I want to use an Arduino to detect a disconnected ethernet cable. I don't need or want the device itself to be connected to the network. I just want to monitor the cable between two other devices and see if it has been disconnected.
Ethernet uses differential signaling, so my thought is to simply watch the twisted pairs used by 100BASE-T and count whenever the voltage on both pairs drops to zero. I'm not sure how to do that. From what I've found, an op-amp seems to be the best fit. However, most posts say to use a feedback loop. I'm not sure what that would look like in a circuit. I also don't have a ground to tie to, so I can't use the standard analog pins on an Arduino.
Is an op-amp the right way to proceed? What might the circuit look like?
An opamp is the right thing for detecting a differential signal. However the inputs must always be between the opamp's supply rails, so it's not totally isolated from the signal you're detecting.
The usual method of voltage isolation is an optocoupler but that will take significant current from the ethernet cable and disrupt the communications.
Keep looking. I'm sure there's an opamp available with enough lattitude in the input common-mode voltage to do what you want. There may even be dedicated chips available for this, because it seems like a thing that other people might want to do.
Also study up on the "magnetics" that terminate an ethernet cable. There's a lot of common-mode voltage isolation built into a standard ethernet jack.
I've never used an op-amp. What would the circuit look like?
Most things I find on the internet want a feedback loop to prevent voltages from getting too high. Wouldn't that also tie one of the wires to one of the rails on the Arduino?