Hi,
I’m designing a simple PCB for a Wheatstone bridge that consists of four resistors and four test points, where wires will connect to the circuit. The board doesn’t have a defined ground — the excitation voltage will be differential square waves, so neither side is referenced to a stable GND.
Given that, I’m wondering: should I add a copper pour at all? Since the board is essentially floating and lacks a ground reference, it seems like filling it with copper might not make sense.
You are correct that it’s not necessary.
There are a few esoteric reasons why it might be nice (manufacturing issues, cost reduction, heat dissipation, etc.), but none of them really apply to your case.
I wouldn’t think about GND in this case. A floating bridge doesn’t need it, and you potentially add parasitic capacitances.
Keep it simple, just make the bridge traces and leave it at that.
Cheers, and welcome.
Thank you very much for the reply! This is my second time making a PCB and for some reason I thought that it’s mandatory to fill the PCB with copper. Now I know a bit better 
It’s correct that the bridge itself will work just fine without a GND plane. In the previous century GND planes were very rare (even for digital designs). So there is about 50 years of PCB design without GND planes, and before that point to point wiring (but that was often in a shielded metal box. Maybe by design, maybe by coincidence).
One of the big reasons for using GND planes these days is because of EMC regulations. Not so important for a hobbyist, but mandatory for all commercial products in most parts of the world. GND planes also improve signal integrity in digital designs (microcontrollers and such) and also in mixed designs (analog and digital combined in one project). And it becomes mandatory by more complex (digital) designs such as SBC’s (Single Board Computers).
But whether your Wheatstone bride would benefit from a GND plane… I don’t know. It probably won’t do much, but that’s also a guess.
If you don’t know what RS485 differential pair communication is then search some information about it.
There are (at two wires) differential square waves (like in your case). Information is in voltage difference (typically 2.5V or -2.5V at driver side) between A,B lines (receiver have to detect only if A>B or B>A). RS485 receivers are tolerant to big common mode offset from GND (up to 7V).
So, we can say signals are not referenced to GND. But even this it is said that RS485 communication is really 3 wire communication.
If you don’t use this third wire RS485 will work by its common mode emission and disturbance sensitivity will be much bigger.
In your case I would say that you gave us too little information to allow for correct answer.
If your signal source is battery powered and your detector in bridge need not be powered or is battery powered than you can think of the circuit as being not referenced to GND. In other case it is in some way referenced to GND, but that doesn’t at once means that you have to have GND copper fill at your PCB.
When you will really deeply understand why this third wire in RS485 is needed you will be able to answer yourself if adding GND copper fill at your PCB will help with anything or not. But to answer you have to look at whole your setup and not only on having at PCB only differential bridge.
Piotr: this is a really simple Wheatstone bridge we’re talking about here, so probably a bit of simple lab test kit. Nowhere is anything like RS485 mentioned. I’ll bet the square-waves just come from a simple audio oscillator box.
(Traditionally, the Wheatstone bridge was used with resistors and a DC source, to measure an unknown resistance. I guess with an AC input, you could measure effective resistance of a capacitor??)
So yeah, your comments are, of course, correct, but relatively irrelevant in this case.
Bridge is simple, but what you connect to it can be important.
I can imagine that ‘audio oscillator box’ is AC powered.
Also, even in past using an electromechanical indicator in bridge would be just standard I can imagine nowadays someone can use there his laboratory AC powered nanoammeter.
And as both devices have some GND references problems are ready.
It is probably not your case but you didn’t said it ‘for sure’.
A wheatstone bridge may appear “simple”, but to get the most out of it does need careful consideration, and it’s not trivial.
The one reason I can think of is that having copper pours (GND or otherwise) decreases the amount of copper waste that occurs during manufacturing when large parts of the PCB are etched off. Some manufacturers point this out if you send them a PCB with large ‘open’ areas.
Then again, it might be that the recycling of etching fluids is now so good that this is no longer an issue.