, it creates an electric field that causes electrons to move--in other words, current!
The electrons bump into some of the metal's atoms, and this "frictional resistance" slows the electrons down. The greater the distance the electrons can travel without bumping into the metal's atoms, the lower the resistance and the greater the conductivity. The average distance an electron can travel without bumping into an atom is known as "mean free path."And how does temperature play a role in all of this? The higher the temperature, the more the metal's atoms jiggle around and get in the way of the electrons, causing the resistance to increase. At lower temperatures, the metal's atoms jiggle around less, so they don't get in the way of the electrons quite as much. The resistance decreases.
That's kind of a simplistic explanation of R = R0[1 + a(T - T0)]--(where R is the new resistance, R0 is the initial resistance, T0 is the initial temperature, T is the new temperature, and a is the temperature coefficient, but jiggling atoms are much more intuitive than mathematical formulas! Ron Hranac is a consulting systems engineer for Cisco Systems, and senior technology editor for Communications Technology. You may reach him at rhranac@aol.com.
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First, again: the copper resistivity of a cable by itself is not enough to tell you about attenuation! You need to know the LOAD! As I mentioned elsewhere on this forum, a 1 Ohm resistance is a cause to a lot of attenuation when you are dealing with say an 8 Ohm speaker. You can not discount math. The attenuation is A=RL/(Rload+Rcable) in this case A=8/9 or in dB it is -1dB. So at 8Ohms it is a lot of loss. But raise the load to say 600 Ohms then A=-.014dB.
You can not talk about the sound of one hand clapping.
Similarly, you can not talk attenuation looking at one hand (the cable) and not the other (the load).
You mentioned 4 reasons for loss, with the conductor resistance being the main one, and you "elaborated some". But besides the fact that you did not mentioned load, you did not touch on the fact that the signal frequency content is also a major KEY.
I keep qualifying my statements over and over, saying "for audio signals" and for "digital audio up to say 25MHz and 100 feet"...
The conductor resistance is important at very high frequencies, when only the thin outer diameter carries current (skin effect). I wrote a paper on skin effect (see it at my forum at
www.lavryengineering.com). But we are not talking about GHz signals. We are talking about up to 25MHz. Also, skin effect increases with cable length and here we are not talking about miles of cable runs...
I am pretty sure that your referenced person from cisco would not have any issues with what I am saying. He will have issues with what you are saying! You are talking out of context! We are talking and dealing with very low frequencies, when referenced to what cisco is doing. On top of it, one should examine the load as well as the cable length.
A thirsty person can be highly impacted by one cup of water. But the same cup will make insignificant difference in the Atlantic ocean. You seem to reach general conclusions about the importance of that cup of water, but in fact it does matter a lot in one case, and it does not in the other.
Similarly, the impact of skin effect in the applications we are talking about is NEGLIGIBLE. The temperature effects are also NEGLIGIBLE. Thank you for "friction" explanation (a very simplistic one) of how the copper resistivity goes up with temperature, but that does NOT alter the fact that the coefficient describing the rise of resistance over temperature is 0.0039 per degree C, nor does it alter that at low frequencies, attenuation is a voltage divider action between series resistance and load.
The audio industry is full of "mention" of things that are there, but are mentioned out of context. The fact is, skin effect does occur even when at 1Hz frequency and 1 inch length. A single drop of water will increase the volume of the ocean. But the effect of 1 billionth of a billionth of a dB can be ignored in the real world. What is missing in such arguments is a real world perspective, and engineering IS of value here. Engineering is not just a bunch of formulas! It is hands on experience and measurement based.
Also, many of those that are less familiar with math, engineering and science, often make a judgment error, by assuming that "things are proportional". For example, if I tell someone that a cable of a certain length causes say 1dB loss at 1GHz, it is WRONG to assume that you will have 0.5dB loss ate 0.5GHz (500Mhz), and .1dB at 100MHz. Not only does the math for dB is not linear. Not only does the math for attenuation is not linear. The physics itself is highly non linear. Again, look at the skin effect paper on my site.
You said:
"That's kind of a simplistic explanation of R = R0[1 + a(T - T0)]".
I say: It is very easy to dismiss a statement. It is simplistic in some cases, and rather accurate in other cases. It is rather accurate at the frequencies and cable length for audio. Just calling something simplistic is of no value. You have to point out why, how and or at least QUANTIFY what you say, which you did not.
I can go on, but it is getting too long.
Regards
Dan Lavry
http://www.lavryengineering.com