Power ratio compared to decibel

2009-09-24T05:41:29Z

212.175.166.246:

[[File:DB table.jpg|right]]

'''[[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'''. (after the British inventor [[Alexander Graham Bell]] (1847-1922)) But in practice, bell is seldom used.

== Gain expressed in dB ==

The definition of power gain in '''dB''' is as follows

<div style="border:2px solid #000000; border-collapse:collapse; width:30%; padding:1em;">

: <math> \mbox{G} = 10\cdot \log{\frac{P_o}{P_i}}</math>

</div>

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 gain in '''dB''' is positive for power increase, 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 ratio. The first column is the power ratio 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 ==

In order to convert gain (in '''dB''') to power ratio, the [[colog]] of '''G/10''' can be used;

: <math> \frac{P_o}{P_i}= 10^{\frac{G}{10}}</math>

But for integer values it is possible to convert the gain to power ratio 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 ≈ '''5 000'''

* '''44 dB''' = 10 db + 10 dB + 10 dB + 10 dB + 10 dB - 3 dB -3 dB

The ratio = 105/ 22 ≈ '''25 000'''

== See also ==

*[[Decibel]]

[[Category:Units of measure]]
[[Category:Telecommunications]]
[[Category:Mathematical tables]]

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Power ratio compared to decibel