What is a Decibel?

Number of dBs = 10log( P 2 P 1 ) where P1 and P2 are the two powers being compared and where the log is to the base 10. The Decibel was invented to represent sound levels but has found many other uses wherever a ratio or comparison of widely differing values is required. because the Decibel is logarithmic small changes in value represent large differences. It must be remembered that the Decibel does not have a unit (being a simple ratio). Therefore, when it is used, frequently a unit is associated with it. It can then be read as X Decibels relative to the unit that is used.

In wireless applications the most frequent unit used in comparisons is the unit of power which is measured in Watts. Because powers vary so much in normal day to day electronics another unit relative to 1 milliwatt or 1 x 10 − 3 W is also frequently used, this is written as dBm. You may also come across some other multiplier units being used so be careful when reading and writing these values.

A signal with a power of 0 dBW is exactly the same as a signal with 1 Watt. A simple table is a good way to get an idea of why Decibels are so useful:

Comparison of Power Ratios using Decibels
Power in Watts
 Power in dBm Power in dBW
1
30
0
100
50
20
1,000
60
30
1,000,000
90
60
0.01
10
-20
0.001
0
-30
0.000001
-30
-60
0.000000001
-60
-90
0.000000000001
-90
-120

By the bottom of the table it is getting hard to count zeros but it is very easy to write or with a little practice "think" about -90dBm or -120dBW! In wireless -120dBW would be quite a strong signal at a receiver for VHF/UHF or microwave frequencies.

Some other useful ratios are:

+/-3dB = double or half the power respectively

+/-6dB = 4 or 1/4 times the power respectively

BE VERY CAREFUL

Just like logarithmic arithmetic Decibel arithmetic does not always do what you might expect. remember adding two logs is the same as multiplying and subtracting is the same as division. The same is almost true for decibels, except they are ten times bigger than the logarithm!

When working with power represented in dB summing two powers (P1 + P2) is not same as adding their Decibel representations (10log(P1) + 10(log(P2)). In calculations we often have to convert values which for convenience are represented in dBW (or similar) back to Watts, do the arithmetic and then convert the answer back to dBW.

-60dBW + -90dBW ≠-120dBW

-60dBW = 1 x 10 − 6 W or 0.000001

-90dBW = 1 x 10 − 9 W or 0.000000001

-60dBW + -90dBW = 0.000001 + 0.000000001 = 0.000001001 = -59.9956...dBW

Links

What is a Decibel? This page gives a fairly complete explanation with examples.from acoustics.
The Decibel Defined A brief definition.
RF Power Values Explained - A CISCO explanation.