Fast & furious WLAN dB math

This post is a different look on Keith Parsons' "Easy dB Math in 5 minutes" but by no means a replacement. I've found that I learn thing faster if I see them from different perspectives and this is just that, a different perspective on the same subject.

There are only 2 things that you need to know really. The first is the linear to logarithmic conversion which Keith describes in Rule #2. This is what you need to remember.

+3dB = times 2 in linear form

-3dB = devide by 2 in linear form

And the other

10dB = 10 in linear form

The last one is important at the beginning when picking a reference point from which to start from. For about 99,9% of things in WLAN design the only 3 reference points will be 10dBm, 20dBm or 30dBm or 10mW, 100mW and 1000mW in linear terms. 

To convert it from one to the other just remember this: The number of zeroes in linear defines the first number of the dBm value and then you just ad a zero after that. For example

1000mW has 3 zeroes which you write as 30 and get the dBm value

And for the other way around the first number in dBm value (or dB or any other dBx value) defines the amount of zeros you add after number 1. For example

20dBm needs to have 2 zeroes after 1 or 100mW

Learn by doing

So to put this to practice, I've said that picking the right starting point is the key to fast conversion. For example, if we wanted to convert 27dBm to mW where would we start. The reference needs to be such that you can either add up to or down from it 3dB to the specified dBm value (27dBm) and then simply convert that to linear value. 

Let's first try to use 20dBm as reference. If we try to add up 3dB from that we couldn't get to 27dBm as 

20dBm +3dB + 3dB is 26dBm and
20dBm +3dB +3dB +3dB is 29dBm

So a better reference would be 30dBm since
30dBm -3dB = 27dBm

Since we know that 30dBm needs to have 3 zeroes after number 1 and -3dB means we need to divide that by 2 we can calculate that

1000mW divided by 2 is 500mW

We can make another example and convert 19dBm. In this example either 20dBm nor 30dBm would be the right starting points since we can't subtract 3dB from either of those to get to 19. But if we take the reference of 10dBm we can count up 3dB to it like so

10dBm +3dB +3dB +3dB = 19dBm

which translates to

10 x2 x2 x2 = 80mW

So as you can see it's pretty easy and hopefully you'll be translating linear to dB and vice versa easier now.