Calculating DeciBels for eg Wi-Fi networks and the conversion to mW

When calculating DeciBels, bear in mind that it is always a comparative number, eg output as compared to input power. This can be used to compare aerial’s etc.

Here are examples of typical dB values:

0dB  =   same power

3dB =      2 *  power

-3dB =     ½ * power

10dB =   10 * power

-10dB = 0.1 * power

Calculating DB with Logs works as follows.. we’ll first review the 10-LOG where I initially use the notation of (10)log :

 (10) log 1000   = 3 as 10³= 1000. 

 (10) log 10,000 = 4 as 10⁴= 10,000

From now on we will just refer to the “LOG” as opposed to (10)log. The button on your calculator (eg HP) is also identified as the LOG button.

The formula to calculate Decibels is:

10 * log(x) where again x is a comparatative number, eg the output signal divided by the received signal.

 10 * log(x) =    0dB -> x => 10^(0/10)=       1 times the power

 10 *log(x) =     3dB -> x => 10^(3/10)=       2 times the power

10 * log(x) =  10dB -> x => 10^(10/10)=   10 times the power

 10 * log(x) =   -3dB -> x=> 10^(-0.3)=      0.5 times the power

 10 * log(x) = -10dB -> x=> 10^(-10/10)=   0.1 times the power, etc.

That’s not too hard right?…

The power levels of Aps are measured in milliWatts. (mW) The REFERENCE power is 1mW!

So a devices that sends at 0dBm sends the same amount of milliwatts as the reference source, so 1 mW.

A device that sends with -3dBm is half as powerfull as the reference source and sends at 0.5 * 1 = 0.5 mW.

So adding 3dBm makes the device  twice as powerfull!So the difference between a 1dBm device and a 7dBm device is two times 3dB = 4 times!

How much would 36 dBm be?… this does not have to be as hard as it sounds :

36 = 3 + 3 + 10 + 10 + 10 so that’s 1mW * 2 * 2 * 10 *10 * 10 = 4 * 1000 = 4,000mW!