Power from the center
PC = GC^2*(Lin^2+Rin^2) + 2*GC^2*Cin^2
Power from the rears depends on the matrix elements we use. We will assume the rear
channels are attenuated by three dB during forward steering, and that LRL is cos(cs) and
LRR is sin(cs). From a single speaker
PREAR = (.71*(cos(cs)*(Lin+.71*Cin) – sin(cs)*(Rin + .71*Cin)))^2
If we assume Lin^2 ~= Rin^2,
For two speakers,
PREAR = .5*Cin^2((cos(cs)-sin(cs))^2) + Lin^2
The total power from all three speakers is PLR + PC + PREAR
PT = (GP^2 + GF^2 + GC^2)*(Lin^2 + Rin^2) + ((GP – GF)^2 + 2*GC^2)*Cin^2 +
PREAR
The ratio of Cin power to Lin and Rin power is: (assume Lin^2 = Rin^2)
RATIO = (((gp(cs)-gf(cs))^2 + 2*(gc(cs)^2) +.5*(cos(cs)-sin(cs))^2))*Cin^2 /
2*(gp(cs)^2 + gc(cs)^2 + gf(cs)^2) + 1) * Lin^2
RATIO = (Cin^2/Lin^2) *((gp(cs)-gf(cs))^2 + 2*(gc(cs)^2) +.5*(cos(cs)-sin(cs))^2) /
2*(gp(cs)^2 + gc(cs)^2 + gf(cs)^2) + 1)
For normal stereo, GC=0, GP=1, and GF=0. The center to LR power ratio is then
RATIO = (Cin^2/Lin^2)*0.5
If this ratio is to be constant regardless of the value of Cin^2/Lin^2 for our active matrix,
((gp(cs)-gf(cs))^2 + 2*(gc(cs)^2) +.5*(cos(cs)-sin(cs))^2) = (gp(cs)^2 + gc(cs)^2 +
gf(cs)^2) + .5)
The equation above can be solved numerically. If we assume the GC above.
