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Table of Contents Appendix References Decibel - A Unit for Expressing Ratios | |
In electronics it is often necessary not only to measure voltage, current and power but also relationships between voltage, current and power. Examples of relationships of two voltages are the voltage gain of an operational amplifier, the noise figure, or the gain of an antenna.
Since the relationship between voltage and power or current and power at a resistance is quadratic, the definition for the unit decibel results an expression which is different for current and voltage, and for power:
Voltage: dB = 20lg(V_{1}/V_{0})
Current: dB = 20lg(I_{1}/I_{0})
Power: dB = 10lg(P_{1}/P_{0})
If a certain value is defined for V_{0}, I_{0} or P_{0}, then the quantity dB indicates the relationship between V_{1}, I_{1} or P_{1} and the defined value. The defined value is called the zero level; the indication in dB is generally denoted as the level. When indicating a level, the base factor must also always be indicated, which usually occurs in the form an additional specification attached to the designation dB (e.g. dBmV, dbW or dBm).
In audio technology, the zero-level is specified as that voltage, which allows 1 mW power loss to develop at a resistance of 600 ohms. This level is indicated by 'dBm', and its zero-level amounts to 0.775 V. The same applies (for example in antenna technology) to dBm and dbW, if it is used for indicating the power. Hence, dBm then refers to 1 mW, and dbW to 1 W.
The following table indicates the appropriate voltage and power relationships for the most important dB-values as well as frequently used voltage levels and power data.
dB | V_{1}/V_{0} | P_{1}/P_{0} | dBW | dBm | Level | Power | |
60 | 1000 | 1000000 | 30 | 60 | 774.6 V | 1 kW | |
50 | 316.2 | 100000 | 20 | 50 | 244.9 V | 100 W | |
40 | 100 | 10000 | 10 | 40 | 77.46 V | 10 W | |
30 | 31.62 | 1000 | 0 | 30 | 24.49 V | 1 W | |
20 | 10 | 100 | -10 | 20 | 7.746 V | 100 mW | |
10 | 3.162 | 10 | -20 | 10 | 2.449 V | 10 mW | |
6 | 2 | 4 | -30 | 0 | 775 mV | 1 mW | |
3 | 1.41 | 2 | -40 | -10 | 244.9 mV | 100 mW | |
0 | 1.0 | 1 | -50 | -20 | 77.5 mV | 10 mW | |
-3 | 0.707 | 0.5 | -60 | -30 | 24.49 mV | 1 mW | |
-6 | 0.5 | 0.25 | |||||
-10 | 0.3162 | 0.1 | dBW = 10 lg(P/1 W) | ||||
-20 | 0.1 | 0.01 | dBm = 10 lg(P/1 mW) = | ||||
-30 | 0.03162 | 0.001 | 20 lg(V/0.775 V) | ||||
-40 | 0.01 | 0.0001 | |||||
-50 | 0.003162 | 0.00001 | |||||
-60 | 0.001 | 0.000001 |
Last Update: 2006-Jän-18