C.7
dB APPLIED TO THE VOICE CHANNEL
625
1.
+13 dBm
mW.
2.
-13 dBm
mW.
3.
+44 dBm
dBW,
W.
4.
-21 dBm
mW.
5.
+27 dBW
W.
6.
-14 dBW
mW.
7.
-11 dBm
mW.
8.
+47 dBW
kW.
Answers: 1: 20 mW. 2: 0.05 mW. 3:
+14 dBW, 25 W. 4: 0.008 mW. 5: 500 W.
6: 40 mW. 7: 0.08 mW. 8: 50 kW.
C.6
ADDITION OF dBs AND DERIVED UNITS
Suppose we have a combiner, a device that combines signals from two or more sources.
This combiner has two signal inputs:
+3 dBm and +6 dBm. Our combiner is an ideal
combiner in that it displays no insertion loss. In other words, there is no deleterious effect
on the combining action, it is "lossless." What we want to find out is the output of the
combiner in dBm. It is not
+9 dBm. The problem is shown diagrammatically as
Some texts provide a nomogram to solve such a problem. We believe the following
method is more accurate and, with the advent of affordable scientific calculators, easier.
It is simple: Convert the input values to their respective numeric values in mW; add and
convert the sum to its equivalent value in dBm.
The
+3 and +6 dBm values are so familiar that we convert them by inspection, namely,
2 and 4 mW. The sum is 6 mW. Now we take 10 log 6 to convert back to dBm again
and the answer is
+7.78 dBm. Remembering that there is an error when we work "3s"
(3, 6, 9, 1, 4 and 7 values), we recalculated using a scientific calculator throughout. The
answer was
+7.76 dBm showing a 0.02-dB error.
On occasion, we will have to combine a large number of input/outputs where each is
of the same level. This is commonly done with frequency division multiplex equipment
or with multitone telegraphy or data.
Suppose we have an FDM group (12 voice channel inputs), where each input was
-16 dBm. What is the composite output? This is stated as
Composite power
dBm
= -16 dBm + 10 log 12,
= -16 dBm + 10.79 dB,
= -5.21 dBm.
The problem of adding two or more inputs in a combiner is pretty straightforward if we
keep in the power domain. If we delve into the voltage or current domain with equivalent
dB values, such as dBmV (which we cover in Section 15.3.2), we recommend returning
to the power domain if at all possible. If we do not, we can open Pandora's box, because
of the phase relationship(s) of the inputs. In the next section we will carry out some
interesting exercises in power addition.
C.7
dB APPLIED TO THE VOICE CHANNEL
The decibel is used to quantify gains and losses across a telecommunication network. The
most common and ubiquitous end-to-end highway across that network is the voice channel