Datasheet

3−19
There are several techniques of volume management for a linear volume control process.
• Precise calculations involving logarithms can be employed.
• A high-resolution gain table, with entries for every 0.5-dB step, can be employed.
• A more coarse gain table (entries in 3 to 6-dB steps with linear interpolation between entries) can be
employed.
• Or approximations involving very simple calculations can be employed.
As an example of using approximations, equations for increasing a linear 5.23 gain setting X by 0.5 dB that involve
only simple binary shift and add operations and the accuracy of these equations are given below.
20log
10
X + 0.5 dB ≈ X + 2
−4
X gives 0.52657877-dB steps
20log
10
X + 0.5 dB ≈ X + 2
−4
X − 2
−8
X gives 0.49458651-dB steps
20log
10
X + 0.5 dB ≈ X + 2
−4
X − 2
−8
X + 2
−11
X gives 0.49859199-dB steps
20log
10
X + 0.5 dB ≈ X[1 + 2
−4
− 2
−8
+ 2
−11
+ 2
−12
− 2
−13
+ 2
−14
− 2
−16
+ 2
−18
] gives
0.4999997332 dB−steps
Approximations can also be found for decreasing a linear 5.23 gain setting X by 0.5 dB that involve using only simple
binary shift and add operations, but the equations differ slightly from those used to increase the gain in 0.5-dB steps.
The approximations to decrease the volume by 0.5 dB and the accuracy of these approximations are given below.
20log
10
X − 0.5 dB ≈ X − 2
−4
X gives −0.56057447 dB-steps
20log
10
X − 0.5 dB ≈ X − 2
−4
X + 2
−7
X gives −0.48849199-dB steps
20log
10
X − 0.5 dB ≈ X − 2
−4
X + 2
−7
X − 2
−10
X gives −0.49746965-dB steps
20log
10
X − 0.5 dB ≈ X[1 − 2
−4
+ 2
−7
− 2
−10
− 2
−12
− 2
−15
− 2
−21
] gives −0.5000006792 dB-steps
Repeated use of a set of the above approximations results in an accumulation of the errors in the approximations.
For example, if an application started at 0-dB volume, and repeatedly used the approximations to increase and
decrease the volume, the exact reference point of 0 dB would be lost. If an application does require the maintenance
of accurate reference points, it is necessary for the application to establish a set of exact gain reference settings and
command these exact settings in place of a computed gain setting whenever the current gain setting and the next
computed gain setting straddle an exact gain setting.
Table 3−4 lists the I
2
C coefficient settings to adjust volume from 24 dB to −136 dB in 0.5-dB steps. For each volume
setting, the gain in dB is presented in one column, the same gain in a floating point number
ǒ
float + 10
Gain
dB
20
Ǔ
is
presented in the adjacent column, and the same gain formatted in the 32-bit hexadecimal gain coefficient format
required to enter the value into the TAS3103 via the I
2
C bus is presented in a third column.