In telecommunications in
general and telephony in particular we worry a lot about signal strength. For
example, a particular local loop should have both a high signal strength and
a low noise figure. We express this relationship as the
Let's go back to the first
example above. We
Part of the term "decibel" refers to Alexander Graham Bell of telephone system fame. It turns out that human hearing works on a logarithmic basis and there is a logarithmic relationship between acoustical power and your perception of loudness. We'll see how the decibel scale works to our advantage in just a minute. The decibel is abbreviated dB. Note the large "B": that's in honor of Alexander Graham Bell. The decibel is based on a ratio of two power levels which are usually specified in milliwatts. (A milliwatt is 1/1000 of a watt and it's a very small amount of energy. However, the human ear is very sensitive and can easily detect a milliwatt signal.) Here's the calculation: dB = 10 log
where P
Let's assume that we have an output signal that is only one half as big as the input signal. What difference does this represent in terms of decibels? The calculation looks like: dB = 10 log
This tells
us that there is a 3 dB How about an amplifier that produces twice as much output as input? Electrical engineers would say that this amplifier has a gain of 2. Here's the calculation: dB = 10 log
Therefore if our amplifier
doubles the input we have a These little exercises show
you two things. The first finding is that the
You can play with the above formula and derive dB values for any particular ratio. In fact most scientific calculators have a base 10 logarithm function so the calculations are pretty easy. Here's a table to give you a perspective on the dB values and on the associated power ratios.
To bring this back to telephony just a bit, the signal to noise ratio of the typical analog local loop is about 1,000 to 1 or 30 dB. Again, note that the dB numbers are a little smaller than their accompanying power ratios and are easier to write and comprehend.
In telephony many comparisons
are referenced to an arbitrary standard of 1 milliwatt or 1/1000 of a watt.
It's important to have a standard so that we can have some uniform base value
against which to make a comparison. Other branches of electrical engineering
may choose other standards but for telephony and audio applications 1 milliwatt
is the accepted standard. When I mentioned the 30 dB signal to noise ratio above
it was based on a reference value of 1 milliwatt for the P Here's an example of the
use of the dBm measure. In telephone testing it's customary to attach a test
set on one end of (say) a local loop and put a 1 milliwatt signal (0 dBm) onto
the line. You measure the signal strength at the other end and you can figure
the loss in the local loop Let's compare some different power levels that are referenced to 1 milliwatt:
Naturally a local loop would be producing losses with negative dBm values. An amplified circuit, on the other hand, would produce positive dBm values. |