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What is noise?
Noise is a random signal inherent in all physical components. It directly limits the detection and processing of all information. The most
common form of noise is white Gaussian, due to the many random processes that make up electric currents or thermal agitation of conductive elements.
Why is it important?
Because electronic noise is ubiquitous, present in all passive and active components, it is critical for engineers to characterize and
understand how it limits the transmission of information.
What does the term “Gaussian” signify?
The term Gaussian refers to the voltage distribution of the source of noise. Due to its random nature, the noise voltage of a component
is usually a Gaussian distribution. This is characterized by its mean value and random voltage excursions that follow a bell shaped Gaussian curve.
What does the term “white” signify?
White refers to the noise source power spectral density, which is ideally flat with frequency. In reality, at some point—often due to mismatch—there is a reduction in the measurable noise level.
What is AWGN?
The term Additive White Gaussian Noise
(AWGN) refers to the fact that noise eventually
is combined with the desired signal and is a
major limiting factor in the transmission of
information.
What are the common uses of a noise
source?
Noise sources are used to measure noise
figure, provide a source of AWGN to generate
CNR or EbNo to measure error rates, and are
used as an economical source of broad band
power for built in test applications such as signal
strength calibrators and radar applications.
They can be used to increase the dynamic
range of analog to digital converters by
dithering and reducing correlated noise. They
are often found in disk drive testing, wireless
testing, CATV both analog and DOCSYS, jamming,
SATCOM for BER and NF, as well
employed as a source of jitter.
What types of noise sources are available?
Noise sources can be a simple noise diode which generates
a low level of noise, to amplified noise sources supplied
in multiple form factors to instrumentation grade
noise generators which amplify, attenuate and process
both the noise and a user added signal. Noise diodes come
in a variety of packages and can be surface mount or DIP
for PCB mount or coaxial for system integration.
What is ENR?
ENR refers to excess noise ratio, which is 10 log
[(Th–290)/290], is essentially a normalized measure of
how much the noise source is above thermal in its power.
At high ENRs >15 dB the density of power can be approximated
by adding the ENR to –174 dBm/Hz.
How are noise sources tested and specified?
Noise sources are typically tested according to their
output level. Noise sources that are used in noise figure
applications are typically 6 to 30 dB in ENR. These usually
require a noise figure meter or a dedicated noise
radiometer due to their low power levels. Since the ENR
value is used to calculate the noise figure directly, low
power noise sources typically are supplied with calibrated
ENR values. Higher power noise sources typically are
supplied with aggregate power measurements such as on
a power meter with spectral flatness observed on a spectrum
analyzer.
What is the crest factor of a noise source?
Noise sources are characterized by their crest factor,
which is the peak to average ratio of the noise. For example
a 5:1 crest factor of the noise voltage is 20 log(5), or 14
dB. This is a measure of the quality of the noise distributions
and one way to measure its Gaussian nature. Noise
theoretically has an unbounded distribution so that it
should have an infinite crest factor but the physical realization
of the noise generator will limit the output excursions,
via the amplifiers, diode junctions etc.
Why and when is crest factor important?
Crest factor is important primarily in bit error rate
applications. In low power applications in which noise
powers are being compared such as NF, it is largely
insignificant. In BER applications it is important because
the BER being measured is a direct function of the carrier
to noise ratio, and if these noise excursions do not occur
as expected the errors will fall off and erroneous results
will occur. One important note is that it is the crest factor
of the resultant noise in the receiver and its bandwidth
that will determine the resultant crest factor. This is significant
because often times the required noise is a much
larger BW than the receiver, for example a tuned receiver
operating over a wide BW requires the noise to cover
the entire RF BW. This can put a strain on the realizable
crest factor because the wide band high power amplifiers
required to cover the entire BW can be cost prohibitive
and degrade system accuracy in other ways such as
excess current or reliability. Since the noise is often filtered
in the receiver, the crest factor of the resultant noise
is improved as the excess BW is stripped away, reducing
the noise power and leaving the noise farther from the
clipping point. Clipped noise becomes Gaussian as the
measurement BW is reduced. The required crest factor
should take into consideration all of the above.
What is BITE?
BITE stands for built-in-test and refers to the utilization
of an internal noise source to test a system. For
example, the noise source may be put on a PCB via a TO-
8 can, DIP or surface mount package, with a coupler or a
switch to selectively inject the noise into the circuit. By
turning on the noise source and detecting the system output
power, various system performance parameters can
be verified automatically and remotely. The noise source
can also be used to calibrate the receiver’s noise figure by
comparing its known value to the receiver’s. Noise temperature,
frequency response, sensitivity and gain are
among the additional parameters that can be measured
using BITE.
What is Eb/No?
Eb/No stands for energy per bit divided by noise density.
It is essentially a normalized carrier-to-noise ratio
for digital systems. Typically Eb/No is plotted versus BER
to measure the effectiveness of the information transfer.
What is CNR?
CNR is carrier-to-noise ratio and it is the relative
power level of the carrier signal to the noise level in a system.
It typically determines the quality of the system and
BER is plotted against CNR. Carrier refers to the information
signal in this case.
What is BER?
Bit error rate is the frequency of errors that occur
when bits are transmitted in a digital system. Critically,
it is a function of signal to noise ratio or carrier to noise
ratio.
What is Noise Figure (NF)?
Noise figure is defined as the ratio of the signal to
noise power at the input to the signal to noise power at
the output of a device, in other words, the degradation of
signal to noise ratio as the signal passes through the
device. Since the input noise level is usually thermal
noise from the source the convention is to adopt a reference
temperature of 290°K. The noise figure becomes the
ratio of the total noise power output to that portion of the
noise power output due to noise at input when the source
is 290°K.
How is noise figure measured and calculated?
Noise figure is typically determined by using a calibrated
noise source which is traceable to international
standards. This noise source is essentially compared to
the unknown noise figure and by measuring this difference
noise figure is computed:
NF = ENR dB – 10 log (Y – 1) + Tcorr
Tcorr is a temperature correction factor that can be
applied if the temperature deviates significantly from
290°K. Y is the Y factor which is the ratio of the output
power with the noise on to the output power with the
noise off. By employing this method of measuring the Y
factor, only relative accuracies are significant which
makes the measurement easier than attempting to measure
exact powers which can be quite low and tough to
measure.
How do noise powers add?
Noise powers add as incoherent signals which means
that their powers must be added. For example if your
inject a noise source into a spectrum analyzer and see
that the noise floor increases 3 dB, then the actual noise
source power is at the original noise floor level. This relationship
allows you to calculate the noise power of signals
below the measurement noise floor:
10 log [{Inverse log (diff/10)} – 1)]
Where diff is the dB difference in measured powers. Of
course, small changes in power occur as the unknown
noise is far below the known and this results in increasing
inaccuracy as the power goes much lower.
Why can’t I see my noise source on a spectrum
analyzer?
If you are attempting to measure a lower power noise
source, <30 dB ENR, in all probability the spectrum analyzer
Noise Figure, which usually is at a minimum of 25
dB and many times is 35 dB, is above the noise level of
noise source. At these levels we can approximate Noise
Figure and ENR and compare directly to see if the noise
source will be detectable. This source could be measured
with an LNA in front of the spectrum analyzer, although
to get an exact ENR we would need to know the NF of the
LNA and its gain. However, we can usually see if the
approximate deflection occurs. For example, a 15 dB ENR
noise source should change the noise level about 10 dB if
the noise figure of the LNA is about 5 dB, as long as the
LNA gain is sufficient to overcome the noise figure of the
analyzer. Higher power noise sources can be measured on
a spectrum analyzer for flatness and on a power meter for
output power.
Why test at high power levels?
Sometimes it is convenient to test at higher power levels.
For example, BER measurements are a function of
carrier to noise ratio, and they can be quite sensitive with
large changes in BER resulting with small changes in
CNR. Rather than test at low power levels that are very
difficult to measure, often times it is easier to inject more
noise power and test at levels that are easier to establish
what is the actual CNR. Also often times tests are done at
lower CNR so that the BER is higher and the low BER
results are extrapolated, which saves test time because
the errors come so infrequently at high CNR.
What is noise power spectral density?
Typically referred to as No, this is the amount of
power the source will output in a one hertz bandwidth. It
is essentially a normalized output power. Since noise
power is proportional to bandwidth, No is used to compute
the power in any bandwidth.
What is –174 dBm/Hz?
This is a convenient number to use, it represents the
amount of power in a one hertz bandwidth that a thermal
noise source has at the reference temperature of 290°K,
which is approximately room temperature. This results
from the equation P = kTB where k = Boltzmann’s constant,
T is temperature in degrees K, and B is the bandwidth
in Hz. For example the available thermal noise
power in a resistor in a 1 MHz bandwidth would be –114
dBm, because 10 log (1 MHz), or 60 dB, is added to the
–174 dBm/Hz.
What is No and how is it used to calculate noise
output power?
No is the noise density of the noise source. It is the
output power per hertz that the source provides. To calculate
the power that the source will have in a BW the No
is increased by the BW in dB. For example, a –80 dBm/Hz
amplified noise module with 1 GHz BW will have a minimum
of –80 dBm/Hz + 10 log (1 GHz) = –80 dBm/Hz + 90
dB = +10 dBm. If this source is measured on a spectrum
analyzer with the Resolution BW set to 1 MHz then –80
dBm/Hz + 10 log (1 MHz) = –20 dBm will be displayed. In
actuality, the noise source will have some out-of-band
noise and the resolution BW has a noise equivalent BW
greater than its setting so some adjustment of these numbers
will be needed for a more accurate number. For many
applications this first order approximation will suffice.
Aggregate output power should be measured on a power
meter, although it could be approximated by adding 10 log
(BWns/RBW) to the number on the spectral analyzer.
Also, when performing power calculations on noise
sources if the ENR is known the output power density can
be approximately calculated by adding the ENR to –174
dBm/Hz.
This is accurate to less than 0.2 dB at 15 dB ENR and
less than .01 dB for ENRs greater than 30 dB. For example
a 34 dB ENR noise source would have a noise spectral
density of –174 dBm/Hz + 34 dB = –140 dBm/Hz. In a 10
MHz BW this would result in –140 dBm/Hz + 70 dB = –70
dBm. For lower ENRs, the Th has to be obtained directly
from the definition of ENR, then the noise density 10 log
kTh would be computed.
Why is Noise Power proportional to BW?
Since noise is a random signal, its power is distributed
over its usable bandwidth, BW, and the noise source is
considered “white” due to its constant spectral density.
This results in the power measured being proportional to
BW. If a certain power is measured in X BW, then if the
BW is increased to 2X the power measured is double, or 3
dB higher. This should be noted when measuring high
level noise sources on a spectrum analyzer. This is critical
because as a system’s BW increases to allow for more
information to be processed, this will also introduce more
noise power and reduce the CNR and potentially reduce
the dynamic range of the system. This is a major trade off
in all communication systems.
How do I calculate the overall output power of my
noise source?
Use the No noise density and add 10 log of the BW of
the device in which you wish to measure the noise.
Why is the bandwidth of the measurement device
important?
Since noise is a distributed broadband signal its power
is proportional to the bandwidth of the measurement
device, as long as it is in the noise source’s frequency
range. Higher power noise sources are typically measured
with a power meter that covers greater than the frequency
range of the noise source so all of the power is measured.
A true RMS power meter and sensor should be
used. Due to the noise source’s Gaussian nature, errors
can result when diode detectors are used.
How can I measure Noise Figure on a spectrum
analyzer?
Spectrum analyzers can be used to measure noise figure
with a coaxial calibrated noise source. The DUT is
assumed to be an amplifier. The noise source is connected
to drive the amplifier input. On the spectrum analyzer
the noise power is noted at the frequency of interest when
the noise source is on and when it is turned off. This is the
Y factor in dB. Convert the Y factor to linear and plug into
the equation NF(dB) = ENR dB – 10 log(y – 1). There are
various pitfalls to watch out for in this measurement
detailed in the next section.
What are some pitfalls to watch out for with noise
measurements on a spectrum analyzer?
Care must be used when making noise figure measurements
on a spectrum analyzer. There are multiple
possible sources of potential error. Since noise sources are
very broadband their powers can increase quickly as gain
is added. Couple this with the fact that the noise has
large peaks that can start to compress the amplifier,
which, when combined with the high noise figure of spectrum
analyzers, results in less range available then one
might think.
What type of noise source should I choose for my
application?
If you are attempting to make a noise figure measurement,
typically you should choose a calibrated coaxial
noise source, with either 6, 15 or 30 dB ENR. This will
allow you to measure noise figure using the calibration
points provided with a noise figure meter or a spectrum
analyzer. 15 dB is the most common as it can comfortably
measure high and low noise figures. Very low noise figures
can use a 6 dB source which will have reduced
VSWR uncertainty and reduced Y factors. 30 dB sources
are used in high noise figure applications, when the noise
may be injected via a coupler, or with a high loss device.
If you are looking to make BER measurements, typically
you would want to choose a higher power noise
source like an amplified module or an instrument. This
will allow you to set carrier-to-noise ratios easier.
Although it can be done with a low power noise source,
the measurement is difficult at these low powers. Since
the BER depends primarily on the ratio of the carrier to
noise, typically the CNR is set at higher powers with a
power meter and a calibrated filter, or by measuring on a
spectrum analyzer.
Author Information
Ed Garcia is the founder of NoiseWave Corporation,
which focuses on broadband noise sources and their application.
He has 20 years of experience in RF/Microwave
and related high frequency design. He has served in the
capacity of design engineer, Chief Engineer and various
technical management positions. His primary focus has
been on noise source components and noise-based instrument
design. He can be reached by e-mail at: egarcia(at)
noisewave.com, or by telephone at 973-386-1119.
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