A non-expert doesn't care about antenna gain - he just wants his wireless connection to work (or his radio signal to be clear). When he starts researching antenna gains he delves into the hobbyist scene. I know that hobbyists are not experts but understanding how dB work is simple enough after you understand the practical rules:
1. A difference of 3 in dB means times 2, a difference of 10 means times 10.
2. Because dB are in logarithmic scale adding dB multiplies the effect.
3. Negative numbers work the same but with loss instead of gain.
Thus a 3 dB gain antenna will double your signal strength while a 9 dB antenna will make it (9=3+3+3) 8 times stronger (8=2x2x2). Another example: 23 dB is a 200 times gain (23=10+10+3).
>1. A difference of 3 in dB means times 2, a difference of 10 means times 10.
How can this be right? Aren't you kind of fudging it a little?
Here's my train of thought:
First I was thinking "What the hell is going on with your math? There's no clear factor to turn base 2 into base 10 what the hell. How can what you say be true? How does this work?"
My next thought (based on your incorrect statement) was, oh, they didn't choose base 2: they chose every 3 to be another factor of 2 - so let's see why that works, why +10 is the same as * 10 if every +3 is * 2. Well, you can get to 10 by going 3 + 3 + 3 + 1 and you can also get 10 by going 2 * 2 * 2 * (1.25) = 10.
Okay, so if every +3 converts to * 2 then why exactly does the last term, +1 convert to * 1.25?
I thought, and thought about it. I couldn't make it work, based on your rules. So I checked. And the answer is it doesn't: 2^(1/3) isn't 1.25 as we would expect, it's 1.2599. That might seem "close enough" but I think it's not exactly how you say and your statements are misleading.
Thus 23 dB isn't 200 times stronger as you state (23 = 10 + 10 + 3), it's only approximately 200 times stronger. 200x stronger is 23.0103 dB, and 23 dB is 199.52 times stronger. [1]
While it's useful, and the error is pretty small, it doesn't help for those of us used to thinking in terms of bitfields or something that converts quite exactly.
It's definitely a very useful mental estimation trick though!
[1] which I checked with an online calculator here - https://www.rapidtables.com/electric/decibel.html (first I entered a level of 200 and clicked the top "convert" button, then I entered a dB of 23 and clicked the second "convert" button)
Well these are practical rules that are more or less used by people working with dBs. These people are usually don't think in term of bitfields - when you have a 43 dB gain antenna you don't care if it amplifies 20 000 times or 19 952 :) Also it's a nice way to show-off to people that do not know this rule!
In any case, I never said that you get 100% accurate results; if you want accuracy then you should use your calculator (or your logarithmic ruler); but why use a calculator when you roughly want to understand how much a 15 dB gain would be?
Finally, there's a nice way to find out how much 1 dB is with the mentioned rule: Notice that 1 = 10-3-3-3 thus it's 10/2/2/2 = 1.25 so 1 dB is approximately 1.25 gain as you said :)
Yeah, it's not exact, but in RF/microwave work you often get on order of a dB of loss through the cable or connectors anyway. Plus signal sources and spectrum analyzers are not spec'ed to be as accurate as you might expect. So you end up with error bars in your head.
1. A difference of 3 in dB means times 2, a difference of 10 means times 10.
2. Because dB are in logarithmic scale adding dB multiplies the effect.
3. Negative numbers work the same but with loss instead of gain.
Thus a 3 dB gain antenna will double your signal strength while a 9 dB antenna will make it (9=3+3+3) 8 times stronger (8=2x2x2). Another example: 23 dB is a 200 times gain (23=10+10+3).