RF Math

Since I am not a maths expert, and had a difficult time keeping track of the differences between mW and dBm when first started learning about wireless I thought I would toss together a reference blog for those who need it.

Definitions

Milliwatt (mW) is the amount of power being transmitted by the intentional radiator (most likely an access point).

Decibel-milliwatts (dBm) is the reference value to 1mW.

Conversion

The full equation for conversions dBm to milliWatt is P(mW) = 1mW ⋅ 10(P(dBm)/ 10), but you don’t need to memorize that to be able to do close-enough conversions.  All you need to remember is the rule of 3 and 10.

  • When you add three dBm multiply the mW by two.  If you subtract three dBm divide the mW by two.
  • When you add ten dBm multiply mW by ten.  If you subtract ten dBm you divide mW by ten.

This chart should help illustrate the rule of 3 and 10.

dBm mW
0 1
3 2
6 4
9 8
10 10
13 20
20 100

It should also be noted that these values are not exact, but do work for your calculations.  If you need a more specific value I recommend you use a calculator like the one available at RapidTables.

EIRP

When it comes time to install access points, especially those with external antennas, you will need to keep your local laws and regulations surrounding maximum Equivalent Isotropically Radiated Power (EIRP) in mind.  If you’re in the United States check out this excellent chart from the fine folks over at Air802.com that maps out the FCCs rules per band, frequency, and function.

EIRP = Transmit Power (mW) – Loss (db) + Antenna Gain (dBi)

Example 1

You are installing an access point with a transmit power of 20mW connected to an antenna with +7dbi of gain over a cable with -1db of loss.  What is your total EIRP?

To solve this questions and find our EIRP lets list out the information we know.

  • Transmit Power = 20mW
  • Cable Loss = -1db
  • Antenna Gain = 7dbi

Now let’s put that together into the formula above:

EIRP = 20mW – 1db + 7dbi

In order to find the total EIRP we need to convert all the values to the same format, either dB or mW.  I personally find it simpler to convert your transmit power to dBm.  So let’s try and convert 20mW into dBm.

To find the value of 20mW in dBm we can use values we know.  Since we know that 10dBm is equal to 10mW.  Then, we can use the rule of 3, because if we add 3dBm we would multiple 10mW by 2 and end up with 20mW.  Using the chart above we can confirm that 20mW is equal to 13dBm.  Now let’s put our answer back into the formula and get our answer.

EIRP = 13dBm – 1db + 7dBi

EIRP = 19dB

Example 2

What is the dBm equivalent of 80mW?

For this example we can start with what is known again – 10dBm is equal to 10mw. Then ,since we know we need to work our way up to 80mW.

  • 10dBm = 10mW
  • 13dBm = 20mW
  • 16dBm = 40mW
  • 19dBm = 80mW

Conclusion

I know these values are not exact, but they will help you when you need to perform a quick conversion or work through your CWNA or CCNA Wireless exam.  Remember to practice the rule of 3 and 10 until it becomes a skill.  If you have any questions or examples you would like to work through, leave a comment and we can work through it together.

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