Decibel (dB)

One decibel (dB) is one tenth of one bel, named in honour of Alexander Graham Bell in 1922. Why has this unit been introduced? The simple answer is to simplify and facilitate calculations. Electronics, telecommunications, and acoustics often use very large, very small or large differences between numerical values with a large number of zeroes. Handling those numbers can be difficult, and that is where the decibel comes in handy. A noteworthy fact is that the decibel is an independent unit, like volt (voltage) or ampere (current). It is a method of showing the ratio of two values.

We must realize, that there are relative and absolute decibel levels.

1. Relative level – a ratio of two voltage, current, power, sound intensity values etc. where no reference level (point) is specified.

For voltage and current ratio:

For power ratio:

Example
Voltage amplitude upstream of the amplifier is 20 mV (U1) and downstream of the amplifier is 3 V (U2), the gain in dB is:

Remember!
If U2 is higher than U1 (similarly P2 > P1), the signal is amplified.
Whereas, if U2 is lower than U1 (similarly P2 < P1), the signal is attenuated.

Table 1. Quick conversion of typical amplification and attenuation value

dB	voltage and current amplification	power amplification
0	1	1
3	1,41	2
6	2	4
12	4	16
20	10	100
40	100	10000
60	1000	1000000
dB	voltage and current attenuation	power attenuation
0	1	1
-3	0,7	0,5
-6	0,5	0,25
-12	0,25	0,063
-20	0,1	0,01
-40	0,01	0,0001
-60	0,001	0,000001

2. Absolute level – a ratio of two voltage, current, power, sound intensity values etc. in relation to a relevant reference level (reference value). A 0 dB level corresponds to the reference value (point).

For voltage and current ratio:

For power ratio:

(ref) – reference value

If the reference value is constant, it is an absolute reference level and in this case, dB is denoted with an additional information e.g. dBm, dBuV.

To simplify, dBm is a power unit relative to 1 mW (one milliwatt). Unit expressed in dB indicates how much the power is higher or lower than 1 mW. 0 dB corresponds to 1 mW.

Example values

0,001 mW = –30 dBm
0,1 mW = –10 dBm
0,5 mW = –3 dBm
10 mW = 10 dBm
100 mW = 20 dBm

dBW − absolute power level unit relative to 1 W
dBV − absolute voltage level unit relative to 1 V
dBμV − absolute voltage level relative to 1 μV
dBi − antenna power gain unit relative to isotropic antenna
dBd − antenna power gain unit relative to half-wave dipole