Figure 1 and figure 2 have the same problem, it's just that in Figure 1 the problem is sidestepped.

You perhaps imagine things look as on the left below, but they actually look more like on the right below:

^{simulate this circuit – Schematic created using CircuitLab}

Then, when a single-ended connection is used:

^{simulate this circuit}

The circuit on the right is equivalent to all of the following circuits:

^{simulate this circuit}

What you end up measuring on the scope is \$V_src+(Z_{cable}||Z_{PE})\,I_{PE}\$

Figure 1 and figure 2 have the same problem, it's just that in Figure 1 the problem is sidestepped.

You perhaps imagine things look as on the left below, but they actually look more like on the right below:

^{simulate this circuit – Schematic created using CircuitLab}

In spite of the non-idealities above, the scope still measures \$V_{src}\$, assuming that \$Z_{in,SCOPE}\gg Z_{cable}\$.

Then, when a single-ended connection is used:

^{simulate this circuit}

Or, equivalently:

^{simulate this circuit}

What you end up measuring on the scope is \$V_{src}+(Z_{cable}||Z_{PE})\,I_{PE}\$.

So, what's the solution when connecting the circuit to an ADC with single ended inputs? Ensure that at least one side is not connected to PE:

^{simulate this circuit}

If that's not possible, then:

1. Break the ground loop next to the ADC by adding an isolation impedance \$Z_{iso}\gg Z_{cable}\$.

2. Add a voltage-controlled voltage source to have the ADC measure the voltage on the source in spite of being ground-referenced.

^{simulate this circuit}

The VCVS can be easily implemented using an instrumentation amplifier. The isolation impedance \$Z_{iso}\$ is then the input impedance of the in-amp.

^{simulate this circuit}

The classical in-amps that have equivalent three-op-amp architecture have a low impedance REF input. It can only be connected to a low-impedance node - an op-amp output or a ground.

In some cases, due to output voltage range limitations of the in-amp, its output may need to be "centered" around a voltage above the COM terminal of the ADC. In that case, it should always be ratiometrically derived from the ADC's reference voltage - that way it will have negligible thermal drift as long as R1 and R2 are tracking each other well.

The in-amp's input common mode voltage range needs to be wide enough that it will contain \$\Delta V_{PE}\$. This interfering ground voltage has AC and DC components that can reach several V within a small building, or much more across larger industrial buildings.

There are in-amps with wide input common mode voltage ranges that extend beyond supply voltages. You'll need to specify the maximum allowed \$\Delta V_{PE}\$ that your data acquisition system will be able to compensate for, and design accordingly.

Figure 1 and figure 2 have the same problem, it's just that in Figure 1 the problem is sidestepped.

You perhaps imagine things look as on the left below, but they actually look more like on the right below:

^{simulate this circuit – Schematic created using CircuitLab}

Then, when a single-ended connection is used:

^{simulate this circuit}

Figure 1 and figure 2 have the same problem, it's just that in Figure 1 the problem is sidestepped.

You perhaps imagine things look as on the left below, but they actually look more like on the right below:

^{simulate this circuit – Schematic created using CircuitLab}

Then, when a single-ended connection is used:

^{simulate this circuit}

The circuit on the right is equivalent to all of the following circuits:

^{simulate this circuit}

What you end up measuring on the scope is \$V_src+(Z_{cable}||Z_{PE})\,I_{PE}\$