Someone was asking about how time domain reflectometers work on a subreddit (/r/AskElectronics). It doesn’t make a whole lot of sense when you think about it when thinking about conductors the way one typically does — that the nodes of a circuit are connected with instantaneous connections.
It’s the difference between thinking of wires as conductors versus thinking of them as transmission lines. Everything acts as both, but normally one of the effects has a far greater contribution to what you’re measuring.
A similar concept is thinking of a normal 50-ohm coax. If you measure it with an ohm meter, you’ll invariably measure it as a dead short from one end to the other, because it is a dead short. So, why is it marked as 50 ohms? Because of the effects when it’s acting as a transmission line, it appears as a 50-ohm load from one point on the wire to the next one based on the capacitance between the conductors and the self-inductance of the conductors themselves.
So, in the case of the TDR, you have a signal generator at one end connected to an unterminated conductor that you’re testing. Let’s assume the conductor is at 0V. (Yes, I know it’s not correct to have an un-referenced volt reading, just ignore it for a second) The signal of let’s say 1V is applied to the end. At the instant the signal is connected there will be current flowing. You have different voltage potentials: 1V and 0V. That voltage will propagate down the line at around 0.6C (signal speed on wires, approximately). When it gets to the end the entire line will be at 1V. But wait, there’s more! Remember the inductance of the wire: you still have current flowing down the line. It will actually reflect back from the unterminated end and that’s the reflection that TDRs measure.
(this is a bit over-simplified, but I think it’s telling the story)
By taking into account the length of time from when you apply the signal to when you get a reflection, you can tell how long the conductor is. If you get back a reflection in 100ns, the signal has traveled around 60 feet (1ns =~ 1ft in a vacuum, ergo around 0.6ft on copper). Since it made a round trip, the break in the wire is 30 feet away from the end.
But then I started thinking about transmission lines themselves. Like, how can you have multiple bits flying down one bit of wire? That’s when it dawned on me: inductance. The line isn’t only capacitive, but the inductance is what makes the signals possible. It’s truly a fascinating thing.
More in a very shortly upcoming video! :-D