I'm sorry but, at this point, you're splitting hairs that just plain aren't worth splitting.
In a fully balanced connection, you have two copies of the signal, out of phase with each other.
They are being sent from identical sources, through identical wires, into identical inputs.
At the receiving end, those two signals are subtracted from each other (one is inverted then added to the other).
The result is that the two signals add together while the noise on the two wires is subtracted.
How well this works depends on how well EVERYTHING is balanced.
You have two identical wires, twisted together, running next to each other.
This helps ensure that any outside noise that makes it into one wire will make it equally into both.
The twisting ensures that, if the noise is coming from one side, both wires have equal opportunity to be exposed to it.
(This would not be true for a coaxial cable - for example.)
At the sending end your two signals are coming out of identical transmitters (outputs)... so they have the same source impedance.
And, at the receiving end, the two inputs are also identical... so they present the same load impedance.
(If either were different then interference of the same "strength" would induce different voltages in the two wires.)
How well it all works depends on ALL of those things being perfectly balanced....
And, to the degree that ANY of them is not perfectly balanced, it works less well....
The other thing to remember is that the "noise cancellation" we're talking about is that noise PICKED UP IN THE WIRE will be cancelled.
(Or you could describe it as "resistance to picking up noise" or "tolerance to a noisy environment".)
However, the important part is that it only matters if you have environmental noise that is likely to be picked up in the wire.
It does NOT improve the quality of the original signal.
And, if there is no noise being picked up to begin with, then it is NOT going to improve anything.
There are a few other rather more obscure benefits....
If there happens to be AC noise present as a voltage difference between the grounds of the two devices being connected....
With luck THAT will also be cancelled out by the balanced connection (because it is also "noise that appears equally on both lines").
It's also possible that distortion in the sending or receiving electronics themselves will be cancelled out to a degree.
That one is especially dubious because this sort of electronics have very little distortion to begin with.
And, because the balanced circuitry is more complex, and requires more parts, it also has more opportunity to add noise and distortion.
In practical terms, having an XLR connector at one, and a twisted pair wire, with balanced circuitry at one end, may give you some slight benefit.
But, if you're using a coaxial cable, then the only benefit you're going to get from it is a nice heavy locking connector.
Boy did THIS thread run amok!
First - As I've explained, "induced noise" is something that is not being generated by either the source or the destination components, but rather hiss, hum, or noise that is picked up by the interconnect itself.
Second - Yes, we all understand that a balanced-circuitry source and destination component combination are more effective in noise cancelling when using XLR interconnects than when used with any other type of interconnects.
Finally - Having an XLR connector at EITHER end of an interconnect provides at least SOME of the noise-cancelling benefits that would exist if both source and destination components used XLR connectors (REGARDLESS of whether their internal circuitry is balanced or not).
My question, specifically, and obviously not well-stated originally, is:
"What percentage of induced noise cancellation will occur if one and only one end of the interconnect uses an XLR connector?" 50%? 90% and WHY?
And not to be rude about it, but this is not an "opinion" question - there IS an objective and factual answer here, and that's the answer that I'm seeking.
Thanks - Boom
