Measurement 35The following defi nition is from the IEEE Standard Dictionary of Electrical and
Electronics Terms, Second Edition :
2.1.2.1 244.62
Voltage Amplifi cation (1) (general). An increase in signal voltage magnitude in
transmission from one point to another or the process thereof. See also: amplifi er. 210 (2)
(transducer). The scalar ratio of the signal output voltage to the signal input voltage.
Warning: By incorrect extension of the term decibel, this ratio is sometimes expressed
in decibels by multiplying its common logarithm by 20. It may be currently expressed
in decilogs. Note: If the input and/or output power consist of more than one component,
such as multifrequency signal or noise, then the particular components used and their
weighting must be specifi ed. See also: Transducer.
2.1.2.2 239.210
Decilog (dg). A division of the logarithmic scale used for measuring the logarithm of the
ratio of two values of any quantity. Note: Its value is such that the number of decilogs
is equal to 10 times the logarithm to the base 10 of the ratio. One decilog therefore
corresponds to a ratio of 10 0.1 (that is 1.25829 ).
2.1.3 The Decibel as a Power Ratio
Note that 20 W/10 W and 200 W/100 W both equal 3.01 dB, which means that a 2 to 1
(2:1) power ratio exists but reveals nothing about the actual powers. The human ear hears
the same small difference between 1 and 2 W as it does between 100 and 200 W.
Changing decibels back to a power ratio (exponential form) is the same as for any
logarithm with the addition of a multiplier ( Figure 2.2 ). The arrows in Figure 2.2 indicate
the transposition of quantities. Table 2.1 shows the number of decibels corresponding to
various power ratios.
2.1.4 Finding Other Multipliers
Occasionally in acoustics, we may need multipliers other than 10 or 20. Once the Δ dB
(the number of dB for a 2:1 ratio change) is known, calculate the multiplier by
log multiplier
Base
Ratiolog
log() dB
()