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# Decibel Based Representation of Wireless Communication Parameters - Converting Between the Parameters

In wireless communication, the magnitudes of certain parameters such as power and voltage vary over several orders- for example; the received signal power level in mobile communications can vary between tenths of a milli-watt to about a few hundred of a milli-watt. For certain wireless communication systems, the received power can vary between a few tens of a watt up to few tenths of a microwatt! This is due to the wireless channel conditions in the form of noise, fading and so on.

The following equations represent the voltage and power gains with reference to 1 V and 1 W respectively.

$$Voltage\:gain(dBV)=20log_{10}(\frac{Voltage\:Value}{1V})$$

$$Power\:gain(dBV)=10log_{10}(\frac{Power\:Value}{1W})$$

Since the received power/voltage levels vary over several orders of magnitude, it is often customary to represent power in decibel. In case of power, the reference power level is usually taken as 1 milli-watt. The received power level is compared with 1 milli-watt and the ratio of the received power and the reference power is mapped on to the decibel scale.

The following equation represents power being expressed in dBmW with reference power as 1 milli-watt.

$$Power\:gain(dBmW)=10log_{10}(\frac{Power\:value}{1mW})$$

The decibel representation proves very convenient for interpreting the data. In the linear (absolute) scale, it is very difficult to represent quantities that vary over a very large dynamic range on a single plot. It is difficult to select a suitable scale for representing the various values. Decibel based representations of power, voltage; current and so on are essentially used for conveniently presenting the values on a single scale.

Some of the commonly used decibel based representations for parameters of wireless communications are dBW (decibel with respect to 1 Watt), dBmW (decibel with respect to 1 mW), dBµW(decibel with respect to 1 micro-watt), dBV (decibel with respect to 1 V), dBmV (decibel with respect to 1 milli-volt), dBµV (decibel with respect to 1 micro-volt) and so on.

$$V(dBmV)=20log_{10}(\frac{Voltage\:value}{1mV})$$

$$V(dB\mu\:V)=20log_{10}(\frac{Voltage\:value}{1\mu\:V})$$

$$P(dB\mu\:W)=10log_{10}(\frac{Power\:value}{1\mu\:V})$$

The following table gives a summary of the commonly used dB values in wireless communication systems including wireless link budgets.

## Quick summary

The following table will be useful for quick problem solving

‘dB’ increase in i/p power | Output power |
---|---|

3 dB | Twice the input power |

6 dB | Fourfold increase in input power |

9 dB | Eightfold increase in input power |

10 dB | Ten times the input power |

The same applies with ‘dB’ decrease. Let us look at one more important conversion table.

## Conversion table

Conversion from | Procedure |
---|---|

‘dBm’ to ‘dBW’ | ‘X’ dBm (or dBmW) = 30 + ‘X’ dBW 6.02 dBW = 36.02 dBmW |

‘dBμW’ to ‘dBW’ | ‘Y’ dBμW = 60 + ‘Y’ dBW 40 dBμW = -20 dBW |

‘dBμV’ to ‘dBV’ | ‘Z’ dBμV = 120 + ‘Z’ dBV 40 dBμV = -80 dBV |

## Numeric examples

**1. Convert 10 dBW to dBm**

**Soln**. We know that, from the table, ‘X’ dBm (or dBmW) = 30 + ‘X’ dBW

Therefore, 10 dBW translates to 40 dBm.

**2. Convert 12 dBV to dBµV**

**Soln**. From the table, ‘Z’ dBµV = 120 + ‘Z’ dBV.

Therefore, 12 dBV translates to 132 dBµV