|
The ratio
between two values of power, P2 and P1, may be expressed in decibels
according to the following formula:
dB = 10 log P2/P1.
Also, since P=V2/R,
then the ratio between two voltages V2 and V1 may be expressed in decibels
as follows:
dB = 10 log (V2/V1)2 = 20 log V2/V1.
Similarly, since P=I2R,
the ratio between currents I2 and I1 in decibels is given by:
dB = 10 log (I2/I1)2 = 20 log I2/I1.
Table 1 below shows the equivalent power or voltage/current ratios of some
dB values.
Table
1. Decibels-to-Power/Voltage/Current Conversion Table
|
dB |
P2/P1 |
V2/V1
or I2/I1 |
|
Gain |
Loss (-dB) |
Gain |
Loss
(-dB) |
|
0 |
1.000 |
1.000 |
1.000 |
1.000 |
|
0.25 |
1.059 |
0.9441 |
1.029 |
0.9716 |
|
0.5 |
1.122 |
0.8913 |
1.059 |
0.9441 |
|
0.75 |
1.188 |
0.8414 |
1.090 |
0.9173 |
|
1 |
1.259 |
0.7943 |
1.122 |
0.8913 |
|
1.5 |
1.413 |
0.7079 |
1.189 |
0.8414 |
|
2 |
1.585 |
0.6310 |
1.259 |
0.7943 |
|
2.5 |
1.778 |
0.5623 |
1.344 |
0.7499 |
|
3 |
1.995 |
0.5012 |
1.413 |
0.7079 |
|
3.5 |
2.239 |
0.4467 |
1.496 |
0.6683 |
|
4 |
2.512 |
0.3981 |
1.585 |
0.6310 |
|
4.5 |
2.818 |
0.3548 |
1.679 |
0.5957 |
|
5 |
3.162 |
0.3162 |
1.778 |
0.5623 |
|
6 |
3.981 |
0.2512 |
1.995 |
0.5012 |
|
7 |
5.012 |
0.1995 |
2.239 |
0.4467 |
|
8 |
6.310 |
0.1585 |
2.512 |
0.3981 |
|
9 |
7943 |
0.1259 |
2.818 |
0.3548 |
|
10 |
10 |
0.1 |
3.162 |
0.3162 |
|
15 |
31.623 |
0.03162 |
5.623 |
0.1778 |
|
20 |
100 |
0.01 |
10 |
0.1 |
|
30 |
1000 |
0.001 |
31.62 |
0.03162 |
|
40 |
10000 |
0.0001 |
100 |
0.01 |
|
50 |
100,000 |
0.00001 |
316.2 |
0.003162 |
|
60 |
1e6 |
1e-6 |
1000 |
0.001 |
|
70 |
1e7 |
1e-7 |
3162 |
0.0003162 |
|
80 |
1e8 |
1e-8 |
10000 |
0.0001 |
|
90 |
1e9 |
1e-9 |
31620 |
0.00003162 |
|
100 |
1e10 |
1e-10 |
100000 |
0.00001 |
Note that a
negative dB value denotes that P1 is greater than P2 (or V1>V2 or
I1>I2), which is actually the same as the 'Loss' column in Table 1
above. For example, -3 dB means that P2/P1 = 0.5012. |
