here to go to our basic concepts of microwaves page
here to go to our page on power meter measurements
Decibels (dB) are used in analog
electronics. Because dB are logarithmic, its a convenient way to
compress the universe into a small scale.
Check out Alexander
Graham Bell in our Microwave Hall of Fame! Also check out John
Napier, he first demonstrated the merits of the logarithmic
Every time you talk to a microwave
engineer it's dB-this and dB-that. What are they talking about?
(if you are a mechanical engineer sitting at a meeting and the topic
shifts to "dB", it's probably a good time to get another
donut...) A decibel is a convenient logarithmic ratio of two RF
power or RF voltage levels (usually input and output levels). If
you are asking "why are logarithmic ratios convenient?",
you are too young to have owned a slide rule. The beautiful thing
about log ratios is that multiplication of "linear" numbers
becomes addition, and division becomes subtraction.
The conversion of linear ratios
to dB is:
Bear in mind that in microwaves
we are most often referring to power levels, not voltage levels.
That's because microwave signals are usually measured in milliwatts,
not millivolts. You can easily convert from power to voltage and
vice-versa if you know the system characteristic impedance (usually
How to "think" in
Decibels are very useful for
talking about increases (gains) or decreases (losses) without talking
about the actual power or voltage levels. Remember, though, that
dB by itself isn't a unit like millimeters or inch, it's all relative.
A negative number of dB indicates loss or reduction in signal strength,
while a positive number indicates gain or increase in signal strength.
When you refer to a loss in dB, it is customary to eliminate the
negative sign. For example, a ten-dB attenuator has 10 dB loss,
while it has -10 dB gain. By the way, the decibel is actually a
tenth of a Bel, a unit named after (you guessed it) Alexander Graham
You'll also see the term dBm
in the field of microwaves (decibels referenced to milliwatts),
or sometimes dBW (decibels referenced to watts). This is simply
the same logarithmic calculation but instead of comparing two power
levels to each
other, you are comparing one
power level to 1 milliwatt. 10 dBm is the same at 10 mW, 20 dBm
is the same as 100 mW, 30 dBm is the same as 1000 mW (or one watt).
How do you "think"
in decibels compared to linear units? Just remember a few key conversions
and you will be all set to impress your friends with quick approximations
of some heavy multiplication and division (that is, if they are
easily impressed). By the way, we rounded these off so they will
be easier to remember, if you need an exact answer, get a calculator!
30 dB is an increase of 1000X
20 dB is an increase of 100X
10 dB is an increase of 10X
6 dB is an increase of 4X
3 dB is an increase of 2X
2 dB is an increase of 1.6X
1 dB is an increase of 1.25X
0 dB is no increase or decrease
-1 dB is a decrease of 20%
-2 dB is a decrease of 37%
in power (roughly a decrease of 1/3)
-3 dB is a decrease of 50%
-6 dB is a decrease of 75%
-10 dB is a decrease of 90%
-20 dB is a decrease of 99%
-30 dB is a decrease of 99.9%
When you input a 5 milliwatt
signal into a power amplifier that has 12 dB of gain, the output
is 80 mW You can easily do the math in your head. Break down the
12 dB into 6 dB + 6 dB, and remember that each 6 dB increases power
by 4X, so you have an increase of 16X ( equal to 4x4). Sixteen times
five is eighty.
Let's try a harder laboratory
calculation. Your signal source has an adjustable power output from
0 to 27 dBm (one milliwatt to half a watt). You have an isolator
on the source output (always a good idea) with one dB loss. Then
you are coupling off a sample of the signal through a ten dB coupler,
attenuating it with a six dB pad before reading the signal strength
in decibels with a power meter. The "through" port of
the coupler is known to have one dB of loss with respect to its
input port, and your device under test (DUT) amplifier resides right on the
output port of the coupler. When Power meter A reads 6 dBm and Power meter B reads 20 dBm, what is the input and output power of the amplifier and its gain?
Start by figuring out the input power. Working backwards from the "known"
power (Power meter A), you have 17 dB loss between it and the source
(the 6 dB pad, the 10 dB coupler, and the isolator at one dB). Therefore
the source is generating a power of 23 dBm, which is 200 milliwatts
(remember that 20 dBm is 100 milliwatts, and you are 3 dB above
that). Then working toward the DUT, you have two dB loss total (one
dB in the isolator, one dB in the coupler), so the DUT sees 21 dBm,
or 15 dB higher than the power meter reading. 21 dBm is 25% more
than 100 milliwatts, or 125 milliwatts. Note that once you know
the +15 dB difference between the power meter and DUT, you can apply
it to any power meter reading A; this is your calibration
factor for input power.
Next the output power is calculated. The calibration factor for the
output power is +10 dB, this is due to the 10 dB pad we added after
the DUT. So if you read 20 dBm on meter B, the amplifier is putting
out 30 dBm (1 watt). If meter A is reading 6 dBm, the input is 21 dBm, and the amplifier
has 9 dB gain (difference between input and output powers). Be sure to keep track of the "polarity"
of the cal factors, so you don't subtract when you should add or
Update April 2012: thanks to Y.S. for pointing out a mistake in the above math that persisted for three years...
Note that in real life, you would
measure calibration factors more exactly (using a network analyzer), because nominal values
are not exact (and will vary when you measure across frequency).
Go to our page on power
meter measurements to learn more.
With a little practice you will
be able to do decibel calculations in your sleep, it's easier than
balancing your checkbook. For homework, try the previous calculation
using "normal" math... let's see, the pad loses 75% of
the signal power, the coupler loses another 90% on top of that and
the circulator loses another 10%... forget about it!