These are extremely handy devices to rid signal cables of common mode currents, and in so doing also correct common mode voltages that exist on any signal cable. In brief, these are currents that exist because of a difference in reference voltages (i.e. Ground) between two devices intended to be connected to each other.
If we examine the diagram above we will see that in our example we have a ground differential between the two sides of 10VACrms. This voltage will be superimposed on the signal voltage of ±12V, but as 10VAC peaks at over 14V there are times the signal never crosses zero to be recognised as having changed.
The way current chokes operate is to utilize the voltage difference and superimpose it 180º out of phase (such that it cancels) on the signal line. The result, the signal reaches the other side free of the offending voltage. This also works in both directions. The fact the transformer 'absorbs' the voltage that exists between the two grounds results in no current flowing on the signal ground lead between the two devices.
Some installations could easily span across two electrical supply points, e.g. between two buildings. Such installations could easily attract ground loop currents, especially during fault conditions. It is this last point that causes the supply companies to get a little upset when a user decides to combine two earthing systems into one. Common mode chokes provide an excellent answer but could lead to extremely high currents if the core manages to saturate. It is strongly advised that impulse protection be placed across the signal line(s) and that both the signal line(s) and the ground return be fused.
Although we have shown this with a digital signal, the exact same principle works with audio signals too. This has been very successfully used on mixer to power amp links where the common ground created such a ground loop it caused issues at the mixing desk. Simply winding a length of shielded twisted pair cable (the link was a balanced audio feed) on a "clip-together" ready made transformer core did the trick.