L/R to M/S and M/S to L/R Conversion
The common left - right stereo format can be converted to the M/S stereo format as well as an M/S signal can be converted to L/R stereo without affecting the signal quality or the sound performance if the matrix is well designed.
The conversion from L/R to M/S follows the formulas:
M = L + R and S = L - R
The conversion from M/S to L/R restores the original, pre conversion signals:
L = M + S and R = M - R
To get to the equations for the reconversion, the above formulas can be arranged like this:
L = M - R ; R = L - S
Inserting the above equations for R and L results in:
L = M - ( L - S ) -> L = M + S - L -> 2L = M + S
R = M - R - S -> 2R = M - S
As you can see, a matrix that simply converts L/R to M/S can also be used to convert M/S to L/R. The only difference is the level, since you end up with 2 × L and 2 × R after conversion and re-conversion; which means that the resulting level is 6 dB higher.
The level relation is not standardized. Checking devices you will find everything from simply ignoring the 6 dB higher level to different ways of compensation. It is better to compensate not in the M/S to L/R conversion but in the L/R to M/S conversion. Since the uncompensated L/R to M/S conversion simply adds the L and R levels, a mono signal on both channels as well as most the typical pop music mixes will result in a level of the M channel that is up to 6 dB higher than the levels of L and R. With a mono signal, it is exactly 6 dB; with a mix, it depends on the phase and level correlation of L and R which determines the width of the stereo image. The instruments that produce a high percentage of the level (kick drum, bass guitar, vocals) are usually placed in or close to the center of the mix. This results in an M channel level that is only a little below the 6 dB boost. To maintain a decent headroom, the L/R to M/S conversion should reduce the level by 6 dB. If this is the case, the re-conversion without level correction, just by correctly signed adding of M and S, result in the original L and R levels.
While appropriately designed active matrix circuits do not alter the sound performance and do not cause a reduction of the headroom, an increase of the noise, and or problems with the frequency and phase response, the crosstalk between left and right is affected. To maintain a sufficient crosstalk a matrix circuits has to be a very precise adder. Using common resistors with 1 % tolerance results in a crosstalk in the range of a little more than 32 dB. To get to values in the range of 50 dB or more, manual trimming is necessary. Since the crosstalk is not only affected by precise level matching but also by very small phase shifts, a 'simple' matrix that maintains crosstalk is not simple at all.