Power ratio compared to decibel: Difference between revisions

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

In this equation, G is the gain in dB, P_o is the output power and P_i 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/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

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

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

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-[[File:DB table.jpg|left]]
+'''[[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.
-'''[[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.
+== Gain expressed in dB ==
-== Ratio expressed in dB ==
+The definition of power gain in '''dB''' is as follows
-The definition of power ratio in dB is as follows
+<div style="border:2px solid #000000; border-collapse:collapse; width:30%; padding:1em;">
-<div style="border:2px solid #000000; border-collapse:collapse; width:40%; padding:1em;">
-: <math> \mbox{Ratio in dB} = 10\cdot \log{\frac{P_o}{P_i}}</math>
+: <math> \mbox{G} = 10\cdot \log{\frac{P_o}{P_i}}</math>
 </div>
-In this equation '''P<sub>o</sub>''' is the output power and '''P<sub>i</sub>''' 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.
+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 accompanying table gives the decibels for power gain. The first column is the power gain 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.)
+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 ==
+In order to convert gain (in '''dB''') to power ratio, the [[colog]] of '''G/10''' can be used;
-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;
+: <math> \frac{P_o}{P_i}= 10^{\frac{G}{10}}</math>
-*10 dB correspands to  x 10
+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;
-*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.
+* '''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 '''
-For example 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 ≈ '''5 000'''
+* '''44 dB''' = 10 db + 10 dB + 10 dB + 10 dB + 10 dB - 3 dB -3 dB
-Thus the ratio is = 10• 10• 10• 10 / 2 ≈ 5000
+The ratio = 10<sup>5</sup>/ 2<sup>2</sup> ≈ '''25 000'''
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 [[Category:Units of measure]]
 [[Category:Telecommunications]]
-[[Category:Tables]]
+[[Category:Mathematical tables]]