[Editor's note: Part 1 can be found at Design of High-Performance Balanced Audio Interfaces]
THE BALANCED INTERFACE
The purpose of a balanced audio interface is to efficiently transfer signal voltage from driver to receiver while rejecting ground noise. Used with suitable cables, the interface can also reject interference caused by external electric and magnetic fields acting on the cable.
The true nature of balanced interfaces is widely misunderstood. For example "Each conductor is always equal in voltage but opposite in polarity to the other. The circuit that receives this signal in the mixer is called a differential amplifier and this opposing polarity of the conductors is essential for its operation."  This, like many explanations in print (some in otherwise respectable books), describes signal symmetry " "equal in voltage but opposite in polarity" " but fails to even mention the single most important feature of a balanced interface. SIGNAL SYMMETRY HAS ABSOLUTELY NOTHING TO DO WITH NOISE REJECTION — IMPEDANCE IS WHAT MATTERS!
A good, accurate definition is "A balanced circuit is a two-conductor circuit in which both conductors and all circuits connected to them have the same impedance with respect to ground and to all other conductors. The purpose of balancing is to make the noise pickup equal in both conductors, in which case it will be a common-mode signal which can be made to cancel out in the load."  The impedances, with respect to ground, of the two lines is what defines an interface as balanced or unbalanced. In an unbalanced interface, one line is grounded, making its impedance zero. In a balanced interface, the two lines have equal impedance. It's also important to understand that line impedances are affected by everything connected to them. This includes the line driver, the line or cable itself, and the line receiver.
The line receiver uses a differential amplifier to reject common-mode voltages. The IEEE Dictionary defines a differential amplifier as "an amplifier that produces an output only in response to a potential difference between its input terminals (differential-mode signal) and in which output due to common-mode interference voltages on both its input terminals is suppressed."  Since transformers have intrinsic differential response, any amplifier preceded by an appropriate transformer becomes a differential amplifier.
The basic theory of the balanced interface is straightforward. (For purposes of this discussion, assume that the ground reference of Device A has a noise voltage, which we will call "ground noise," with respect to the Device B ground reference.) If we look at the HI and LO inputs of Device B with respect to its ground reference, we see audio signals (if present) plus the ground noise. If the voltage dividers consisting of Zo/2 and Zcm on each of the lines have identical ratios, we'll see identical noise voltages at the two inputs of Device B. Since there is no difference in the two noise voltages, the differential amplifier has no output and the noise is said to be rejected. Since the audio signal from Device A generates a voltage difference between the Device B inputs, it appears at the output of the differential amplifier. Therefore, we can completely rejects the ground noise if the voltage divider ratios are perfectly matched. In the real world, we can't perfectly match the voltage dividers to get infinite rejection. But if we want 120 dB of rejection, for example, we must match them to within 0.0001% or 1 part per million!