34 Chapter 2
10 10
40
10
602
1
2
log log
.
P
P
W
W
dB (2.3)
10 20
20
10
602
12
2
log 2 log
.
E
E
V
V
dB (2.4)
2.1.2 The dBV
One of the most common errors when using the decibel is to regard it as a voltage ratio
(i.e., so many decibels above or below a reference voltage). To compound the error, the
result is referred to as a “ level. ” The word “ level ” is reserved for power; an increase in the
voltage magnitude is properly referred to as “ amplifi cation. ”
However, the decibel can be legitimately used with a voltage reference. The reference is
1.0 V. When voltage magnitudes are referenced logarithmically, they are called dBV
(i.e., dB above or below 1.0 V). This use is legitimate because all such measurements
are made open circuit and can easily be converted into power levels at any impedance
interface.
R 1 10 Ω
R 2 10 Ω
Rs
Rs
10 V
20 V
P 1 E^1
2
R 1
^10010
10 W
P 2
E 22
R 2
^40010
40 W
(a) Initial voltage
(b) Voltage doubled
Figure 2.1 : Voltage and power relationships in a circuit.