Engineers have to deal with numbers on an everyday basis, and some of
these numbers can be very large or very small. In most cases, what is
most important is the ratio of two quantities. For example, a mobile radio
base station might transmit approx. 80 W of power (antenna gain included).
The mobile phone receives only about 0.000 000 002 W, which is
0.000 000 002 5 % of the transmitted power.
Whenever we must deal with large numerical ranges, it is convenient to use
the logarithm of the numbers. For example, the base station in our example
transmits at +49 dBm while the mobile phone receives -57 dBm, producing
a level difference of +49 dBm – (-57 dBm) = 106 dB.
Another example: If we cascade two amplifiers with power gains of 12 and
16, respectively, we obtain a total gain of 12 times 16 = 192 (which you can
hopefully calculate in your head – do you?). In logarithmic terms, the two
amplifiers have gains of 10.8 dB and 12 dB, respectively, producing a total
gain of 22.8 dB, which is definitely easier to calculate.
When expressed in decibels, we can see that the values are a lot easier to
manipulate. It is a lot easier to add and subtract decibel values in your head
than it is to multiply or divide linear values. This is the main reason we like
to make our computations in decibels.
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