User Guide

Sound System Design Reference Manual
3. What power level is represented by 4
milliwatts? As we have seen, the power level of 1
milliwatt is –30 dB. Two milliwatts represents a level
increase of 3 dB, and from 2 to 4 milliwatts there is
an additional 3 dB level increase. Thus:
–30 + 3 + 3 = –24 dB
4. What is the level difference between 40 and
100 watts? Note from the table that the level
corresponding to 4 watts is 6 dB, and the level
corresponding to 10 watts is 10 dB, a difference of 4
dB. Since the level of 40 watts is 10 dB greater than
for 4 watts, and the level of 80 watts is 10 dB greater
than for 8 watts, we have:
6 – 10 + 10 – 10 = –4 dB
We have done this last example the long way,
just to show the rigorous approach. However, we
could simply have stopped with our first observation,
noting that the dB level difference between 4 and 10
watts, .4 and 1 watt, or 400 and 1000 watts will
always be the same, 4 dB, because they all
represent the same power ratio.
The level difference in dB can be converted
back to a power ratio by means of the following
equation:
Power ratio = 10
dB/10
For example, find the power ratio of a level
difference of 13 dB:
Power ratio = 10
13/10
= 10
1.3
= 20
The reader should acquire a reasonable skill in
dealing with power ratios expressed as level
differences in dB. A good “feel” for decibels is a
qualification for any audio engineer or sound
contractor. An extended nomograph for converting
power ratios to level differences in dB is given in
Figure 2-1.
Voltage, Current, and Pressure
Relationships
The decibel fundamentally relates to power
ratios, and we can use voltage, current, and pressure
ratios as they relate to power. Electrical power can
be represented as:
P = EI
P = I
2
Z
P = E
2
/Z
Because power is proportional to the square of
the voltage, the effect of doubling the voltage is to
quadruple the power:
(2E)
2
/Z = 4(E)
2
/Z
As an example, let E = 1 volt and Z = 1 ohm.
Then, P = E
2
/Z = 1 watt. Now, let E = 2 volts; then,
P = (2)
2
/1 = 4 watts.
The same holds true for current, and the
following equations must be used to express power
levels in dB using voltage and current ratios:
dB level = 10 log
E
E
20 log
E
E
, and
1
0
1
0






=






2
dB level = 10 log
I
I
20 log
I
I
.
1
0
1
0






=






2
Sound pressure is analogous to voltage, and
levels are given by the equation:
dB level = 20 log
P
P
.
1
0






Figure 2-1. Nomograph for determining power ratios directly in dB
2-2