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yet need to work with gain and attenuation in dB. The
solution is to use a single fixed reference level for all
measurements. The value for P1 in the equation shown
(the one in the denominator) is the ratio’s reference level.
By using the same absolute reference value for all of your
calculations, you also know the absolute power of the
For example, if you use one milliwatt (1 m W) as your
reference level, all of your dB values will be calculated
“with respect to one milliwatt.” This is so common in
wireless that the abbreviation dBm was created. A power
level of 10 dBm is 10 times 1 m W or 10 m W; 3 dBm is 2
m W; - 20 dBm is 0.01 m W; and so forth. Because values in
dB are added or subtracted when the quantities are
multiplied or divided, you can easily use dBm values
throughout your radio system.
For example, when a 1W transmitter signal ( 30 dBm)
is amplified with a gain of 15 dB, it becomes a 30 + 15 =
45 dBm signal. A received signal of - 47 dBm experiencing
a cable loss of 6. 2 dB is reduced to - 47 – 6. 2 = - 53. 2 dBm.
Other common abbreviations you’ll encounter in the
wireless world are the dBW (reference level of one watt),
dBV (reference level of one volt), and dBuV (reference
level of 1 µV). When you see a letter appended to “dB,” it
is specifying a common reference value.
Another common measurement expressed in dB is the
signal-to-noise ratio, or SNR or S/N. SNR compares the
signal power to the power of the background noise: SNR
= 10 log10 (PSIGNAL / PNOISE). Often left out of the
discussion is the bandwidth of the channel over which
noise is measured.
For example, a telephony circuit (mobile or landline)
may be assumed to have a communications-quality
bandwidth of 3 kHz. It’s usually assumed to be the
receiver or amplifier bandwidth, but don’t assume that’s
always the case. If you really need to know SNR with full
accuracy, specify the bandwidth of the measurement.
In the case where interfering signals are also present
— such as for a data link in a shared unlicensed frequency
band like 900 MHz or 2. 4 GHz — a better measurement
might be signal-to-noise plus interference ratio or SNIR.
(This measurement is also written as signal-to-interference
plus noise ratio, or SINR.) If your data link will be
operating in a crowded band, this might be a better way
to measure and plan your communications link.
Finally, each step in the modulation/demodulation and
signal amplification chain adds some distortion products
to the desired signal. The measurement signal-to-noise plus
interference and distortion, or SINAD accounts for these
effects: SINAD = 10 log10 [(PSIGNAL + PNOISE + PDIST) /
(PNOISE + PDIST)].
Gain: Power or Pattern
I have mentioned “gain” several times so far in this
column and it’s time to explain there are two common
definitions, both specified in dB. The most used definition
and probably the one you imagine when you see the
word is power gain. This is what happens when an active
device such as an op-amp or transistor or vacuum tube
uses a low level input signal to control a more powerful
output signal. The output signal has more power than the
input signal. That input-to-output power ratio is the gain of
the circuit or device — pretty straightforward.
The other type of gain is created by antenna
designers. You’ll frequently see antennas specified to have
some value of gain in dB. The antennas themselves do not
add any power to the signal applied to their feed point. In
fact, due to resistance, the antenna has a slight loss. The
gain being referred to — pattern gain — comes from
focusing the signal in a certain direction so that it appears
stronger in the favored direction. This is equivalent to
having amplified the signal by the same amount.
An antenna’s pattern gain, however, is always
measured or specified with respect to some standard
reference antenna. The two most common references are
the isotropic antenna which radiates equally in all three-dimensional directions, and the dipole which radiates best
broadside to the antenna and very weakly off the ends.
(Dipoles and their radiation patterns were discussed in the
September 2016 column.)
If you imagine the isotropic antenna’s radiation
pattern as a spherical balloon filled with radiated power, a
directional antenna like a beam or dish creates pattern
gain by “squeezing” the sphere. Where the signal is
focused, the sphere extends farther from the center than
without focusing. The ratio between the focused direction
and the original equal-in-all-directions is the antenna’s gain
in that direction.
Since the ratio depends on the reference antenna’s
pattern, antenna gain must always be specified with
respect to the reference antenna. If the reference was an
isotropic antenna, the abbreviation dBi is used; dB with
respect to an isotropic antenna. If a dipole was used, the
abbreviation dBd is used with the understanding that the
dipole’s pattern is used where the dipole’s radiation is
strongest: broadside to the dipole. In fact, a dipole has a
■ BY WARD SILVER N0AX
Noise in Analog-to-Digital Converters (ADCs)
It’s the norm these days to digitize analog signals and
manipulate them in software. As such, it’s important to understand
the noise performance of ADCs. The Analog Devices’ tutorial —
“Understand SINAD, ENOB, SNR, THD, THD + N, and SFDR So You
Don't Get Lost in the Noise Floor” (AD MT-003) — is an excellent
tutorial on different noise metrics of ADCs.
You can download it for free at www.analog.com/media/en/
January 2017 17