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The bel, decibel , the dbm and the dbmv
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The Decibel or Just db.
The dB is a mathematical abbreviation for Decibel, this term is a kind of shorthand to manipulate relations of large numbers specially in electronics, communication and audio systems and circuits.
For the understanding of dB, the dBm and the dBmv it is necessary to have a basic understanding of logarithms, please refer to the logarithms section for learning.
The bel
Originally the term Decibel was used by Alexander Bell and associates as a measure of the change of signal attenuation levels in their “standard telephone cable” that was about 10 miles long, when the signal was attenuated 10 times they called a Bell, this level of attenuation was used as a standard measure for the attenuation during the installation of the telephones cables.
As a result the loss of power in bels is given by:
Loss in bels for power is = log10 (input power) / (output power)
In other words, when the input is 10 times the output power result in a loss, this loss expressed in bels = log10 = 1, or in a simpler manner a loss of 1 bel corresponds to a reduction of 10:1 in power.
The decibel
In many occasions the bel unit resulted too big to be practical, so a more useful unit was derived from the bel, called the decibel or one tenth of a bel.
Loss in decibels for power is= 10 log10 (input power) / (output power)
The decibel can be used to calculate the loss for voltage and current ,
For voltage the loss in bels is= 20 log10 (input voltage / output voltage)
The decibel is similarly used to calculate power and voltage gain with only exchanging the numerator and denominator in the relation as follows:
Power gain in decibels is= 10 log10 (output power) / (input power)
Voltage gain in decibels is= 20 log10 (output voltage / (input voltage)
If we plug in some numbers in the power equation it can be seen that the power doubles each 3.0103 decibels of gain, while for voltage is doubled each 6.02059 decibels, this relation is accurate only in circuits with the same impedance levels at the input and the output.
The dbmv and the dbm
The radio frequency, microwaves and telecommunications industry has standardized two terms to easily manipulate voltage and power gains referred to a fix levels, these are:
The dbmv
The decibel millivolt which is a voltage level referred to one millivolt and it is abbreviated as dbmv, normally standardized to a 75 ohms impedance level for input and output and mostly used in the TV and CATV industry.
The voltage given in dbmv is = 20 log10 ( v /0.001v)
Example:
How much a 0.002, 0.010, 0.10 and one volt correspond in dbmv?
Answer:
0.002 volts = 20 log10 (0.002/0.001v) = 20 log10 (2) = 6.02 dbmv
0.10 volts = 20 log10 (0.010/0.001v) = 20 log10 (10) = 20 dbmv
1volts = 20 log10 (1/0.001v) = 20 log10 (1000) = 60 dbmv
From this example it can be concluded that each time the voltage is doubled, the voltage gain in dbmv is 6, if the voltage gain is 10 times the voltage gain in dbmv is 20, and if the voltage gain is 1000 times the voltage gain in dbmv is 60.
Based on the above a table of correspondence for different values can be constructed as below:
The dbm
The decibel milliwatt which is a power level referred to one milliwatt and it is abbreviated as dbm, normally standardized to a 50 ohms impedance level for input and output and mostly used in the radio frequency and microwaves communications industry in general.
The power in dbm is = 10 log10 ( P /0.001w)
Example:
How much a 0.002, 0.010, 0.10 and one wat correspond in dbm?
Answer:
0.002 watts = 10 log10 (0.002 /0.001w) = 10 log10 (2) = 3.01 dbm
0.10 watts = 10 log10 (0.010 /0.001w) = 10 log10 (10) = 10 dbm
1watt = 10 log10 (1 /0.001w) = 10 log10 (1000) = 30 dbm
Based on the above a table of correspondence for different values of watts and dbm can be constructed as below:
The bel, decibel or db, The dbm and The dbmv
volts 
dbmv 
Times vs 1 millivolt 
0.001 
0 
1 
0.002 
6.02 
2 
0.004 
12.04 
4 
0.010 
20 
10 
0.100 

100 
0.200 

200 
1.00 
60 
1000 
10.00 
80 
10000 
watts 
dbm 
Times vs 1 milliwatt 
0.001 
0 
1 
0.002 
3.01 
2 
0.004 
6.02 
4 
0.010 
10 
10 
0.100 
20 
100 
0.200 
23.01 
200 
1.00 
30 
1000 
10.00 
40 
10000 
100.00 
50 
100000 
For voltage levels less than 0.001 volts a negative dbmv number will result, for example for a 0.0001 volts (100 microvolts) the voltage level in dbmv is 20dbmv as can be calculated.
Note:
For power levels less than 0.001 watts a negative dbm number will result, for example for a 0.0001 watts (100 microwatts) the power level in dbm is
10 dbmv as can be calculated.
Note: