Power ratio compared to decibel

File:DB table.jpg

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{Ratio in dB} = 10\cdot \log{\frac{P_o}{P_i}}</math>

In this equation P_o is the output power and P_i 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/P_i) 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. Only the following should be known;

• 10 dB correspands to x 10
• 3 dB correspands to x 2

All integer numbers in dB can be expressed in terms of either addition or subtraction of threes and tens.

For example 37 dB = 10 dB + 10 dB + 10 dB - 3 dB

Thus the ratio is = 10• 10• 10• 10 / 2 ≈ 5000

See also

• Decibel