User Guide

Sound System Design Reference Manual
The normal reference level for voltage, E
0
, is
one volt. For sound pressure, the reference is the
extremely low value of 20 x 10
-6
newtons/m
2
. This
reference pressure corresponds roughly to the
minimum audible sound pressure for persons with
normal hearing. More commonly, we state pressure
in pascals (Pa), where 1 Pa = 1 newton/m
2
. As a
convenient point of reference, note that an rms
pressure of 1 pascal corresponds to a sound
pressure level of 94 dB.
We now present a table useful for determining
levels in dB for ratios given in voltage, current, or
sound pressure:
Voltage, Current or
Pressure Ratios Level in dB
10
1.25 2
1.60 4
26
2.5 8
3.15 10
412
514
6.3 16
818
10 20
This table may be used exactly the same way
as the previous one. Remember, however, that the
reference impedance, whether electrical or
acoustical, must remain fixed when using these
ratios to determine level differences in dB. A few
examples are given:
1. Find the level difference in dB between 2
volts and 10 volts. Directly from the table we observe
20 – 6 = 14 dB .
2. Find the level difference between 1 volt and
100 volts. A 10-to-1 ratio corresponds to a level
difference of 20 dB. Since 1-to-100 represents the
product of two such ratios (1-to-10 and 10-to-100),
the answer is
20 + 20 = 40 dB.
3. The signal input to an amplifier is 1 volt, and
the input impedance is 600 ohms. The output is also
1 volt, and the load impedance is 15 ohms. What is
the gain of the amplifier in dB? Watch this one
carefully!
If we simply compare input and output voltages,
we still get 0 dB as our answer. The voltage gain is in
fact unity, or one. Recalling that decibels refer
primarily to power ratios, we must take the differing
input and output impedances into account and
actually compute the input and output powers.
Input power =
E
Z
=
1
600
watt
2
Output power =
E
Z
=
1
15
2
T 10 log
600
15
= 10 log 40 = 16 dBhus,






Fortunately, such calculations as the above are
not often made. In audio transmission, we keep track
of operating levels primarily through voltage level
calculations in which the voltage reference value of
0.775 volts has an assigned level of 0 dBu. The
value of 0.775 volts is that which is applied to a 600-
ohm load to produce a power of 1 milliwatt (mW). A
power level of 0 dBm corresponds to 1 mW. Stated
somewhat differently, level values in dBu and dBm
will have the same numerical value only when the
load impedance under consideration is 600 ohms.
The level difference in dB can be converted
back to a voltage, current, or pressure ratio by
means of the following equation:
Ratio = 10
dB/20
For example, find the voltage ratio
corresponding to a level difference of 66 dB:
voltage ratio = 10
66/20
= 10
3.3
= 2000.
2-3