Power ratio compared to decibel

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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. 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, 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;

<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 ≈ 5000

See also

• Decibel