Understanding dB Math

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You need to know dB Math

One of the “Wireless LAN Design Rules”

is, as a designer

you need to understand dB math

because you’re going to be using it for all sorts of things

So, in this little video we’re going to talk about some

quick ways you can learn to do dB math, even in your head

and we’ll finally end up with a little Excel spreadsheet

you can play with so you can reinforce the knowledge

I’ve been teaching dB math for

literally decades

They’ve called it “Rules of 10s and 3s” and all sorts of things

and built little tables and charts

and you can always look up online and get a dB to mW table

dBm stands for

decibels compared to 1 milliwatt

So everything we’re doing is comparing it to a milliwatt

so, 0 dBm is 1 milliwatt

everything else comes off of there

well, anway…

like other math tricks

there’s a bunch of math tricks that exist out there like…

crazy, silly ones like if you want to count on you knuckles…

January, February, March, April

and you can use your knuckles to count things

you can use your fingers to count…

this is a technique we can use to

kind of “cheat” on math… and how we do that…

is we just simplify up what’s really a complex logarithmic function

and turn it into really simple math

let’s give it a try

easy dB math in just five minutes

and it probably won’t take me five minutes to show you

and here it is… there’s two rules. First rule

the left side is going to be dB’s

and the right side is going to be what I call “regular math”

and all you need to do is draw a line down the page

and put those two sides

so the dB stuff stays on the dB side

and the regular math stays on the regular and never do they cross

Ok? That’s the first rule

Ok? That’s the first rule

The second rule is kind of a compound rule

and what it is, you’re going to need to memorize a couple of things

they’re not terribly difficult to memorize

so, first one is, the “plus sign” (+)

looks like a plus sign (+). You’re going to rotate it…

and it will become “times” (x)

so, “pluses” (+) live ONLY on the dB side

“times” (x) live ONLY on the “regular math” side

so, “plus” (+) rotates to “times” (x)

“minus” (-) rotates to “divide” (÷)

so, the “minus” (-) is on the dB side becomes a “divide” (÷)

on the other side

10 on the dB stays 10 on the regular side

so those first three are pretty easy

“plus” (+) rotates. “minus” (-) rotates. 10 stays 10

and the last one you’re just going to have to memorize

3 on the dB side become a 2

Don’t ask me “why?” It’s a rule. It’s just a cheat thing.

And that’s how it works and that’s all you have to do

Leave the dBs on the dBs side

Leave the regular math on the regular math side and life goes on

So, let’s try a couple and see how this works.

On the left side it says, “What is 13dBm?”

Well, let’s convert it into its component parts.

13 is 10 + 3

So, on the left side of your page just write

10 + 3

Remember, left side is for dB only

Now to go over to the right side

we’re going to have to use those little conversion rules

10 stays a 10, that’s a rule

plus (+) becomes a times (x)

remember plus (+) rotates to a times (x)?

So on the right side you’re going to go 10 x

And then, what does the 3 become?

the 3 on the left becomes a 2 on the right

So, it becomes 10 x 2 or 20

13dBm is = to 20

Let’s try 36… Now, if we’re going to write that out

it’s going to be a little long you’re going to go…

10 + 10 + 10 + 3 + 3

phew! On the right side you’re going to convert that to

10 x 10 x 10 x 2 x 2

and that’s going to give you the correct answer

10 x 10 = 100 x 10 = 1000

double is 2000 double again is 4000

36dBm is 4000mW

Now we said dBm so the answer’s going to be in milliwatts

Well, what about 27?

How do I get to 27 and all I have are 10s and 3s?

Well in that case I’m going to take 10 + 10 + 10 – 3

And remember the minus (-) on the left becomes a divide (÷)

So this is going to be 10 x 10 x 10 ÷ 2

10 x 10 = 100 x 10 = 1000 ÷ 2 = 500

27dBm = 500mW

Well, how would you get to 15?

You can go 10 + 5 but there is no 5s on the left side there’s only 3s

I could go 10 + 10 and then try to subtract 5

but again there’s still no 5s on the left side

We have to stay with ther rule the way it is

So, to get to 15 it’s…

3 +3 +3 +3 +3 five times

When you get it over to the right side it will be…

2 x 2 x 2 x 2 x 2

2, 4, 8, 16, 32

15dBm = 32mW

and you can do the 45 on your own

Anything you have in dB can follow this same very quick rule

Now there’s a way we can show this

and we teach this in some of our classes

is to use a table that we’re going to build

Say you walk into a testing center and you want to take a test

And you forgot all the rules about this

So you only know a little bit, so you want to wish

you had a cheat sheet with you

While you’re taking the test you sit down

they give yo ua piece of scratch pad

you can build your own dB chart really fast

kind of like this…

now this is just a subset. I’ve included

if you go to wlanpros.com

blog where this YouTube video is

There’s a link that also says

you can download this file and you can print it out as well

So, we know that 3 equals 2

So, 3 is 2. Well if we have three 2s is 6

a 6 is going to be 2 x 2 and that’s going to be 4

and then when you get to 9 it’s going to be 8

when you get to 12 it’s going to be 16

and so those are the green ones. And then it says “Do 3s”

So, the first time you just build a little chart

1 – 36 whatever you want. And then do the 3s

3 is 2 , 6 is 4, 9 is 8

12 – 16. And you just do 2, 4, 8, and fill all of those in

it’s really easy. And that’s going to do all the 3s

Then you would come back and do the 10s

10 is what? 10 is equal to 10. So 10 is 10.

How about a 20?

Well a 20 is two 10s so that would be 10×10

or 100 so you could put a 100 there

And so you do all the 10s

then you go back and do the 10 1/2s

Cause we know if you go up by 3 you’re going to double

3, 6, 9 we double

But when we go the other way, we’re going to go

divide by 2 or 1/2

so, you start at the 10 and then you do the 10 1/2s

10 – 3 you go up 3 to 7

is going to 5. Oh that’s what it looks like on the screen

and then you go from 7 up 3 – 1, 2, 3

to 4 and you get 2.5

You go up again 1, 2, 3 till you get to 1 and you get 1.25

So, you just fill this chart in. You do the 3s

then the 10s, then the 10 1/2s

and then you do the 20 1/2s. So if you go up to 20

20 – 3 = 17, so that’s going to be 1/2

up to 50, and you fill them all in

and eventually you fill all these things out

just following these little rules

But what I’m going to leave you with today

is an Excel spreadsheet that does the same things here

but we’re going to talk a little bit about some of the differences

between the methods we can use

So, I’m now going to switch over to Excel

and we’re going to look at an Excel spreadsheet

Here’s our Excel spreadsheet for dBm to mW conversion

and I’ve highlighted here is the big

formula itself that we’re going to be using

mW = 1 * (10 ∧ (dBm/10) )

that’s the log that we’re doing

anyway this is the Excel formula that I used

and I used three different tables here

to show you the difference of how you calculate

the actual calculation for dB math

it’s the formula, it’s a logarithm

but most of us can’t do logarithms in our head

but we can use some of these other techniques

to do dB mW conversion in our head all the time

So, using the calculation you can see the number is 1.26 and 1.58

but, some of the numbers like 100 is the same across the board

because the math is exactly the ame

Now, if we use the doubling method

3 doubles, and highlighted those in bold

2, 4, 8, 16, 32, 64, 128, 256, 512

and when we get up her to 1000

and I got there by doublling

double, double, double, double, double, double, double

and I got it… wait.. that’s 1024

but if I use the actual function

it came out to be 100

so my doubling “trick” – it’s just a trick, a technique

isn’t perfect, but it gets you really close

so, when I do the doubling

and you see it gets a little further out, as we double further

and further and go to really big numbers like a million over here

it’s off, you know, substantially

but as a percentage it’s pretty low

So, the “doubling method” works

I could also do the “doubling method” on all of them

I could take the 1.25 and double it

to 2.5 and double it to 5 and double it to 10

and double, double, double

So, I can double starting anywhere and the doubling process works

So you can use the “doubling method” as well

And then the next one is, “What if I use the “Times Ten” version?”

And if I just go x 10 x 10 x 10

So, if we go over here to the 1.25 x 10 = 12.5

x 10 again 125

And both techniques, that are both “cheats”

get you really close to what you’re looking for

So, the previous PDF where you just fill it in

you do the 3s, then the 10s, then the 10 1/2s , then the 10 doubles

you can fill in and make your chart yourself

you can build it in Excel

you can decode the one I gave you here

so you can kinda see how I built it

to do either the “doubling” or the “10s”

and you can see why they’re slightly off

but on any exam question you ever have

or basically anything you would do in the real world

any of these methods will give you an answer that’s close enough

to put in your controller or to answer whatever test question you have

dB Math, something you need to know

it’s a rule – follow it

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