Noise Analysis in Precision Analog Designs
This white paper is an executive summary of a webcast of the same title on June 1, 2016, sponsored by Analog
Devices and Avnet.
Introduction
There are articles explaining component-level
noise analysis for amplifiers or for analog-to-digital
converters (ADCs), but very few that explain how to
budget noise or analyze noise from the system
level. This paper reviews the basics of noise analysis
in precision designs, relates those calculations to
system-level specifications such as sensitivity,
dynamic range, and resolution, and answers some
of the big questions about low-noise design
N
oise is a central topic in analog design, but
unfortunately there is a large amount of
confusion and misinformation regarding noise.
In broad terms, the noise of a circuit affects its
precision, its accuracy, and sets the limit for the
smallest signal that can be measured. It is important
not only to reinforce the basics of noise in order to
successfully design sensitive analog circuits, but also to
relate them to the specifications of the end system in
order to make them more meaningful.
A popular definition of noise is: any unwanted signal
that interferes with the measured value of the signal of
interest. This is a very broad definition, encompassing
DC or AC noise sources, intrinsic or extrinsic, random or
repeatable, reducible or irreducible. To constrain this
definition further, random noise can be defined as
anything that interferes with the repeatability of the
measurement. Random noise is what puts a limit on the
smallest signal that can be measured in the system.
Noise is generated in all components of a circuit,
including the sensor, amplifiers, converters, digital
processing, transmitters or radios, and power supplies.
Noise can also be coupled in from the outside world.
Extrinsic Noise vs Intrinsic Noise
It is important to make the distinction between
extrinsic noise, which comes in to the circuit from the
outside, and intrinsic noise, which is generated within
the circuit. There is a gray area here, for example, if a
power supply ripple is coupled into the circuit through
the finite power-supply rejection ratio of an amplifier, the
noise source is external to the signal path, but internal
to the whole circuit. For the purpose of this discussion,
this can be considered extrinsic noise because the power
supply ripple comes into the signal path from the outside
and it can be reduced.
Extrinsic noise requires three elements: a source of the
noise, a coupling path into the circuit, and a receiver,
which is generally a sensitive node in the signal path.
Extrinsic noise is often at discrete frequencies and may
be intermittent. Extrinsic noise is difficult to calculate in
most cases, but generally it is reducible, meaning it can
be mitigated by good circuit design practice, such as
proper grounding techniques, shielding, layout, and
decoupling.
Intrinsic noise, on the other hand, is generated within
the signal path of the circuit. In many cases, the intrinsic
noise is caused by fundamental physical properties, such
as the random thermal movement of particles. In these
cases, the intrinsic noise is not reducible for a given
frequency, and is spread out across a wide range of
frequencies. This irreducible source of noise sets the limit
for the smallest signal that can be measured, assuming
the right design choices were made to reduce the
extrinsic noise.
The Units of Noise
Figure 1 describes several units that are used to
specify noise; specifically, peak-to-peak noise, rootmean-square (RMS) noise, and noise spectral density
(NSD). Peak-to-peak noise depends on just two points in
an entire waveform, and those two points are outliers.
The peak-to-peak noise is not a very repeatable
measurement, and it is dependent on the bandwidth of
the circuit. It is useful in certain situations, such as
comparing against a converter input range in an
oversampled system with high gain. RMS noise is
dependent on all of the points in the waveform, and is
related to the noise power, which is much more
predictable and much easier to quantify. Like the peakto-peak noise, the RMS noise is also dependent on the
bandwidth of the circuit.
The NSD removes the bandwidth as a factor by
normalizing the RMS noise for a 1Hz-wide frequency
band for all points along the frequency spectrum. NSD is
difficult to measure, but it is the most general because it
can be used to determine the RMS noise of the circuit for
any frequency range. More specifically, the RMS noise of
a circuit with a spectrally flat NSD is equal to the NSD
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times the square root of the noise equivalent bandwidth
(NEB). The NEB is the theoretical brick-wall filter that
would let in the same total noise as the real filter. For a
single pole filter, the NEB is 1.57 times the -3dB
bandwidth, and the NEB can be looked up for various
types of higher-order filters.
Combining Noise Sources
When combining the various noise sources in the
circuit into a total noise value, there are some common
problems that must be avoided. First is matching the
units. It’s usually preferable to use RMS noise rather
than NSD because RMS noise has already taken
bandwidth into account and some noise sources may
have different bandwidths than others. Whatever units
are chosen, it is important to be consistent throughout
the calculation in order to avoid errors. Second, refer
noise sources to the same point in the circuit. Noise is
usually referred to the input of the circuit (RTI)
because that allows the noise to be compared directly
against the signal, but in some cases it is referred to
the output (RTO). Whether the calculation is RTI or
RTO, use the gain or propagation of gains through the
circuit to refer all noise sources to the same point
before combining them. For example, if a noise source
at the output of a gain stage is calculated (RTO), but
the noise will be combined with other sources at the
input of the gain stage (RTI), then the RTO noise
source should be divided by the gain to get the
equivalent RTI noise. Third, the noise power adds
directly, which means the noise voltage adds as the
root sum of squares (RSS).
Common Types of Intrinsic Noise
There are many types of intrinsic noise, but most
engineers will only use a few of these types in day-today analysis. Voltage noise is associated mainly with op
amps and other types of amplifiers. It is a noise voltage
modeled in series with the amplifier input. Voltage noise
does not scale with the source resistance, which is
defined as the total resistance that is presented to the
input of that amplifier by the sensor or external
resistors. Current noise, on the other hand, is a noise
current generated at the input of a device. The current
noise generates a voltage as it flows through the source
resistance, in accordance with ohms law. The NSD curve
starts to climb upward at very low frequencies. The noise
in this region where the NSD is increasing for lower
frequencies is the 1/f noise; so named because the slope
of the noise power is approximately 1/f. White noise, or
broadband noise, is the term for the region with flat NSD
at the higher frequencies of the NSD curve. Johnson
noise, also called thermal noise or resistor noise, is a
source of noise in all resistors associated with the
random thermal motion of electrons in the resistive
material. Other types of noise, encountered less
frequently, include quantization noise, shot noise,
popcorn noise, and avalanche noise.
Component Noise: Resistors, Amplifiers, and ADCs
The equation for the RMS noise of a resistor R over a
bandwidth B is √(4kTRB), as shown in Figure 3, where k
is Boltzmann’s constant and T is the temperature in
Kelvin. The bandwidth, B, is often taken to be 1Hz, which
changes the result to NSD rather than RMS noise. Two
useful shortcuts to this equation are that at 25°C, 1Ω is
about 0.128 nV/√Hz and that 1kΩ is about 4nV/√Hz.
Then the noise scales with the square root of the
resistance, for example, 100Ω has an NSD of
1.28nV/√Hz. Although temperature is a factor in this
equation, it is rarely an important factor, since a
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Figure 2. Combining multiple noise sources in a circuit.
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temperature increase from 25°C to 85°C only produces a
10% increase in noise.
Amplifiers and converters specify noise differently.
Amplifier data sheets typically provide a voltage noise
and a current noise. The voltage noise specification will
be the NSD in the flat band region, 1kHz or higher, and
often a peak-to-peak noise from 0.1Hz to 10Hz to
indicate the 1/f noise level. Current noise is typically
specified as a flat band NSD and only occasionally as a
peak-to-peak value from 0.1Hz to 10Hz.
ADC datasheets usually specify signal-to-noise ratio
(SNR) with a nearly full-scale signal applied, or in some
cases RMS noise is specified directly. Converting the ADC
noise component to RMS is very useful to compare to the
other noise sources in the signal chain. Signal-to-noise
ratio is the RMS input range divided by RMS noise.
Rearranging the equation, the RMS noise can be obtained
by dividing the RMS input range (the analog input range
divided by 2√2) by the SNR converted to V/V.
The source resistance in front of an amplifier is what
translates voltage noise and current noise, and allows
them to be combined. Therefore the value of the source
resistance is needed in order to determine the total noise
of an amplifier circuit. The noise component caused by
the current noise increases proportional to the source
resistance, so the current noise will dominate for high
source resistance. If the current noise dominates, a
lower-current-noise amplifier, such as a FET input, can
usually be found. For very low source resistance, voltage
noise becomes the dominant factor for the noise. If the
voltage noise dominates, a low voltage noise amplifier
should be chosen, but the designer should be aware that
the tradeoff to get lower voltage noise is generally higher
power consumption. There may be a point for medium
source resistances where the thermal noise of the source
resistance itself is the dominant noise component, in
which case the best way to reduce the noise is to reduce
the source resistance if that is possible.
DESIGNING A SYSTEM FOR NOISE
PERFORMANCE
From a system level, a few terms must be defined in
order to determine what it means to optimize the noise
of a system. These are resolution, dynamic range, and
sensitivity. Different systems will optimize one or the
other of these parameters, for example one might
sacrifice dynamic range to get higher sensitivity. This
section quotes the definitions obtained from test and
measurement companies, please see the webcast for the
sources that are referenced.
There is more than one answer to the question of how
low the noise needs to be in an analog design. In many,
but not all cases, the system is designed for the best
possible noise performance in the target category, but
there are always constraints to observe in a real world
system. These constraints include power, performance,
cost, and complexity. Many of these constraints will
tradeoff directly or indirectly against the noise, so it is
critical to understand the tradeoffs from a cost and
benefit perspective in order to successfully design a low
noise system. Even in other cases, where there is a
definite noise level below which the system noise is good
enough and there is no benefit to designing for the
lowest possible noise, the correct tradeoffs must be
made.
Definitions in System Noise
Resolution is defined as the total number of discrete
levels that can be detected by the instrument. The
resolution is specified in units of bits, counts, or digits,
depending on the output of the instrument. This is fixed
by the ADC in the device, so it does not depend on the
noise. Effective resolution, on the other hand, depends
on the noise, and can be defined as the smallest portion
of the input signal change that the instrument can detect
reliably.
Sensitivity refers to the smallest change in the
measurement that can be detected. The sensitivity of
the instrument is specified in units of the measured
value such as volts, ohms, amps, or degrees. To quote
Keysight: “Whereas resolution is a measure of the
smallest change in the output (or indication) that is
possible, sensitivity refers to the smallest change in the
input (or stimulus) that causes a discernible change in
the output.”
Dynamic range is the ratio of the maximum level of a
3
parameter to the minimum detectable value of that
parameter. Dynamic range relates the full-scale signal
range to the sensitivity of the device, and is generally
specified in dB. It is often synonymous with the
effective resolution.
System Noise Considerations
Figure 4 shows an example signal chain where
different noise sources have different noise equivalent
bandwidth (NEB). In such cases, the NSD of each
source cannot be added together. The RMS noise must
be used instead because the bandwidths for each noise
source are taken into account separately. The smallest
NEB after the noise source is used for noise calculation.
To see why that is, consider the gain amp at the left,
which is generating noise across its full 50kHz
bandwidth, but the noise between 1kHz and 50kHz is
filtered out in the Sallen-Key filter that follows, so the
total noise is only affected by the noise generated by
the gain amplifier from dc to 1kHz. Looking only at the
NSD of these components, it appears that the gain
amplifier, which is 300 nV/√Hz RTO, should dominate
the total noise. This is misleading because the gain
amplifier has the smallest bandwidth, and in fact, all of
the noise sources have similar RMS noise values once
the NEB of each stage is taken into account.
A common question to consider for noise
performance is how much gain to take and where to
take it. The usual answer is to take as much gain as
possible as early as possible in the signal chain. But
what is the effect of taking gain? Gain reduces the
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Figure 4. Considering noise source density in system design.
contribution of the noise sources after the gain stage,
but at the same time it makes the input range smaller.
To elaborate, the input signal range is the ADC input
range divided by the gain, which is the reason
increasing the gain reduces the input signal range.
Noise sources after the gain stage are divided by the
gain when they are referred to input to compare to the
signal. In other words, higher gain increases the signal
amplitude at the output of the gain stage, but it does
not affect the noise sources after the gain stage, so the
signal is stronger relative to the noise. Because of
these two effects of taking gain, it is apparent that at
low values of gain where the output noise sources are
dominant, the dynamic range is constant, but the
sensitivity improves with increasing gain. At higher
gains where the input noise sources are dominant, the
sensitivity is constant, so the dynamic range goes
down inversely proportional to the gain. Though this
may sound like it sets a maximum useful level for the
gain, keep in mind the components after the gain stage
aren’t necessarily fixed. When dynamic range is not
critical, high gain can be taken and cheaper, lower
power, and noisier devices can be used after the gain
stage without affecting the noise performance.
Be clear about the benefits of a trade-off. The most
commonly over-designed component in a signal chain
is the ADC driver. The datasheet might suggest to use
an ADC driver amplifier with 1/10th the noise of the
ADC. This makes sense when measuring the
performance of the ADC, but most circuits are not
designed to benchmark the ADC performance. While
it’s true that there is 3dB more noise in a system where
the ADC driver and the ADC have the same noise, the
first-order relationship is that amplifier noise goes
down with the square root of power, meaning it might
take 100 times more power to choose an amplifier with
1/10th the noise of the ADC, and the benefit is only
3dB improvement in noise. Instead of making design
choices this way, keep the system goals in mind. For
example, in a sensor interface design, start with the
sensor and make the tradeoffs that give the best
representation of the sensor signal within the design
criteria.
A Low Noise Design Flow
For a simple signal chain in the case where the input
signal is known, a low noise design flow can be defined
as follows: first, know the signal characteristics,
including the maximum signal range, frequency range,
View the original webcast at www.analog.com/en/education/education-library/webcasts/
noise-analysis-in-precision-analog-designs.html.
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noise, and source impedance. Then, set the desired
filter frequencies, setting the pass band as small as
possible without affecting the signal in order to
minimize out-of band noise. Third, calculate the sensor
noise and choose the input amplifier based on noise
and any other design criteria, such as errors, power,
function, and configuration of the device. Fourth,
choose the gain and determine the noise requirements
and other requirements for the output circuitry. Finally,
choose real output components, re-adjusting the gain
as necessary to match requirements. In this way, it is
possible to arrive quickly at a design with excellent
noise performance without overdesigning, as shown in
the step-by-step example in this webcast.
Author/Presenter Scott Hunt is a system
applications engineer specializing
in precision instrumentation in
the Linear & Precision Technology
Group of Analog Devices in
Wilmington, MA. Scott joined
Analog Devices in 2011 as a
product applications engineer for
high-performance integrated
precision amplifiers such as
instrumentation amplifiers. He has a Bachelor's degree
in electrical and computer systems engineering from
Rensselaer Polytechnic Institute. Scott has authored
content in trade publications worldwide, and has
traveled internationally to present at technical
conferences.
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