Audio Engineering

Measurement 55

An alternative dB addition technique is given through the courtesy of Gary Berner.

LT smallest number

diff in dB





10 log 10 10 1

()

() (2.30)

Example
If we wish to add 90 dB to 96 dB, using Eq. (2-33), take the difference in dB (6 dB) and
put it in the equation:

LT 



10 10 1 90

96 97

106

log

.

()

dB.

Input signals to a mixing network also combine in this same manner, but the insertion
loss of the network must be subtracted. Two exactly phase-coherent sine wave signals of
equal amplitude will combine to give a level 6 dB higher than either sine wave.

The general case equation for adding sound pressure, voltages, or currents is

Combined LP

E E E

 20 10 10 2 10

201 2 202 201

log ()

⎛

⎝

⎜⎜

⎜⎜

⎞

⎠

⎟⎟

⎟⎟

⎟

⎛

⎝

⎜⎜

⎜⎜⎜⎜

⎞

⎠

⎟⎟

⎟⎟

⎟

⎛

⎝

⎜⎜

⎜⎜⎜

⎞

⎠

⎟⎟

⎟⎟

⎟

(^10) ()
2
(^2012)
E
cos[aa ]. (2.31)
Table 2.9 shows the effects of adding two equal amplitude signals with different phases
together using Eq. (2-36).
2.13.2 Subtracting Decibels
The difference of two levels expressed in dB may be found as follows:
Ldiff
Total Level Level with one source off


10 log 10 10 10

⎛^

⎝

⎜⎜

⎜⎜⎜

⎞

⎠

⎟⎟

⎟⎟

⎟

. (2.32)

2.13.3 Combining Levels of Uncorrelated Noise Signals

When the sound level of a source is measured in the presence of noise, it is necessary
to subtract out the effect of the noise on the reading. First, take a reading of the source