RF Math (1)

If you ask me what one of my favorite subjects was in high school, I’d definitely pick math. When I did the CWNA training I loved the math part and now during my preparation of CWAP, I’m getting a review of math. I believe not everybody is good in (or likes) math, so writing this blog is also to explain the math in an easier way so people who have problems with math can maybe understand it better.

First, and I think it is the easiest calculation, is working with dB.
A gain of 3 dB, multiply the output with 2
A loss of 3 dB, divide the output with 2
A gain of 10 dB, multiply the output with 10
A loss of 10 dB, divide the output with 10

Those are the most important rules. Keep them in your mind and you can calculate everything.

GAIN
25 mW and a gain of 3 dB gives you 50 mW.
25 mW * 2 = 50 mW

25 mW and a gain of 6 dB gives you 100 mW.
6 dB is 3 dB + 3 dB, so 25 mW * 2 * 2 = 100 mW

25 mW and a gain of 9 dB gives you 200 mW.
9 dB is 3 dB + 3 dB + 3 dB, so 25 mW * 2 * 2 * 2 = 200 mW

25 mW and a gain of 10 dB gives you 250 mW.
25 mW * 10 = 250 mW

LOSS
250 mW and a loss of 3 dB gives you 125 mW.
250 mW / 2 = 125 mW

250 mW and a loss of 6 dB gives you 62.5 mW.
6 dB is 3 dB + 3 dB, so 250 mW / 2 / 2 = 62.5 mW

250 mW and a loss of 9 dB gives you 31.25 mW.
9 dB is 3 dB + 3 dB + 3 dB, so 250 mW / 2 / 2 / 2 = 31.25 mW

250 mW and a loss of 10 dB gives you 25 mW.
250 mW / 10 = 25 mW

So, after some basic rule examples, let’s expand this.

25 mW with a gain of 16 dB gives you 1000 mW.
16 dB is 10 dB + 3 dB + 3 dB, so 25 mW * 10 * 2 * 2 = 100 mW

25 mW with a gain of 17 dB gives you 1250 mW.
This is the first that is a little bit harder. 10 dB + 3 dB + 3 dB is 16 dB and 10 dB + 3 dB + 3 dB + 3 dB is 19. 17 dB is in the middle, so how do we calculate this? We want to be in the 10s and the 3s, so, 17 dB is 10 dB + 10 dB – 3 dB.
25 mW * 10 * 10 / 2 = 25, 250, 2500, 1250

Now, let’s combine everything together in the last example.
25 mW + 8 dB – 6 dB + 13 dB – 7 dB gives 156.25 mW

You can start to calculate one by one, but you should first do the math on the dB’s.
So, +8 -6 +13 -7 will be a gain of 8 dB.

25 mW with a gain of 8 dB will be 156.25 mW. Again, find the 10’s and the 3’s.
10 + 10 – 3 – 3 – 3 – 3 will be 8.
25 mW * 10 * 10 / 2 / 2 / 2 / 2 = 25, 250, 2500, 1250, 625, 312.5, 156.25

Below is a summary of the above examples, keeping the 10s and the 3s.

Keep in mind that a gain of 9 dB is *2 *2 *2 and not *6 (2+2+2)