Wireless Math

 Hi guys, and happy thanks giving. Today I will keep the short for the sake of the holidays but topic in question is something that I find important to cover. We are going to learn how to do basic RF math. 

The reason behaind having to use this RF math is because in wireless we have attenuation while the signal propagates trough the medium, similar to the attenuation on the ethernet cables on long distances but in wireless we are far more suceptible and also far more tolerant to the decrese on the signal

As you know our most basic measurements are the RSSI, Noise floor and SNR, all of them usually measured on dBm but, do you know where this comes from? Well you might know that the Decibels are a comparative measurement value and you will be correct but what are we comparing to? As usual, let's take a step back and start on what are we actually measuring with this value.

Miliwatts (mw)

The miliwatts is a sub unit of the Watt that comes from the power an electrical system has, it is derived from the voltage times the amperage of the system and represent the potency of the system, you might have even seen it some car specs now that the electrical cars are so popular. Anyway, 1 miliwatt is 0.001 watts and you might be thinking, what can I do with this low power and the answer can be transmit a WiFi signal. In our world we don't need a massive amount of power to transmit, we are basically sending a electromagnetic signal with relatively good penetration across the airo, without any interference it can actually travel a very decent distant. To give you an ideap, on the CWNA text book it is mention that a 7 watt light bulb can be seen from a 50 mile distance on a clear night. other example that you might not see as much on today's world is the radio, you can see on lower frequencies a better penetration and even from miles away from the station you are able to hear your music on your radios even trough obstacles and interferences.

For use on indoors on north America the typical Wi-Fi device is allowed to use a max of 100mW to transmit the signal, you can find this kind of power level specially on infrastructure devices as the APs but the client signal is usually limited to somewhere around 20-30mW, so keep in mind this when designing so you don't encounter a near-far issue later on.

Decibel (dB)

As I mentioned before the decibel is comparative measurement, so knowing that we are actually measuring mW on the signal you might have figure out we are actually comparing the signal to a standard power level already defined, and that is 1mW; meaning that if you see a signal of 0 dBm it is actually 1mW what you are seeing there. In other words and traslating to something more typical, if you see a -30dBm signal it means you have a signal of 0.001mW measured on that point. 

The actual math

 So, I know the last example might be a bit confusing and I want to keep it simple so let's try again.There are 2 rules that you need to know by heart if you're doing RF math. 

First a 3dBm diference means a increase/decrease of the signal by double or half respectively; so if you see a +3dBm from a reference point you will see the signal has doubled and a -3dBm is that the signal has halfed.

The second rule is if you see the diference of 10dBm it either increse/decrese the signal time 10, similar to what we saw before a +10dBm is an increase of 10 time and -10dBm is a decrese to 1/10 of the signal

To ilustrate I will give you a couple examples

10mW + 10 dBm = 100mW

50mW - 3 dBm = 25mW

Up to this point everything should be fairly easy, but what happens when we encounter something like -12dBm, well it won't be as complicate as it might seem, you will only need to find the exact factor that you're dividing by 3 and by 10 and do the math secuentially, as an example:

100mW - 12dBm =  100mW - 3 dBm - 3 dBm - 3 dBm - 3 dBm = ((((100mW / 2) /2) /2) /2)  = 6.25mW

Let's use another example:

100mW - 13dBm = 100 mW -10dBm - 3dBm = (100mw ) /10 ) /2 ) = 5mW

As you can see up to this point it should be fairly easy, you just need to found the correct factors that when you add them you can see the exact number of dBm either summed or sustracted: and up to this point you will be thinking, well not everything is divisible by 3 and 10 and you will be rigth, keeping the 100mW example so keep comparing the perspective of the result let's do first and easy one -7dBm, what you will do here is first substrack 10dBm  and then add 3dBm and it will give use  something like this:

100mW - 7dBm = l00mW - 10 dBm + 3 dBm = (((100mW) /10 ) * 2) = 20mW

And that is how you break "complex" with logarithms into basic math, you will need to figure out how to break the number of dBm by adding or substracting multiples of 3 or 10. To close the article let's do one more

100mW - 17dBm = 100mW - 10dBm -10 dBm + 3dBm = ((((100mW ) /10 ) /10 ) * 2)  = 2mW

Easy right? Ok, so now you know the 0 dBm is equal to 1 dBm, let's translate to something more familiar again, let's say we measure our Wi-Fi at -53dBm and you don't get any extra information; well,  now you now your reference level is 1mW which would mean something like this

1mw - 53dBm = 1mW - 10dBm - 10dBm - 10dBm - 10dBm - 10dBm - 3dBm 

1mw - 53dBm = (((((1mW / 10 ) / 10 ) / 10 ) / 10 ) / 10 ) / 2 ) = 0.0000005 mW

And that's all my friends, as you can see the math is fairly easy.

Thanks for reading 

Dan