User Guide
Sound System Design Reference Manual
Chapter 2: The Decibel
Introduction
In all phases of audio technology the decibel is
used to express signal levels and level differences in
sound pressure, power, voltage, and current. The
reason the decibel is such a useful measure is that it
enables us to use a comparatively small range of
numbers to express large and often unwieldy
quantities. The decibel also makes sense from a
psychoacoustical point of view in that it relates
directly to the effect of most sensory stimuli.
Power Relationships
Fundamentally, the
bel
is defined as the
common logarithm of a power ratio:
bel = log (P
1
/P
0
)
For convenience, we use the
decibel
, which is simply
one-tenth bel. Thus:
decibel = 10 log (P
1
/P
0
)
The following tabulation illustrates the
usefulness of the concept. Letting P
0
= 1 watt:
P
1
(watts) Level in dB
10
10 10
100 20
1000 30
10,000 40
20,000 43
Note that a 20,000-to-1 range in power can be
expressed in a much more manageable way by
referring to the powers as levels in dB above one
watt. Psychoacoustically, a ten-times increase in
power results in a level which most people judge to
be “twice as loud.” Thus, a 100-watt acoustical signal
would be twice as loud as a 10-watt signal, and a
10-watt signal would be twice as loud as a 1-watt
signal. The convenience of using decibels is
apparent; each of these power ratios can be
expressed by the same level, 10 dB. Any 10 dB level
difference, regardless of the actual powers involved,
will represent a 2-to-1 difference in subjective
loudness.
We will now expand our power decibel table:
P
1
(watts) Level in dB
10
1.25 1
1.60 2
23
2.5 4
3.15 5
46
57
6.3 8
89
10 10
This table is worth memorizing. Knowing it, you
can almost immediately do mental calculations,
arriving at power levels in dB above, or below, one
watt.
Here are some examples:
1. What power level is represented by 80
watts? First, locate 8 watts in the left column and
note that the corresponding level is 9 dB. Then,
note that 80 is
10 times
8, giving another 10 dB.
Thus:
9 + 10 =
19 dB
2. What power level is represented by 1
milliwatt? 0.1 watt represents a level of minus 10 dB,
and 0.01 represents a level 10 dB lower. Finally,
0.001 represents an additional level decrease of 10
dB. Thus:
–10 – 10 – 10 =
–30 dB
2-1