APPENDIX
DEFINITION OF TERMS: dB, dBV, dBm and dB SPL
The term dB, which means decibel ( 1 / 1 0 t h of a Bel)
expresses a ratio. The dB notation allows us to represent
very large ratios with small numbers which are easier
to understand and use. The ratio in dB of two power
levels is equal to 1 0 times the (base 10) logarithm of
their simple numeric ratio:
d B = 1 0 log P
1
/ P
2
The ratio in dB of two voltages (V
1
and V
2
) or
sound pressure levels (P
1
and P
2
) is equal to 20 times
the logarithm (base 1 0 ) of their simple numeric ratio:
d B = 2 0 l o g V
1
/ V
2
Examples:
Power: The ratio in dB of 100 watts and 50 watts.
dB = 10 log 100/50 Answer: +3dB
Note that this means that 100 watts is 3dB above 50
watts. If we had compared 50 watts to 100 watts (dB =
1 0 log 50/100), the answer would have been -3dB.
Similarly, any time the ratio of two powers is 2 : 1 , their
ratio in dB is +3dB. When the ratio is 1:2, the ratio in
dB is
-3dB.
Voltage: The ratio in dB of 100 volts to 50 volts.
dB = 20 log 100/50 Answer: +6dB
Note that a ratio of 2:1 in voltage means a ratio in
dB of +6dB. If the ratio is 1:2, the ratio in dB is -6dB.
SPL: SPL ratios, expressed in dB, are similar to voltage
ratios. For example, two SPL levels with a numeric ratio
of 2:1 would have a ratio in dB of +6dB. SPL ratios are
seldom given as numeric ratios. Simple numeric SPL
levels would have the units of dynes per square centi-
meter (pressure per unit area).
The term "dB" implies a ratio. To express a single,
specific quantity in dB, there must be a reference
quantity. There are standard reference quantities for
SPL, voltage, and power, which extend the usefulness
of the dB notation system.
dBV expresses a voltage. It is not directly related to
current or circuit impedance. 0dBV is usually referenced
to 1 volt rms.
Example: The level in dBV of 10 volts rms:
dBV =20 log 10/1 =20 x 1 20dBV
dBm expresses a power. It is related to the voltage
or current across a low impedance. The 0dBm reference
is 1 milliwatt, which is equal to 0.775V rms in a 600-ohm
circuit.
Example: The level in dBm of 1 watt:
dBm = 1 0 log 1/0.001 = 1 0 x 3 Answer: +30dBm
dB SPL expresses an acoustic pressure (not power).
The 0dB SPL reference is 0.0002 dynes/square cm,
which is the approximate threshold of human hearing
at 1kHz.
NOTE: Since SPL values in dynes/square cm are un-
common, an example is not given.
dB expresses the difference between two levels (power,
voltage, sound pressure, etc.) and is a relative term.
The difference b10dBm and +4dBm is 6dB.
The difference between -20dBV and -10dBV is 10dB.
dBV and dBm are not numerically equal when dealing
with 600-ohm circuits, although they are close (OdBV is
+2.2dBm at 600 ohms). As the impedance is changed to
other than 600-ohms (given a constant voltage), the
value of dBV remains constant while the value of dBm
changes. For example, consider a +4dBm output ter-
minated by 600 ohms. The voltage level is +1.8dBV.
This circuit has a voltage drop of 1.23V rms, and a power
dissipation of 2.5 milliwatts. Assume that the voltage
now remains constant, but the termination is changed
to 1200 ohms. The voltage level r1.8dBV, but
the power dissipation drops to 1.23mW, +1dBm, Con-
tinuing this illustration, we raise the termination
to 47,000 ohms. The voltage level r1.8 dBV
(1.23V rms), but the power level drops to a mere 32
microwatts, -15dBm.
The above illustration points out that the power
dissipation in high impedance circuitry is negligible.
Therefore, dBV is most often reserved to express signal
levels in high impedance lines. The term dBm is com-
monly used to express signal (power) levels in low
impedance lines, roughly between 4 ohms and 1200
ohms. However, dBm is also widely used to express
levels in high impedance lines, rather than dBV. This is
because at 600 ohms the voltage for a given dBV value
is not the same as the voltage for the same number of
dBm, so the use of the term dBV could be misleading.
Summary:
An increase of 3dB is equivalent to double the power.
An increase of 10dB is equivalent to ten times the
power.
A decrease of 3dB is equivalent to half the power.
A decrease of 10dB is equivalent to 1 / 1 0 the power.
An increase of 6dB is equivalent to double the
voltage or SPL.
An increase of 20dB is equivalent to ten times the
voltage or SPL.
A decrease of 6dB is equivalent to half the voltage
or SPL
A decrease of 20dB is equivalent to 1 / 1 0 the voltage
or SPL.
SPECIAL USE OF dB (volts) IN THIS MANUAL
Assume that a Yamaha PM-Mixer has a constant
input voltage, such as the sinewave signal from a test
generator. The mixer output then acts very much like
a perfect sinewave voltage source because the mixer's
output impedance is much lower than the load
impedance. That is, even when the load impedance
varies from the lowest rated load to an extremely high
impedance, the output voltage from the mixer will
remain relatively constant. However, the mixer's output
power does vary with the load impedance. dBm is a
power rating, and if the PM-Mixer's maximum output
were rated in dBm, that rating would change with the
load impedance. Thus, a dBm-rated output level would
