When Ain and Bin are played through a conventional stereo system, the sound power in
the room will be proportional to Lin^2 + Rin^2 + Cin^2. If all three components have
roughly equal amplitudes, the power ratio of the center component to the left plus right
component will be 1:2.
We would like our decoder to reproduce sound power in the room with approximately the
same power ratio as stereo, regardless of the power ratio of Cin to Lin and Rin. We can
express this mathematically. Essentially the equal power ratio requirement will specify
the functional form of the center matrix elements along the cs axis, if all the other matrix
elements are taken as given. If we assume the Dolby matrix elements, calibrated such that
the rear sound power is 3dB less than the other three outputs when the matrix is fully
steered – i.e. 3dB less than the standard calibration, then the center matrix elements
should have the shape shown in Figure 12. We can do the same thing for the standard
calibration, and the results in Figure 13 emerge.
Figure 12 - solid curve, the center matrix
value as a function of CS in dB, assuming
sound power ratios identical to stereo, and
using Dolby matrix elements with 3dB less
power in the rear than typically used.
The dotted curve is the actual value of the
center matrix elements in Pro-Logic. Notice
that while the actual values give reasonable
results for an unsteered signal and a fully
steered signal, they are about 1.5dB too
low in the middle.
Figure 13: Solid curve – the value of the
center matrix elements needed to produce
equal center power as a stereo playback,
given the matrix elements and calibration
used in Dolby Pro-Logic. Dotted curve – the
actual values of the center matrix elements
in Pro-Logic. Notice that the actual values
are more than 3dB too low for all values of
cs.
