For the experienced this will be a bit of re-inventing the wheel. But I am hoping that it will bring further clarification to those who could not make out what we were talking about.
Again, just to clarify that, when I say ground loop I am not defining it, but meaning the loop formed by the ground paths between the two equipment.
So, the loop formed is shown in the below first diagram.
However, I have reinstated the mains safety earth impedance as part of the loop as this is what we are concerned with. In my previous test we discovered that the mains safety earth impedance had no effect and appeared as open when the noise source was the offending equipment itself.
Just to refresh our minds again that the Audio and Audio' are the audio circuit impedances. The noise voltage developed on the ground is imposed onto them and appears at the output with the actual signal. Strictly speaking, from analysis point of view we should be showing the output impedance of the circuit but am keeping it all out of this analysis now as it is irrelevant to what we are looking for.
I will not repeat what the impedances stand for as one can refer to the diagram in my first post. But briefly, Path A and A' are the internal ground path impedances of both equipment and all the others are the impedances of signal and mains earth wires and the contact resistances of the connectors.
The ground node shown between Contact B and Path A is where the signal/circuit ground of the equipment is tied to the mains safety earth, normally at a chassis stud point immediately after the IEC inlet,
The diagram on the left reduces to the diagram on the right when we add the impedances connected in series.
As mentioned before the mains safety earth is tied to neutral at the distribution point and earthed. The earthing is again irrelevant to us here. All we have to bear in mind that the safety earth wire has connection to neutral at this point.
So, I have put together a simple test set up as shown in the below picture, and a diagram to simulate the actual mains wiring.
I wired two transformers back to back and used the low voltage secondaries. TX1 represents the step-down transformer at the distribution point to step down the high voltage to consumer level (in UK). Point A is where the mains safety earth is tied to neutral and the node is earthed. Again, we are not interested in the earthing. I also used a fuse for safety.
TX 2 is the transformer of the equipment that is plugged into the mains. Point B is again where the circuit ground is tied to mains safety earth at the chassis stud point.
Assume that a mains born noise voltage is developed at point B through source impedance R1. The current will seek for a path to neutral through the mains safety earth. However, since R3, R5, R3' and R4' are all connected in series, and the total resistance is in parallel to R4, the noise current will also flow through this path, offending the other equipment too.
The circuit simplifies to the one in the below diagram.
Here the ground loop impedance is sandwiched between the noise source impedance and safety ground impedance, and forms a voltage dividing network. R1 and R2 are fixed and there is nothing we can do about them. But if we reduce R3 then the noise voltage developed at Point B, will also reduce. So, clearly what Thor had suggested holds.
However, it is clear that we are limited by the mains safety earth impedance. So, there comes a time, particularly multiple equipment are interfaced, the only option open to us is to bring discontinuity to the loop to be able to eliminate the hum. In other words, cutting the physical hard wiring. We can not disconnect the mains safety earth as it is illegal, but more importantly it is there to save our lives. I do not know what the regulations say about isolating the signal ground from the safety ground inside the equipment. So, this could be done on the signal connection between the two equipment by introducing an isolation transformer which Bill's paper explains expertly.
In terms of verifying my test, I have used 2k resistors throughout.
R3', R5, R3' and RR4' are all in parallel to R4. So, R4 = 8k || 2k = 1.6k.
The coupled noise voltage at point B is 10.8VRMS with reference to point A.
Plugging in 1.6k at the high side and 2k on the low side of voltage divider gives 6V at point C. I measured 5.9V. This agrees that the noise current is flowing through mains safety earth and into neutral.
Finally, this is just one scenario. Things can and do get much hairier than that.