Power ratio compared to decibel
Decibel is a practical unit which expresses a ratio in logarithmic scale. It is used in many engineering applications. For example the ratio of output power with respect to input power can be given in decibels (abbreviation dB). As the name of the unit imply, decibel is actually a submultiple of the unit bel. But in practice bell is seldom used.
Ratio expressed in dB
The definition of power ratio in dB is as follows
- <math> \mbox{G} = 10\cdot \log{\frac{P_o}{P_i}}</math>
In this equation, G is the gain in dB, Po is the output power and Pi is the input power. It can be seen that the ratio in dB is positive for power gain, and negative for power loss. So the gain of an amplifier is expressed by positive decibels and the attenuation of an attenuator or a power splitter is expressed by negative decibels.
The table
The accompanying table gives the decibels for power gain. The first column is the power gain in terms of the quotient (P0/Pi) and the second column is the decibel equivalent. (The same table can be used for the power loss also. But in this case, the the reciprocal of the power loss must be used and the correspanding dB figure must have a minus sign.)
From decibel to ratio
If a ratio is known in decibels it is usually possible to convert it to power gain without using a logarithmic table. Since, all integer numbers in dB can be expressed in terms of either addition or subtraction of threes and tens, only the following should be known;
- 10 dB correspands to x 10
- 3 dB correspands to x 2
- -sign correspands to division
Examples
- 19 dB = 10 dB + 3 dB + 3 dB + 3 dB
The ratio = 10 • 2 • 2 • 2 ≈ 80
- 37 dB = 10 dB + 10 dB + 10 dB - 3 dB
The ratio = 10• 10• 10• 10 / 2 ≈ 5000