Amplitude panning originates from stereophony, initially developed by Blumlein in the early 1930s. In essence, this system transforms the phase and amplitude difference of a signal recorded by stereophonic reception systems (mic stereo pairs, or the ears for that matter) into amplitude differences reproduced by two speakers. 

Different methods of multi-loudspeaker configurations are generally based on implementing amplitude panning. There are a number of methods of amplitude panning techniques, and the two most common will be mentioned below:

Pairwise amplitude panning

First is pairwise amplitude panning. It’s most commonly present in traditional horizontal configurations with adjacent speakers that can reproduce amplitude differences. 

Here, an identical sound signal is outputted from a set of speakers equidistant from the listener but located in different positions. When both speakers output the same level, a virtual sound source will appear in the center between them. This virtual source of sound will shift gradually towards the higher output speaker as the differences in amplitude increase. It will coincide with the actual location of a speaker when that is the only source actually reproducing any sound. In such an instance we can achieve the best possible directional output. This happens since virtual sources will inevitably be less defined or focused. The behavior of virtual sources in such a system is based on a derivation of the tangent law of trigonometry.

Vector base amplitude panning

On the other hand is VBAP, short for Vector Base Amplitude Panning. It’s an amplitude panning method to position virtual sources in arbitrary 2-D or 3-D loudspeaker setups. Such setups are rare in domestic use but are common in public venues such as theatres, concert halls, and in some cinemas. These configurations can have loudspeakers above or below the level of the listener’s ears. In this case, a natural approach to extend traditional pairwise panning behavior has been to use triangle loudspeaker setups to reproduce virtual sources. We know this as triplet-wise panning. 

However, these kinds of 3-D loudspeaker setups are problematic for amplitude panning reproduction. A generalized tangent law can’t calculate panning from arbitrary speaker locations or for spherical coordinates. The latter case might be needed in cinemas, to optimize the listening experience of the whole audience.

For that reason, we use a generic reformulation of the tangent law. This defines panning with vector bases, and the positions of virtual sources abstractly using directional angles. Data can specify the layout of the loudspeakers.

When the configuration changes, that data can be modified. Thus, various loudspeaker configurations can use the same control mechanism. This is helpful when the same signal is reproduced in different places with different speaker configurations.