# Understanding connection of floating function generator to oscilloscope

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!

Connecting an earthed scope to a floating signal generator with a BNC cable will connect the BNC grounds together so the signal genetator becomes earthed too.

• That makes sense. So upon connection, does the function generator adjust the output on its center conductor to given a sine wave relative to the earth ground? Commented Jun 16, 2023 at 4:40
• the function generator does not do any adjusting ... the center conductor is already a sine wave relative to the outer conductor Commented Jun 16, 2023 at 5:19
• No it does not adjust anything. It's like a 9V battery, there's always 9V between the terminals no matter how you externally define the voltage of one of the terminals. So there will be same signal between center pin and connector shell as the center pin is referenced to local ground of the device which is connected to the shell. Commented Jun 16, 2023 at 7:25

Here's the equivalent circuit of the floating function generator:

simulate this circuit – Schematic created using CircuitLab

It is very much like an ideal voltage source with a series resistor added.

The oscilloscope can be thought of being a ground-referenced voltmeter:

simulate this circuit

When we connect the two, everything is all right:

simulate this circuit

Here's what happens when the function generator is not floating:

simulate this circuit

Except that is not true. Real PE connection points are like ideal Earth with some series impedance paralleled with a current source:

simulate this circuit

That's not a problem - yet. But real BNC cables and connections have some impedance as well:

simulate this circuit

Since IPE1, IPE2, ZPE1 and ZPE2 are not equal, there's a non-zero voltage across Zinterconnect. This voltage adds in series with whatever the scope ("voltmeter") is supposed to measure.

Furthermore, the current across Zinterconnect can be fairly high. See what happens when there's a live-to-PE fault in something plugged into the same outlet as the oscilloscope:

simulate this circuit

The fault current flows through Z(PE)2 || (Zinterconnect+Z(PE)1).

Oh, but such faults are rare you say? Here's how you get such a fault without any actual fault inside the equipment:

simulate this circuit

Vtransient above is someone's breaker tripping while welding :) TVS is the transient overvoltage protection in that 3rd piece of equipment plugged next to the oscilloscope.

I think you are missing the point that the function generator produces a varying potential difference, and the oscilloscope is measuring a potential difference.

A potential difference implies two conductors (nodes), each having a different potential with respect to each other. To measure a potential difference, the voltmeter or oscilloscope has both its nodes connected to both nodes of the source being measured. And the reading is simply the difference between the potentials of those two nodes.

In all cases, the absolute potential of either node (with respect to earth, or the sun or the centre of the universe, wherever you choose to be the ultimate "zero" point) is irrelevant. Both scope and function generator are dealing with the difference between two potentials, and do not care about anything else.

All of that is true regardless of whether your scope's "shield" is "earthed" or not. Connect it to the sun, if you like, that doesn't change the potential difference between the nodes.

If you only connect one node between scope and function generator, you are no longer measuring the potential difference of the function generator's output. Now you are measuring the potential difference between one node of the generator and something else. That something else will be whatever potential that the environment imposes there, which will be a lot of noise (like mains voltage, or radio signals) coupled capacitively and electromagnetically to that now "floating" node, and maybe a little of the original intended signal, also coupled capacitively.

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?

OP's tests and the intuitions derived from them are good.
Conventional oscilloscopes will have a power chord with earth connection (GND) to which its front-panel BNC are hard-wired. So connecting such an oscilloscope to a floating function generator causes the function generator to become GND-referenced.
When you connect the ground-side of an oscilloscope to anything (including a floating function generator), assume you're connecting to hard-GND....that floating generator will no longer be floating.

Many function generators are versatile, and have more than one front-panel BNCs. Generally, all of its BNCs have their shells common, so if you connect your oscilloscope to any one of those BNCs, the function generator no longer floats, but is grounded via the oscilloscope connection.

There are oscilloscopes that have differential inputs, but these are not so common, and may not use BNC inputs. These 'scopes will clearly state that inputs measure differentially, with neither input GND-connected.