LEARNING DECIBEL BASICS
One excellent recourse is the scientific calculator. Here we apply a formula (C1.1).
For example, let us deal with the following situation:
Because the output of this network is greater than the input, the network has a gain. Keep
in mind we are in the power domain; we are dealing with mW. Thus:
= 10 log 4/2 = 10 log 2 = 10 × 0.3010 = +3.01 dB.
We usually roundoff this dB value to
+3 dB. If we were to do this on our scientific
calculator, we enter 2 and press the log button. The value 0.3010--appears on the display.
We then multiply (
×) this value by 10, arriving at the +3.010 dB value.
This relationship should be memorized. The amplifying network has a 3-dB gain
because the output power was double the input power (i.e., the output is twice as great
as the input).
For the immediately following discussion, we are going to show that under many
situations a scientific calculator is not needed and one can carry out these calculations
in his or her head. We learned the 3-dB rule. We learned the
+10, +20, +30 dB; -10,
-20, -30 (etc.) rules. One should be aware that with the 3-dB rule, there is a small
error that occurs two places to the right of the decimal point. It is so small that it is hard
With the 3-dB rule, multiples of 3 are easy. If we have power ratios of 2, 4, and 8,
we know that the equivalent (approximate) dB values are
+3 dB, +6 dB, and +9 dB,
respectively. Let us take the
+9 dB as an example problem. A network has an input of
6 mW and a gain of
+9 dB. What power level in mW would we expect to measure at
the output port?
One thing that is convenient about dBs is that when we have networks in series, each
with a loss or gain given in dB, we can simply sum the values algebraically. Likewise,
we can do the converse: We can break down a network into hypothetical networks in
series, so long as the algebraic sum in dB of the gain/loss of each network making up
the whole is the same as that of the original network. We have a good example with the
preceding network displaying a gain of
+9 dB. Obviously 3 × 3 = 9. We break down the
+9-dB network into three networks in series, each with a gain of +3 dB. This is shown
in the following diagram:
We should be able to do this now by inspection. Remember that
+3 dB is double the
power; the power at the output of a network with
+3-dB gain has 2× the power level
at the input. Obviously, the output of the first network is 12 mW (point A above). The