I'm new here; pardon me for just "jumping in"; however, I've been dealing with "data cabling" since before "AppleTalk" first started exploring twisted pair usage -- and "Ethernet" referred to some sort of "coax installation for your DEC computer."
Here are several of points that I did not see completely clarified:
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1. Yes, the "twist rate" will be different between different pairs within the same cable and, it will generally vary between types of cable from the same manufacturer and between different cable manufacturers. The purpose of having a variable twist rate is to keep the cables from "nesting" inside of the overall cable housing. (Think of the way two threaded rod with the same "tread pitch" will "lock together" in their package.) When they nest together, you get increased cross talk. I have dealt with cable manufacturers who had dividers to keep the pairs separate and with manufacturers who used a left-hand twist on two pair, and a right-hand-twist on the other two pair -- making it necessary to have only two twist ratios instead of four.
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While "twist is good" is a rule of thumb, it comes at a cost. The higher the twist rate, the shorter the distance covered by the same amount of wire (I've seen deltas of up to three feet in a 100 meter run). The higher the twist rate, the harder it becomes to terminate the cable -- whether using plugs or jacks (I've crimped thousands of plugs on to Cat 6 Cable, when doing it regularly my failure rate was 0.5%) -- you have to test with a high-quality tester every time.
There is no sure and certain guarantee that the "green pair" or the "orange pair" or any of the other pairs will be the "best" pair. In fact, at one point, Avaya claimed the "Blue Pair" was the "best pair" in their cables.
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2. The twist rate not only affects how much the cable pairs nest and how much they cross-talk, it also affects the cable's immunity to environmental noise. All things being equal, the higher the twist rate, the more noise immunity you tend to get. Thus, I have seen some devices on some cable that would work on one set of cable pairs, but not on another. Now this was in a situation where we were pressing some first-generation "Level 3" (remember, they called it "Level 3" before there was a "Category 3" designation?) cable that was being used for a 100 meg connection. So, we were "at the margin" to say the least -- technically, it should NOT have worked at all. But, in order to achieve functionality, we rotated the "Blue Pair" (see above) into use along side of the "Green Pair" to get 100mbps with an acceptable (but still non-zero) error rate.
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3. But ALL of this begs the question of the difference between 568A and 568B relative to your camera installation. As has been stated before, in 568A places the "green pair" on pin numbers 1 & 2 while the "orange pair" goes to pin 3 & pin 6. By contrast, 568B puts the "orange pair" on pins 1 & 2 and lands the "green pair" on pins 3 & pin 6. The fact I did not see anyone raise (I apologize if I missed a comment), is that pins 1 & 2 and pins 3 & 6 are ALL part of the SAME bidirectional communications channel.
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From the DTE (Data-communications Terminating Equipment) perspective, pin one is essentially Tx+ pin 2 is Tx- pin 3 is Rx+ and Rx- lands on pin 6. What is "transmit" to one device is "receive" to the other -- which is why you may see the pins designated as "BI_DA+" and "BI_DA-" and "BI_DB+" and "BI_DB-" respectively. So, basically, you are not "improving" the channel by switching the pairs within the channel. You are simply changing which end is "driving" which pair. Assuming both pair meet specs, there should be no problem. If they do not meet specs, it's not like you were swapping a pair that was not part of the link into the connection. Let's say say NEXT (Near End X-Talk) is too high and the camera "hears itself" thereby causing phantom collisions. The inductive and/or capacitive coupling that is causing your issues is bidirectional -- if the green pair "hears" transmissions made on the orange pair, the orange pair will "hear" transmissions made on the green pair and the camera will still fail to transmit -- regardless of which pair it drives and which pair is driven by the other end.
Oh, and one final point, the whole reason for specifying 568A as opposed to 568B has to do with backwards compatibility, not quality of operation.
The 568B option matches the old "Ma Bell" 258A color code (can anyone say, "WICO"?) and only matches single (one) pair USOC wiring schemes. Since the Ma Bell or AT&T (Alotta Time & Trouble) spec wiring was far and away the most common in private homes and private companies. This is because, at one time, the "phone company" had to do the wiring, or you would
not get service from them. That restriction is why we occasionally had phone jacks screwed to desks -- wanna move your desk? gotta call the phone company! The 568B wiring pattern tends to flow "naturally" in those places.
Meanwhile, 568A provides "backwards compatibility" with two pair USOC -- which is why the Federal Government generally specifies 568A.
My $0.02 Worth
(and that's inflation)
