Maybe asked before:
what about the effective ratio of feedback compression?
Is is defined as shown below?
Let's start with feed forward steady state equation, hard knee:
if we have some derived detector signal x (of the input, for example an envelope follower output, transformed into log domain) in the dBFS-domain ABOVE the threshold (in dBFS), the negative gain G [in dB], responsible for gain reduction, is given to
G = (x - thr) * (1/R-1) = -a*(x - thr)
with a = (1-1/R)
This is what somebody would see applying a tone with given level for long enough attack/release.
Now if we think of a hard-knee feedback compressor with settled gain G and ratio R applied in the feedback path, we have
y = x + G
y here is the output signal where the (negative) gain G has been applied. Compared to the feed forward case, the feedback makes a "role change" of x with y, and we get
G = (y - thr) * (1/R-1) = (x + G - thr) * (1/R-1) = -a * (x + G - thr)
or
G = -a/(1+a) * (x-thr)
So when the compressor has settled, the effective equivalent feed forward ratio R2 can be derived as follows:
G = -a/(1+a) * (x-thr) = -b * (x-thr)
but b can also be written as b = 1-1/R2 with some effective ratio R2 which an equivalent feed forward compressor would have. Then we get:
-(1-1/R2) = -a/(1+a) or
1/R2 = 1 - a/(1+a) or
1/R2 = 1/(1+a) or
R2 = 2-1/R
This looks like the feedback transforms the compressor into one which has a maximum effective feed forward ratio of R2=2 when R goes to infinity.
In general, the dynamic behavior as a differential equation is changed for the feedback case, but the steady state equation for ratio seems to be like that shown above.
Now the question is: either there is a mistake here or when vendors write about ratios they don't mean the actual effective ratio R2. Is it true? Because it looks like a feedback compressor can never exceed a ratio of R2=2 and therefore squash the signal like a feed forward could do.
EDIT: just simulated with Matlab and got the proof.
what about the effective ratio of feedback compression?
Is is defined as shown below?
Let's start with feed forward steady state equation, hard knee:
if we have some derived detector signal x (of the input, for example an envelope follower output, transformed into log domain) in the dBFS-domain ABOVE the threshold (in dBFS), the negative gain G [in dB], responsible for gain reduction, is given to
G = (x - thr) * (1/R-1) = -a*(x - thr)
with a = (1-1/R)
This is what somebody would see applying a tone with given level for long enough attack/release.
Now if we think of a hard-knee feedback compressor with settled gain G and ratio R applied in the feedback path, we have
y = x + G
y here is the output signal where the (negative) gain G has been applied. Compared to the feed forward case, the feedback makes a "role change" of x with y, and we get
G = (y - thr) * (1/R-1) = (x + G - thr) * (1/R-1) = -a * (x + G - thr)
or
G = -a/(1+a) * (x-thr)
So when the compressor has settled, the effective equivalent feed forward ratio R2 can be derived as follows:
G = -a/(1+a) * (x-thr) = -b * (x-thr)
but b can also be written as b = 1-1/R2 with some effective ratio R2 which an equivalent feed forward compressor would have. Then we get:
-(1-1/R2) = -a/(1+a) or
1/R2 = 1 - a/(1+a) or
1/R2 = 1/(1+a) or
R2 = 2-1/R
This looks like the feedback transforms the compressor into one which has a maximum effective feed forward ratio of R2=2 when R goes to infinity.
In general, the dynamic behavior as a differential equation is changed for the feedback case, but the steady state equation for ratio seems to be like that shown above.
Now the question is: either there is a mistake here or when vendors write about ratios they don't mean the actual effective ratio R2. Is it true? Because it looks like a feedback compressor can never exceed a ratio of R2=2 and therefore squash the signal like a feed forward could do.
EDIT: just simulated with Matlab and got the proof.
Statistics: Posted by synthpark — Thu Apr 25, 2024 12:45 pm — Replies 0 — Views 48