Measurement 37If a 2:1 change is equivalent to 6.02 dB, then
log multiplier
Base
log.
log()602
2
20
o r
20 log 2 6.02.
Finally, if a 2:1 change is equivalent to 8 dB, then
log multiplier
Base
log
log.
()8
2
26 58
o r
26.58 2 log 8.
For any Δ dB corresponding to a 2:1 ratio change involving logarithms to the base 10, this
may be reduced to
log multiplier 3 332. ΔΒ.d (2.7)2.1.5 The Decibel as a Power Quantity
We have seen that a number of decibels by themselves are only ratios. Given any
reference (such as 50 W), we can use decibels to fi nd absolute values. A standard
reference for power in audio work is 10 ^3 W (0.001 W) or x V across Z Ω. Note that when
a level is expressed as a wattage, it is not necessary to state an impedance, but when it is
stated as a voltage, an impedance is mandatory. This power is called 0 dBm. The small
“ m ” stands for milliwatt (0.001 W) or one-thousandth of a watt.
2.1.6 Example
The power in watts corresponding to 30 dBm is calculated as follows:
10
0 001
30
0 001 10 1
log
.
.xx(^3010)
W.