# dB calculator - Explanation of dB and decibel

dBs are brilliant and fun and make radio and signal level calculations a lot easier. Read here for an explanation plus a handy calculator which will convert dB values into watts and vice versa.

In radio communications you have many items (amplifiers, attenuators, signal splitters and combiners, lossy cables etc) that either increase or decrease the signal level.  To work out the end result for a signal going through a chain of such devices you use the dB gain or dB attenuation of each device and simply add all the dB values together.

## dB calculator Conversion of dB to Ratio..

 Input dB value here

 Output here is the ratio

## dB calculator Conversion Ratio to dB

 Input ratio value here

 Output here is dB

The use of dBs is illustrated by this example.  Read it slowly and try to understand it because if you get to understand this dB example the whole business will become much easier to understand.

dB calculation problem:  What is the output power level in the following situation and will the transmitter output amplifier be overloaded ?. For reference, note the information table on the right

Input signal power level = 1 milliwatt or -30 dBW (or 0 dBm)
Devices in series:
A two transistor amplifier:  Gain 16 dB   (forty times increase in level, x40)
An adjustable 20 dB range attenuator, initially set half way, by you, at the 10 dB setting:   10 dB attenuation (10 times reduction)
Long coax cable:   Loss 3 dB attenuation  (reduction to half the level)
High power 10 watt amplifier: Gain=30 dB (increase in signal level by a factor of 1000 times. Note the 3 zeros = 30 dB)

Calculation:   Output = -30 + 16 -10 - 3 + 30  = 3 dBW = 2 watts

Comment: This should work, but note that if the adjustable attenuator were to be turned to its minimum attenuation value ( 0 dB ) the system would attempt to output +13 dBW or 20 watts.  This is not acceptable with a 10 watt amplifier as it will distort the signal badly and may damage the amplifier.  It will also cause interference to other people on the adjacent frequencies.   In the above case I would add an extra 3 dB attenuator (also called a 3 dB pad) somewhere along or at an end of the cable.  This would mean that a 0 dB setting on the attenuator would cause a 10 watt output and thus just saturate the amplifier.  This avoids risk of accidental interference to other people and damage to the expensive power amplifier.

Formulas:

To convert a ratio to dB, do log and then times by 10.
Example:   ratio = 1234 times.   Log(1234) =  3.09.   Ten times 3.09 = 30.9 dB

To convert dB to ratio, divide by 10 and then do ten to the x, like 10x
Example: dB = +12.5 dB.   Divide +12.5 by 10 = +1.25.    Do 101.25 = 17.8 ratio.

### dB and ratios

 dB value times by +30 dB 1000 +20 dB 100 16 dB 40 13 dB 20 10 dB 10 9 dB 8 8 dB 6.31 7 dB 5.01 6 dB 4 5 dB 3.16 4 dB 2.51 3 dB 2 2 dB 1.58 1 dB 1.26 0 dB 1 -3 dB 0.5 -10 dB 0.1 -20 dB 0.01 -30 dB 0.001 -40 dB 0.0001

### dBW and Watts W

 dBW scale Watts +30 dBW 1000 watts +20 dBW 100 watts +10 dBW 10 watts 0 dBW 1 watt -10 dBW 0.1 W -30 dBW 0.001 W -30 dBW 0 dBm

### dBm and milliwatts mW

 dBm scale milliWatts +30 dBm 1000 mW 0 dBm 1 mW -10 dBm 0.1 mW

Definition: dBW means dB relative to 1 watt, so 0 dBW = 1 watt, -3 dBW = half watt.  +3dBW = 2 watts etc.
Definition: dBm means dB relative to 1 milliwatt, so 0 dBm = 1 milliwatt (one thousandth of 1 watt or 0.001 watt).   Also equal to -30 dBW.
Definition: dBi means gain of an antenna relative to a theoretical reference antenna with an isotropic, omni-directional, spherical radiation pattern.
Definition: dBd means gain of an antenna relative to a reference antenna with dipole radiation pattern.  The reference antenna might be an actual dipole antenna.

### Interesting facts:

A 50 dBW eirp downlink satellite beam, means that it looks like a 100,000 watt transmitter connected to an omni-directional satellite antenna.  You could get the same effect using a 100 watt (+20 dBW) satellite transmitter connected to a directional downlink antenna, with a small coverage beam diameter, having a gain of 30 dBi, and you located on the ground at the centre of the satellite beam coverage pattern.

An uplink power flux density (at the satellite) due to a 1 watt VSAT transmitter on the ground is typically around -119 dBW/m^2 or 0.0000000000012589 watts per square metre at the satellite height. So, if you have a receive antenna on the satellite with an effective collecting area of 1 square metre then the signal power going into the satellite receiver is -119 dBW.

 There may be errors; any problems or comments please e-mail me eric@satsig.net This dB calculator page is copyright (c) 2006 Satellite Signals Ltd, All rights reserved Page started 26 Dec 2006, last amended 9 March 2022.