Power ratio compared to decibel: Difference between revisions
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'''[[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. | |||
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== Gain expressed in dB == | |||
The definition of power gain in '''dB''' is as follows | |||
The definition of power | |||
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In this equation, '''G''' is the gain in '''dB''', '''P<sub>o</sub>''' is the output power and '''P<sub>i</sub>''' is the input power. It can be seen that the | In this equation, '''G''' is the gain in '''dB''', '''P<sub>o</sub>''' is the output power and '''P<sub>i</sub>''' 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 table == | ||
The accompanying table gives the decibels for power | The accompanying table gives the decibels for power ratio. The first column is the power ratio in terms of the quotient '''(P<sub>0</sub>/P<sub>i</sub>)''' 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 == | == 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''' | * '''10 dB''' correspands to '''x 10''' | ||
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* '''37 dB''' = 10 dB + 10 dB + 10 dB - 3 dB | * '''37 dB''' = 10 dB + 10 dB + 10 dB - 3 dB | ||
The ratio = 10• 10• 10• 10 / 2 ≈ ''' | 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 = 10<sup>5</sup>/ 2<sup>2</sup> ≈ '''25 000''' | |||
Latest revision as of 05:36, 30 November 2010
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
- <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 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