At which point is differential signaling for analog signals warranted?

[John Celo]

I have an analog signal from a sensor in 0-5V range, frequency of the signal less than ~40 kHz, that I'm going to digitize using - say 12bit ADC.
That means the signal resolution is down to 5V/(2^12) = ~ 1.2mV. (or it could be 10bit ADC giving step resolution of around 5 mV).

Lets say I'm going to send it over some distance L with a basic twisted cable consisting of (measured signal, gnd).
At which length L (10cm, 20cm, 50cm, 1m?) would it make sense to convert the single ended analog reading to a differential one given the desired resolution?

I feel like I lack the tools to properly reason about scenarios like this, I'd appretiate any tips...

[jmelson]

Length doesn't matter as much as if there is any difference in the ground voltage at each end.  Assuming typical single-ended connection, there's one signal wire and one ground wire.  If there is even a few mV difference in ground between the two ends, then that will cause errors in the measurement.  Now, you can also use pseudo-differential, where the sending end is about the same.  But, add one more ground wire.  A ground to ground between each unit, and then a differential amp computing the difference between the signal wire and the ground wire that is floating at the receive end.
Or, you can go full differential, where the sending unit sends a positive and negative value on two wires.
Jon

[Benta]

Differential transmission (both analog and digital) is used when you have outside electrical interference (which you have everywhere, question is only how bad).
As the outside interference signal will impact both signal equally, net impact on your signal balances out (ideally).
A good example is the classic audio cabling on stage equipment (600-ohm balanced).

[John Celo]

I'd imagine, it's an order of magnitude harder to flip a bit from threshold voltage of high->low or low->high, than it is to introduce electrical noise in order of 10-100mV which will flip a whole multitude of bits in the reading of a 10 or 12bit ADC converting a signal in 0-5v range.

In case of digital signals, the length of cable also has to much, much longer for the signal attenuation and similar to degrade the timing of leading or falling edges to render high/lows irrecognizable, etc.

Susceptibility to noise there is just on a completely different order of magnitude. I don't think those cases are at all comparable.

Needless to say, I'm have no tools or mental framework to think about the problem in case of analog.

In case of digital, there's RS422/RS485/Ethernet and various other "off-the-shelf" type solutions that are also quite cheap and relatively simple to implement with various cheap driver ICs as far as I can tell.

[ssashton]

If 5v is 0dBFS then 12 bits resolution gives is -72 dB. Coming from an audio systems POV, this should be easily achieved with single ended connections unless you run the signal past a mains transformer or something. Ensure the signal has a ground line directly next to it, so there is a small loop area over the length of the wire.

Bare in mind as well, that a differential line driver has twice the number of resistors and amps as a single-ended equivalent, so noise from the differential driver is actually higher all being equal.