Alexander Graham Bell, after which the bel, and therefore the decibel, is named. |

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dB

The decibel (dB) is a dimensionless unit used for quantifying the power ratio between two values. The unit is useful for describing the gain or loss in a system. It is used when characterizing amplifiers, attenuators, mixers, or RF chains as a whole. It is based on the bel and is defined as follows:A power ratio is defined as:

power ratio = ouput_power / input_power

A bel is defined as:

power in bels = log10(output_power / input_power)

A decibel is 1/10 as large as a bel so ten decibels make up one bel:

1 bel = 10 decibels

And therefore power in decibels is defined as:

power in decibels = 10 * log10(output_power / input_power)

The table below shows the loss/gain as a power ratio compared to the loss/gain in decibels for several different values:

The table below shows a amplitude ratio, power ratio (which is just the amplitude ratio squared), and associated dB value. Note that the dB range for corresponding power ratios is much smaller, i.e, -100 dB to +100 dB corresponds to 0.0000000001 to 10000000000 power range. That makes the use of dBs desirable when dealing with large power ranges. An example would be a satellite communications system where transmit antenna signal power is +14 dBW and receiver antenna signal power is -160 dBW.

dB | power ratio | amplitude ratio | ||
---|---|---|---|---|

100 | 10 000 000 000 | 100 000 | ||

90 | 1 000 000 000 | 31 623 | ||

80 | 100 000 000 | 10 000 | ||

70 | 10 000 000 | 3 162 | ||

60 | 1 000 000 | 1 000 | ||

50 | 100 000 | 316 | .2 | |

40 | 10 000 | 100 | ||

30 | 1 000 | 31 | .62 | |

20 | 100 | 10 | ||

10 | 10 | 3 | .162 | |

6 | 3 | .981 | 1 | .995 (~2) |

3 | 1 | .995 (~2) | 1 | .413 |

1 | 1 | .259 | 1 | .122 |

0 | 1 | 1 | ||

−1 | 0 | .794 | 0 | .891 |

−3 | 0 | .501 (~1/2) | 0 | .708 |

−6 | 0 | .251 | 0 | .501 (~1/2) |

−10 | 0 | .1 | 0 | .316 2 |

−20 | 0 | .01 | 0 | .1 |

−30 | 0 | .001 | 0 | .031 62 |

−40 | 0 | .000 1 | 0 | .01 |

−50 | 0 | .000 01 | 0 | .003 162 |

−60 | 0 | .000 001 | 0 | .001 |

−70 | 0 | .000 000 1 | 0 | .000 316 2 |

−80 | 0 | .000 000 01 | 0 | .000 1 |

−90 | 0 | .000 000 001 | 0 | .000 031 62 |

−100 | 0 | .000 000 000 1 | 0 | .000 01 |

An example scale showing power ratios x and amplitude ratios √x and dB equivalents 10 log_{10} x. It is easier to grasp and compare 2- or 3-digit numbers than to compare up to 10 digits. |

As you can be seen from the table above, 1 dB is approximately 26% power gain, 3 dB is approximately 2× power gain, and 10 dB is 10× power gain. This is useful to know for "back of the envelope" power calculations.

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dBW

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dBW is an abbreviation for the power ratio in dB of the measured power referenced to one watt (1000 mW):

power in dBW = 10 * log10((output_power_watts) / 1W)

For 1mW of power, you get -30 dBW.

For 2mW of power, you get -27 dBW.

For 1W of power, you get 0 dBW.

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dBm

dBm, also written as dBmW, is an abbreviation for the power ratio in decibels (dB) of the measured power referenced to one milliwatt (mW):power in dBm = 10 * log10((output power in watts)/1mW) = 10 * log10((output power in watts) / 0.001)

For 1mW power, you get 0 dBm.

For 2mW power, you get about 3 dBm.

For 1W power, you get 30 dBm.

So doubling the power is equivalent to about a 3 dBm increase.

## dBm to dBW Conversion

We know the following:power in dBW = 10 * log10(output power in watts/ 1W) = 10 * log10(output power in watts)

and

power in dBm = 10 * log10(output power in watts/ 1mw) =

10 * log10(output power in watts / 0.001) =

10 * log10(output power in watts * 1/1000)

So we need to divide the dBW power ratio by 1000 to equate it to the dBm power ratio. But we know that 10 * log10(1/1000) is -30 dB.

And since we know:

log10(X * Y * Z) = log10(X) + log10(Y) + log10(Z)

we can just subtract 30 dB from the dBm value instead of dividing the power ratio by 1000 to arrive at the dBW value.

So for example, 50 dBm - 30 dB = 20 dBW.

Both dBm and dBW are used for measuring absolute power.

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References

https://en.wikipedia.org/wiki/DBmhttps://en.wikipedia.org/wiki/Decibel_watt

https://en.wikipedia.org/wiki/Decibel

http://www.allaboutcircuits.com/textbook/semiconductors/chpt-1/decibels/

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