Have you ever wondered how balanced audio cables work? For the longest time I have until finally deciding to look into it. Turns out the principle is actually rather straightforward.

In a normal, unbalanced wire an analogue signal S is sent over a pair of wires: one carries the signal while the other a reference zero. Receiver interprets voltage between the two as the signal. The issue is that over the length of a cable noise is introduced. While transmitter sends S, receiver gets S + e (where e denotes the noise).

A balanced cable addresses this problem by sending the information over three wires: hot (or positive), cold (or negative) and ground. Hot wire carries the signal S as before, cold one carries the inverse of the signal -S and ground is zero as before. Like before, when information travels over the cable, noise is introduced. Crucially, because it’s a single cable, noise on the positive and negative wires are strongly correlated. Receiver therefore gets S + e on hot wire and -S + e on cold wire. All it needs to do is inverse the signal on negative wire and add both signals together. Inversion changes phase of the noises on the cold wire such that it cancels out error remaining on the positive wire: (S + e) + -(-S + e) = S + e + S - e → S.