The decibel (dB) represents a ratio, expressed logrithmicaly, between two quantities, a reference quantity and the quantity to be compared. The generally used measure of the deciBel is one tenth of the Bel (thus the odd capitalization). It is used to describe the level of something with respect to something else, such as the amount of noise created by idling locomotives or departing aircraft over the ambient (background) noise. For the radio amateurs and other electronic types out there, deciBels is usually used in broadcast and other radio frequency applications to compare power levels (sound, signal strength, noise, etc.).
The Bel or deciBel is unitless: it exists as a ratio with respect to however the event being measured is itself measured, thus any dB measure is "with respect to . . . " For example, a measure of dB of milliwatts gain is "with respect to one milliwatt."
The "with respect to" part is often implicit, but is often included in the abbreviation: when the ratio is specifically referred to in terms of a specific unit of measurement that measure is generally indicated by a suffix (e.g., dBm is referenced against one milliWatt; dBV is referenced against one volt) thus dBm would be construed as dB gain — in milliwatts — with respect to one milliwatt: a gain of three dBm would indicate two milliwatts (with respect to a base power of one milliwatt) and in practice this would imply ten watts output with respect to five watts input [see the math following].
Apparently, the measure of the Bel was at first exclusively a ratio for power, with the basic formula being B = log_{10} (P_{1}/P_{2}).
Where
The deciBel simply increases the units by ten to make measurements of small changes more readable; thus, dB = 10 log_{10} (P_{1}/P_{2}).
Where
As power is proportional to voltage or current squared, the ratio of voltages or currents across a constant impedence is given by dB = 20 log_{10}(V_{1}/V_{2}) or dB = 20 log_{10}(I_{1}/I_{2})
Where
A gain of 100 volts per volt (e.g., in an amplifier, with 1 volt in and 100 volts out), 100/1, equals
A gain of 1000 volts per volt, 1000/1, equals
When working with power, 3 dB is twice, 10 dB is 10 times; When working with voltage or current, 6 dB is twice, 20 dB is 10 times:
0 dB = | no change | ||
1 dB = | a power gain of | 1.256 (~26%) | |
3 dB = | a power gain of | ~2.0 (-3 dB = power loss of ~50%) | |
6 dB = | a power gain of | ~4 | |
10 dB = | a power gain of | 10 | |
20 dB = | a power gain of | 100 |
This information is courtesy of NC2S .
A gain of 100 volts per volt (40 dB) through a constant load produces a power gain of 10,000 watts per watt (also 40 dB). Under constant load conditions, e.g., a 50 ohm impedance dipole antenna, a gain of n dB, corresponding to a voltage or current gain of y (e.g., 3 dB gain is voltage or current gain of V*2 or I*2, and is equivalent to a power gain of y², P*4. At any given dB, the voltage or current gain will have the foregoing correspondence to the power gain under constant resistance or impedance values; thus, the voltage or current gains—through a constant load—correspond to the power gains as indicated.
dB | Ratio | |
---|---|---|
Power | Voltage/Current | |
(10 log) | (20 log) | |
0 | 1.0 | 1.0 |
1 | 1.256 | 1.122 |
2 | 1.585 | 1.259 |
3 | 1.997 | 1.413 |
3.01 | 2.0 | 1.414 |
4.0 | 2.240 | 1.585 |
4.77 | 3.0 | 1.732 |
5 | 3.161 | 1.778 |
6 | 3.980 | 1.995 |
6.02 | 4.0 | 2.0 |
6.99 | 5.0 | 2.236 |
10 | 10.0 | 3.162 |
12 | 15.820 | 3.990 |
13.979 | 25.0 | 5.0 |
14 | 25.118 | 5.012 |
20 | 10^{2} | 10 |
30 | 10^{3} | 31.623 |
40 | 10^{4} | 10^{2} |
60 | 10^{6} | 10^{3} |
80 | 10^{8} | 10^{4} |
100 | 10^{10} | 10^{5} |
120 | 10^{12} | 10^{6} |
140 | 10^{14} | 10^{7} |
Note: These figures for gain are also used to express loss (e.g., -3db is a power loss of nearly 1/2, reference power divided by 1.997; -6dB is a power loss of nearly three quarters, reference power divided by 3.980).
dB | Ratio | |
---|---|---|
Power | Voltage/Current | |
(10 log) | (20 log) | |
0 | 1.0 | 1.0 |
-3 | 0.50 | 0.71 |
-6 | 0.25 | 0.50 |
-10 | 0.10 | 0.32 |
-12 | 0.05 | 0.25 |
-14 | 0.04 | 0.20 |
-20 | 10^{-2} | 0.10 |
-30 | 10^{-3} | 0.03 |
-40 | 10^{-4} | 10^{-2} |
-60 | 10^{-6} | 10^{-3} |
-80 | 10^{-8} | 10^{-4} |
-100 | 10^{-10} | 10^{-5} |
-120 | 10^{-12} | 10^{-6} |
-140 | 10^{-14} | 10^{-7} |
(Power in MilliWatts)
(dBm)
Power (dBm) | MilliWatts unless noted |
---|---|
0 | 1.0 |
3 | 1.9953 |
5 | 3.1623 |
7 | 5.0119 |
10 | 10.0 |
13 | 19.953 |
15 | 31.623 |
17 | 50.119 |
20 | 100.0 |
23 | 199.53 |
25 | 316.23 |
27 | 501.19 |
30 | 1.00 watt |
33 | 1.99 watts |
35 | 3.16 watts |
37 | 5.01 watts |
40 | 10.00 watts |
Power (dBm) | MilliWatts |
---|---|
0 | 1.0 |
-3 | 0.5012 |
-5 | 0.3162 |
-7 | 0.1995 |
-10 | 0.10 |
-13 | 0.0501 |
-15 | 0.03162 |
-17 | 0.01995 |
-20 | 0.01 |
-23 | 0.00601 |
-25 | 0.00316 |
-27 | 0.002 |
-30 | 0.001 |
-33 | 0.00050 |
-35 | 0.00032 |
-37 | 0.00019 |
-40 | 0.00010 |
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