AN-940
APPLICATION NOTE
One Technology Way • P.O. Box 9106 • Norwood, MA 02062-9106, U.S.A. • Tel: 781.329.4700 • Fax: 781.461.3113 • www.analog.com
Low Noise Amplifier Selection Guide for Optimal Noise Performance
by Paul Lee
INTRODUCTION
When evaluating an amplifier’s performance for a low noise
application, both internal and external noise sources must be
considered. This application note briefly discusses the funda-
mentals of both internal and external noise and identifies the
tradeoffs associated in selecting the optimal amplifier for low
noise design.
Noise from surrounding circuit components must be accounted
for. At temperatures above absolute zero, all resistances act as
noise sources due to thermal movement of charge carriers called
Johnson noise or thermal noise. This noise increases with resis-
tance, temperature, and bandwidth. Voltage noise is shown in
Equation 1.
V
n
½
4
kTBR
(1)
EXTERNAL NOISE SOURCES
External noise includes any type of external influences, such
as external components and electrical/electromagnetic interfer-
ence. Interference is defined as any unwanted signals arriving
as either voltage or current, at any of the amplifier’s terminals
or induced in its associated circuitry. It can appear as spikes,
steps, sine waves, or random noise. Interference can come from
anywhere: machinery, nearby power lines, RF transmitters or
receivers, computers, or even circuitry within the same equip-
ment (that is, digital circuits or switching-type power supplies).
If all interference is eliminated by careful design and/or layout
of the board, there can still be random noise associated with the
amplifier and its circuit components.
where:
V
n
is voltage noise.
k
is Boltzmann’s constant (1.38 × 10
−23
J/K).
T
is the temperature in Kelvin (K).
B
is the bandwidth in hertz (Hz).
R
is the resistance in ohms (Ω).
Current noise (noise associated with current flow) is shown in
Equation 2
I
n
½
4
kTB
R
(2)
where:
I
n
is current noise.
k
is Boltzmann’s constant (1.38 × 10
−23
J/K).
T
is the temperature in Kelvin (K).
B
is the bandwidth in hertz (Hz).
R
is the resistance in ohms (Ω).
Rev. D | Page 1 of 12
AN-940
TABLE OF CONTENTS
Introduction ...................................................................................... 1
External Noise Sources .................................................................... 1
Internal Noise Sources ..................................................................... 3
Input-Referred Voltage Noise ..................................................... 4
Input-Referred Current Noise .................................................... 4
Flicker Noise.................................................................................. 5
Application Note
Popcorn Noise ...............................................................................5
Summing the Noise Sources ........................................................5
Noise Gain ......................................................................................6
Selecting Low Noise Op Amp ..........................................................7
Conclusion..........................................................................................9
References ........................................................................................ 12
Rev. D | Page 2 of 12
Application Note
Resistors
For the purposes of this application note, the resistor noise is
limited to thermal (Johnson) noise. To keep a low level of this
type of noise, resistance values should be as low as possible
because RMS voltage of thermal (Johnson) noise is proportional
to the square root of the resistor value. For example, a 1 kΩ
resistor has a thermal noise of ~4 nV/√Hz at room temperature.
For an in-depth analysis and low noise designs, other types of
resistor noise should be accounted for, such as contact noise
and shot noise. A few practical notes follow and they should
be considered when selecting a resistor.
AN-940
INTERNAL NOISE SOURCES
Noise appearing at the amplifier’s output is usually measured as
a voltage. However, it is generated by both voltage and current
sources. All internal sources are generally referred to the input,
that is, treated as uncorrelated or independent random noise
generators in series or in parallel with the inputs of an ideal
noise-free amplifier (see Figure 1). Because these noise sources
are considered random and/or exhibit Gaussian distribution
behavior, it is important to take proper care when summing the
noise sources as discussed in the Summing the Noise Sources
section.
If the same noise appears at two or more points in a circuit (that
is, input bias current cancellation circuitry), the two noise sources
are correlated noise sources and a correlation coefficient factor
should be included in the noise analysis. Further analysis of
correlated noise is limited in this application note as typical
correlation noise sources are less than 10% to 15% and they
can usually be disregarded.
Internal amplifier noise falls into four categories:
Choose the largest practical wattage resistors, as the contact
noise is decreased with a larger volume of material.
Choose low noise resistive element material
Resistive elements composed of pure metals and/or
metal alloys in bulk exhibits low noise characteristics.
Such as Vishay Bulk Metal® foil technology resistors
(such as, S102C, Z201)
Wirewound technology resistors composed of metal
alloys have similar noise characteristics as Bulk Metal
foil technology, but are much more inductive.
Metal film technology resistors as thin film are noisier
than Bulk Metal foil or wirewound technology resistors
because of significant noise contributions from occlusions,
surface imperfections, and nonuniform depositions.
Thick film and carbon composition resistors are the
nosiest resistors.
Input-referred voltage noise
Input-referred current noise
Flicker noise
Popcorn noise
Reactances
Reactances, such as capacitors and inductors, do not generate
noise, but the noise current through reactances develops noise
voltage as well as the associated parasitic.
Practical Tips
Output noise from a circuit can be reduced by lowering the
total component resistance or by limiting the circuit bandwidth.
Temperature reduction is generally not very helpful unless a
resistor can be made very cold, because noise power is propor-
tional to the absolute temperature,
T(x)
in Kelvin =
x°C
+ 273.15°
(3)
All resistors in a circuit generate noise. The effect of generated
noise must always be considered. In practice, only resistors in
the input and feedback paths (typically in high gain configu-
rations) are likely to have an appreciable effect on total circuit
noise. The noise can be considered as coming from either
current sources or voltage sources (whichever is more conve-
nient in a given circuit).
Input-referred voltage noise and input-referred current noise
are the most common specifications used for amplifier noise
analysis. They are often specified as an input-referred spectral
density function or the rms noise contained in Δf bandwidth
and usually given in terms of nV/√Hz (for voltage noise) or
pA/√Hz (for current noise). The /√Hz is needed because the
noise power adds with (is cumulative over) bandwidth (Hz) or
the voltage and current noise density adds with square root of
the bandwidth (√Hz) (see Equation 1 and Equation 2).
e
n
–+
R
S
–
+
i
n
i
n
Figure 1. Op Amp Noise Model
Rev. D | Page 3 of 12
07053-001
R
2
R
1
AN-940
INPUT-REFERRED VOLTAGE NOISE
Input-referred voltage noise (e
n
) is typically viewed as a noise
voltage source.
Voltage noise is the noise specification that is usually empha-
sized; however, if input impedance levels are high, current noise
is often the limiting factor in system noise performance. It is
analogous to offsets, where the input offset voltage often bears
the blame for output offset, when in reality the bias current
causes the output offset where input impedances are high.
Note the following points about input-referred voltage noise:
Application Note
INPUT-REFERRED CURRENT NOISE
Input-referred current noise (i
n
) is typically seen as two noise
current sources pumping currents through the two differential
input terminals.
Shot noise (sometimes called Schottky noise) is current noise
due to random distribution of charge carriers in the current flow
through a potential barrier, such as a PN junction. The shot
noise current, i
n
, is obtained from the formula
i
n
½
2
I
B
qB
where:
I
B
is the bias current in ampere (A).
q
is the electron charge in coulomb (1.6 × 10
−19
C).
B
is the bandwidth in hertz (Hz).
The current noise of a simple bipolar and JFET op amp is typically
within 1 dB or 2 dB of the shot noise of the input bias current.
This specification is not always listed on data sheets.
Note the following points regarding input-referred noise:
The current noise of typical bipolar transistor op amps,
such as the
OP27,
is about 400 fA/√Hz, where I
B
is 10 nA,
and does not vary much with temperature except for bias,
current-compensated amplifiers.
The current noise of JFET input op amps (such as the
AD8610:
5 fA/√Hz at I
B
= 10 pA) while lower, doubles
for every 20°C chip temperature increase, because JFET
op amp bias currents double for every 10°C increase.
Traditional voltage feedback op amps with balanced inputs
usually have equal (correlated and uncorrelated) current
noise on both their inverting and noninverting inputs.
Many amplifiers, especially those amps with input bias
current cancellation circuits, have considerably larger
correlated than uncorrelated noise components. Overall,
noise can be improved by adding an impedance-balancing
resistor (matching impedances on both positive and
negative input pins).
(4)
Op amp voltage noise can be lower than 1 nV/√Hz for the
highest performance amplifiers.
Although bipolar op amps traditionally have less voltage
noise than FET op amps, they also have substantially
greater current noise.
Bipolar amplifier noise characteristics are dependent on
the quiescent current.
Present day FET op amps are capable of obtaining both low
current noise and voltage noise similar to bipolar amplifier
performance, though not as low as the best bipolar input
amplifiers.
Rev. D | Page 4 of 12
Application Note
FLICKER NOISE
The noise of op amps is Gaussian with constant spectral density
(white noise), over a wide range of frequencies. As frequency
decreases, the spectral density starts to rise because of the fabri-
cation process, the IC device layout, and the device type at a
rate of about 3 dB per octave for CMOS amplifiers, 3.5 dB to
4.5 dB per octave for bipolar amplifiers, or up to 5 dB per
octave for JFET amplifiers.
This low frequency noise characteristic is known as flicker
noise or 1/f noise because the noise power spectral density
goes inversely with frequency (1/f). It has a −1 slope on a log
plot. The frequency at which an extrapolated −3 dB per octave
(for a CMOS-type amplifier) spectral density line intersects the
broadband constant spectral density value is known as the 1/f
corner frequency and is a figure of merit for the amplifier (see
Figure 2). Bipolar and JFET amplifiers typically have lower 1/f
corner frequency than CMOS amplifiers.
100
AN-940
POPCORN NOISE
Popcorn noise (not specified or advertised) is an abrupt shift in
offset voltage or current lasting for several milliseconds with
amplitude from several microvolts to hundreds of microvolts.
This burst or pop is random. Low temperatures and high source
resistances usually produce the most favorable conditions for
popcorn noise. Although the root cause of popcorn noise is
not absolute, both metallic contamination and internal or
surface defects in the silicon lattice can cause popcorn noise
in ICs. Although considerable work has been done to reduce
the sources of popcorn noise in modern wafer fabrication, it
cannot be eliminated. Further analysis of popcorn noise is
beyond the scope of this application note.
SUMMING THE NOISE SOURCES
If the noise sources are uncorrelated (that is, one noise signal
cannot be transformed into the other), the resulting noise is
not their arithmetic sum, but the square root of the sum of
their squares.
V
ni
,
TOTAL
½
(
e
n
)
2
(
R
S
i
n
)
2
V
n
(
R
EX
)
2
(5)
VOLTAGE NOISE (nV/√Hz)
EXTRAPOLATED 1/f
SPECTRAL NOISE DENSITY
10
1
EXTRAPOLATED
CONSTANT SPECTRAL
NOISE DENSITY
1/f CORNER FREQUENCY
where:
V
ni, TOTAL
is the total noise referred-to-input (RTI).
e
n
is input-referred voltage noise.
i
n
is input-referred current noise.
R
S
is an equivalent source or input resistance to the amplifier.
V
n
(R
EX
)
is voltage noise from external circuitry.
Note the following:
1k
10k
07053-005
0.1
0.1
1
10
100
FREQUENCY (Hz)
Figure 2. Spectral Noise Density
Any resistance in the noninverting input has Johnson noise
and converts current noise to a voltage noise.
Johnson noise in feedback resistors can be significant in
high resistance circuits.
Figure 3 visually shows the Equation 5 as the summation of
vectors by using the Pythagorean Theorem.
V
ni, TOTAL
V
n
(R
EX
)
07053-006
R
S
×
i
n
e
n
Figure 3. Vector Summation of Noise Sources
Rev. D | Page 5 of 12
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