Integers, Decibels, and Graphs

There's a simple trick that can be used to convert between db and absolute values. Most engineers use this and may feel like magic to people unaware of it. First of all, remember the two calculations:

* 3 db = x 2

* 10 db = x 10

These are enough (the article mentions more but they are not needed since you should be able to create all db values from these).

Now, when you've got a db value, try to write it as the sum or difference of these values. For example,

* 1 db = 10 db - 3 * 3 db

* 7 db = 10 db - 3 db

* 12 db = 3 db * 4

* 17 db = 2 * 10 db - 3 db

Now, you can convert these to absolute values using multiplication and division

* 1 db = 10 db - 3 db - 3 db - 3db = 10 / 2 / 2 / 2 = 1.25

* 7 db = 10 db - 3 db = 10 / 2 = 5

* 12 db = 3 db + 3 db + 3 db + 3 db = 2 * 2 * 2 * 2 = 16

* 17 db = 10 db + 10 db - 3 db = 10 * 10 / 2 = 50

* 36 db = 10 db + 10 db + 10 db + 3 db + 3 db = 10 * 10 * 10 * 2 * 2 = 4 000

The same algorithm of course can be used to convert from absolute numbers to decibels:

2000 = 2 * 10 * 10 * 10 = 3 + 10 + 10 + 10 = 33 db

Notice these all are approximations however these are really good approximations and more than enough to very quickly understand what a gain of 50 db means!

John's graph was enough to convey the point, but I agree this one is an improvement. I don't know that I've seen this exact plot style before, but it's exactly what came to mind for me after reading the intro of this article. It's the "stem plot" version of a side-by-side bar chart.