I'm working with a function generator that has a floating output. At one point, I looked at the signal on both the center conductor of the BNC connector and on the shield of the BNC connector relative to earth ground, and I found that while neither of them looked like a sine wave on their own, their difference was equal to a sine wave. I think this makes sense, as the center conductor's signal should be taken relative to the floating "ground" on the shield of the BNC.
However, the simple act of connecting this function generator to an oscilloscope with a BNC cable confuses me. The shields of the BNC connectors on the oscilloscope I'm using are earth grounded, though I still see a perfect sine wave on the oscilloscope. My confusion is: what happens when the BNC cable is connected on one side to a (time-dependent) floating "ground", and connected to earth ground on the other side? I assumed the oscilloscope measures the signal of the center conductor relative to earth ground, which I know should not give a sine wave on its own.
So does the shield of the oscilloscope remain at earth ground when I connect the BNC cable, or does it change to the floating "ground" of the function generator? Thanks!