Application Note 1560
Author: Don LaFontaine
Making Accurate Voltage Noise and Current Noise
Measurements on Operational Amplifiers Down to
0.1Hz
Abstract
Making accurate voltage and current noise
measurements on op amps in the nano volt and femto
amp range can be challenging. This problem is often
addressed by two different approaches. Both approaches
concentrate on reducing the noise of the amplifiers used
to measure the Device Under Test (DUT). The 1
st
approach uses conventional cross-correlation techniques
to remove un-correlated noise and a procedure to
remove the correlated noise contributions made by the
amplifiers used to measure the DUT [1]. The 2
nd
approach, and the subject of this Application Note,
consists of designing a test platform with an effective
background noise at least 10dB lower than the DUT.
To obtain a test platform with this level of performance
requires: the removal of environmental electrical
disturbances, the use of batteries for low noise voltage
sources, the use of a Post Amplifier (PA) to raise the DUT
noise above the measurement system’s noise floor,
control software to measure accurate noise data down to
0.1Hz and processing software to eliminate external
noise and generate the DUT’s voltage (e
n
) and current
(i
n
) noise plots.
This Application Note will discuss the procedures used to
obtain a test platform that is capable of measuring nano
volts and femto amps down to 0.1Hz. The test platform’s
capability is illustrated by measuring the voltage and
current noise of Intersil’s ISL28190 (Bipolar inputs,
1nV/√Hz) operational amplifier and Intersil’s ISL28148
(MOS inputs, 16fA/√Hz) operational amplifier.
This Application Note will:
1. Discuss basic noise equations (external and
internal) and then use these equations to extract
the DUT noise from our test platform’s noise.
2. Discuss the use of a Post Amplifier (PA) to lower our
HP35670A Dynamic Signal Analyzer’s (DSA)
effective noise floor from 20nV/√Hz to 3nV/√Hz.
3. Illustrate the effectiveness of our Faraday cage to
remove environmental noise.
4. Discuss AC coupling of DUT, PA and DSA.
5. Determine the required gain of the DUT to enable
the test platform to measure voltage noise below
3nV/√Hz.
6. Discuss considerations for choosing the optimum
series resistor R
S
to measure current noise.
7. Discuss the Test Platform Algorithm.
8. Present conclusions.
Basic Equations For Calculating
Noise
Johnson noise is the only resistive noise source
considered in this controlled lab study. Other resistive
noise sources such as contact noise, shot noise and
parasitics associated with particular types of resistors
could also be contributing noise in an application.
A typical figure of merit for amplifier noise is noise
density. Voltage-noise density is specified in nV/√Hz,
while current-noise density is usually in units of pA/√Hz
[2]. For simplicity, these measurements are referred to
the amplifier inputs; thus removing the need to account
for the amplifiers gain.
Introduction
To measure an accurate internal noise of an Op Amp, for
a data sheet spec, two types of external noise sources
(Environmental and Johnson) must be removed from the
measurement. Environmental noise is any unwanted
signals arriving as either voltage or current, at any of the
amplifiers terminals or surrounding circuitry. It can
appear as spikes, steps, sign waves or random noise.
This noise can come from anywhere: nearby machinery,
power lines, RF transmitters, lab power supplies or lab
computers. The Environmental noise is minimized by
isolating the DUT in a Faraday cage and powering the
DUT with batteries.
The second external noise source is Johnson noise.
Johnson noise is the noise generated by the external
biasing and gain setting resistors of the DUT and test
platform. Johnson noise is subtracted out from the total
noise measurement through processing software so only
the internal noise of the DUT is reported.
External Johnson Noise
At temperatures above absolute zero, all resistances
generate Johnson noise due to the thermal movement of
charge carriers. This noise increases with resistance,
temperature and bandwidth. The voltage and current
noise are given by Equations 1 and 2 respectively
[3, 4, 5].
External Johnson Voltage Noise
V
n
=
e
n
=
4kTBR
(EQ. 1)
External Johnson Current Noise
i
n
=
4kTB
--------------
-
R
(EQ. 2)
Where:
k is Boltzmann’s constant (1.38 x 10
-23
J/K).
January 19, 2011
AN1560.1
1
CAUTION: These devices are sensitive to electrostatic discharge; follow proper IC Handling Procedures.
1-888-INTERSIL or 1-888-468-3774
|
Intersil (and design) is a registered trademark of Intersil Americas Inc.
Copyright Intersil Americas Inc. 2010. All Rights Reserved
All other trademarks mentioned are the property of their respective owners.
Application Note 1560
T is the temperature in Kelvin (273.15 + Ambient
°C).
R is the resistance (Ω)
B is the bandwidth in Hz.
Note: Bandwidth is 1Hz for all measurements and not
shown in all Equations presented in the Application Note.
1/F NOISE REGION
Internal Noise of the DUT
Figure 1 shows the internal noise of an Op Amp
referenced to the amplifiers inputs. Measurements
Referenced To
the
Input
are referred to as RTI. To
generate this curve, the external noise has been
removed from the final values shown along with any gain
the measurement circuits may have added. The internal
noise of an amplifier has two distinct frequency ranges.
At very low frequencies, the noise amplitude is inversely
proportional to frequency and is referred to as the 1/f
noise. At frequencies above the corner frequency, the
noise amplitude is essentially flat.
Equation 3 is used to calculate the total noise voltage
Referenced To
the
Output
for the basic Op Amp in
Figure 2. Measurements referenced to the output are
referred to as RTO.
e
t
=
e
n
+
(
R
S
×
i
n
)
+
(
R
1
||
R
2
×
i
n
)
+
4kT
(
R
S
+
R
1
||
R
2
) ×
A
V
(EQ. 3)
e
n
+-
+
2
2
2
CORNER
FREQUENCY
SHOT NOISE OR WHITE
NOISE FLAT BAND REGION
FIGURE 1. AMPLIFIER INTERNAL VOLTAGE NOISE
(RTI) vs FREQUENCY
R
1
R
2
-
i
n
DUT
i
n
e
t
Where:
e
t
= Total voltage noise RTO at a given frequency.
e
n
= RTI voltage-noise of DUT at a given frequency.
R
1
|| R
2
= R
1
R
2
/(R
1
+ R
2
)]Ω
i
n
= RTI current-noise of the DUT at a given frequency.
k = Boltzmann’s constant (1.38 x 10
-23
J/K).
T = Ambient temp in Kelvin (273.15 + Ambient
°C).
A
V
= Gain of Op Amp (1 + R
1
/R
2
).
R
S
A
V
= 1 + R
1
/R
2
FIGURE 2. OP AMP NOISE MODEL
Procedure to Improve the
DSA’s Effective Noise Floor
Figure 3 shows the noise floor of the HP35670A DSA
measured with the input grounded. From this graph, the
minimum noise floor is around 20nV/√Hz. A technique to
improve the measurement noise floor of the test
platform is to add a Post Amplifier to gain the noise being
measured above the noise floor of the DSA. Figure 4
shows the final test platform schematic which includes
the DSA, HA-5147 PA, DUT and the AC coupling of the
DUT offset and the PA offset voltage. Note: the HA-5147
was cherry picked for its low (11nV/√Hz at 0.1Hz) 1/f
noise performance.
FIGURE 3. NOISE FLOOR OF THE HP35670A DYNAMIC
SIGNAL ANALYZER
Intersil Corporation reserves the right to make changes in circuit design, software and/or specifications at any time without notice. Accordingly, the
reader is cautioned to verify that the Application Note or Technical Brief is current before proceeding.
For information regarding Intersil Corporation and its products, see www.intersil.com
2
AN1560.1
January 19, 2011
Application Note 1560
R
1
R
g
x 10
-
DUT
+
SW1
R
S
R
3
1000
C
2
141µF
-
PA
+
HA-5147 R
6
R
5
20k
20k
A
V
= A
PA
R
2
R
g
R
4
10
measurements down to 0.1Hz. For frequencies above
100Hz, environmental noise was not a factor for our
given lab conditions.
DSA
HP35670A
DSA NOISE
FLOOR
C
1
141µF
A
V
= A
DUT
FIGURE 4. COMPLETE LOW NOISE TEST PLATFORM
SCHEMATIC
The minimum gain of the PA is the gain that overcomes
the noise floor of the DSA down to 0.1Hz frequency.
Figure 5 shows the noise floor of the HP35670A DSA
(pink curve), the RTO noise voltage of the PA with the
gain set to 26 (blue curve), and the RTO noise voltage of
the PA with the gain set to 101 (green curve). Notice that
the gain of 26 is not enough and the PA’s RTO noise
voltage is swamped out by the DSA’s noise floor for
frequencies less than 10Hz. Setting the PA’s gain to 101
is enough to overcome the DSA noise floor by 20dB at
1kHz and 3.3 dB at 0.1Hz.
PA NOISE (RTI)
AT A
V
= 101
FIGURE 6. EFFECTIVE RTI 3nV/
√
Hz NOISE FLOOR OF
THE PA AND DSA
PA NOISE (RTO)
AT A
V
= 101
PA NOISE (RTO)
AT A
V
= 26
HA-5147 TESTED OUTSIDE
FARADAY CHAMBER
HA-5147 TESTED INSIDE
FARADAY CHAMBER
DSA NOISE
FLOOR
FIGURE 5. SETTING THE GAIN OF THE POST
AMPLIFIER TO OVERCOME THE RTO DSA
NOISE FLOOR
FIGURE 7. EFFECTS OF FARADAY CAGE ON LOW
FREQUENCY ENVIRONMENTAL BOISE
Figure 6 shows the RTI noise voltage of our PA set to a
gain of 101 (green trace) and the original DSA noise floor
(pink trace) repeated for comparison purposes. By
referencing the PA noise to the input, (dividing by
A
v
= 101) we are now able to effectively measure a flat
band RTI noise of 3nV/√Hz, which is the noise floor of
our HA-5147.
AC Coupling of the Post Amp
and the DUT
The output of the PA and DUT need to be AC coupled to
avoid over-driving the DSA’s input or railing the output of
the PA, as a result of the DC offset caused by VOS and Ib
(reference Figure 4). The subsequent measurements
were performed on the PA and DSA to minimize any
errors before measuring any noise on the DUT.
Initially, the test platform used the internal AC coupling of
the HP35670A DSA. Test results at frequencies below 10Hz
were artificially low, when compared to the expected
results for HA-5147 at 1Hz. The cause of the error was
determined to be the internal AC coupling circuitry of our
DSA. Figure 8 shows the effective roll-off in gain of the
DSA’s internal AC coupling circuit (red trace) compared to
the roll-off in gain when using an external AC coupling
AN1560.1
January 19, 2011
Faraday Cage to Remove
Environmental Noise
Figure 7 shows the result of testing an HA-5147
(A
v
= 101) inside and outside our Faraday cage. The
Faraday cage enables us to maintain a noise floor of
3nV/√Hz over an additional decade of frequency in the
flat band region. For frequencies below 100Hz, the
improvement in the noise floor is critical in making noise
3
Application Note 1560
circuit (blue trace). The curves were generated by taking
3 measurements, with the goal of detecting amplitude
loss. The input signal was a 2mV
P-P
sine wave. The 1st
measurement was with the DSA DC coupled to get the
base line. The 2nd was measured using the DSA’s
internal AC coupling and the 3rd was with an external AC
coupling. The AC loss was determined by the ratio of the
AC amplitude to the DC amplitude (normalized to zero).
noise floor in the flat band range to 0.3nV/√Hz, which
meets our requirement of 10dB higher than the systems
noise floor. Before committing to running the full battery
of sweeps to average out the readings, we 1st run a
single sweep (SW1, Figure 4 closed) to verify the 1/f
noise is not being swamped out by the 100nV/√Hz noise
floor of the test platform at 0.1Hz. If so, then the gain of
the DUT needs to be increased to insure the
measurement is not that of the test system’s noise floor.
DSA INTERNAL DC COUPLED WITH
EXTERNAL AC HIGH-PASS FILTER (0.05Hz)
INPUT/OUTPUT AC COUPLED 1 MIN SETTLE TIME
DSA INTERNAL AC COUPLED
INPUT/OUTPUT AC COUPLED 30 MIN
SETTLE TIME
The built-in AC coupler of the DSA (Agilent 35670A)
is inadequate at frequencies below 1Hz. A high pass
filter, made up of a 141µF capacitor and a 20k
resistor, is used instead
FIGURE 8. EFFECT OF DSA’s INTERNAL AC COUPLING
vs EXTERNAL AC COUPLING ON THE PA’s
LOW FREQUENCY GAIN
FIGURE 9. EFFECTIVE RTI NOISE FLOOR OF THE
PA-DSA WITH EXTERNAL AC COUPLING
The results show the gain of the signal cannot be
considered constant for frequencies below 10Hz when AC
coupled via the DSA or 0.5Hz when externally AC
coupled with the C
2
and R
6
in Figure 4. This error in gain
accounted for the lower than expected calculated noise.
The final solution was to go with the external AC coupling
(DSA DC coupled) and account for the drop in the gain by
performing gain measurements for each frequency of the
PA across the entire frequency range. Through software,
the individual gain values were subsequently used in the
calculation for the RTI current and voltage noise of the
DUT for each frequency plotted in the curve.
Figure 9 shows the final optimized noise floor of the
PA-DSA (blue trace) and the effect of the RC time
constant of the external AC coupling circuit (pink trace).
Because of the long RC time constant of the external
filter (20kΩ and 141µF) we need to allow time for the
coupling circuit to settle out before starting to test. The
pink curve is the noise measurement of the HA-5147
1 minute after power is applied to the PA. The blue trace
is the same measurement after waiting 30 minutes for
the circuit to settle out.
Considerations for Choosing
the Series Resistor to Measure
the Current Noise
The goal of selecting the value for R
S
is to make it as
large as possible to raise the DUT’s input current noise
(dropped across R
S
) above the background and R
S
voltage noise, all without driving the DUT’s output
voltage into the rails or limiting the noise bandwidth of
the amplifier. Reference the section titled “Measurement
Algorithm” for the details of the process to measure
current noise and then voltage noise of the DUT.
Figure 10 illustrates the voltage noise power relationship
between the 4kTR
S
and the product of R
S2
i
n2
(reference
Equations 4 and 5).
Johnson Voltage Noise of R
S
:
V
n
=
4kTR
S
→
V
n
=
4kTR
S
2
(EQ. 4)
Johnson Current Noise contribution of R
S
:
V
n
2
=
R
S
i
n
2 2
(EQ. 5)
Determining the Required Gain
of the DUT
The optimized noise floor of the PA-DSA is 100nV/√Hz at
0.1Hz and 3nV/√Hz in the flat-band range (Figure 9).
Measuring the noise of an amplifier like the ISL28190
(Bipolar inputs, 1nV/√Hz), is achieved by gaining up the
output of the DUT by 10. This will lower the effective
Figure 10 can be used as a tool for selecting the value of
the R
S
resistor. The almost diagonal curve in Figure 10 is
the 4kTR
S
Johnson noise. The other parallel lines are the
(R
S2
I
n2
) current noise contributions. A good starting
point is to choose a value of R
S
that results in the current
noise contribution being larger than the Johnson noise
contribution.
4
AN1560.1
January 19, 2011
Application Note 1560
Notice in Figure 10, that the current noise contribution
(R
S2
I
n2
) is very small at low resistances in comparison
with the dominant 4kTR
S
noise. At higher values of R
S
,
the squared function of the noise current quickly makes it
the dominant noise source.
R
S
VALUES USED FOR
BIPOLAR DEVICES
R
S
VALUES USED
FOR MOS DEVICES
FIGURE 11. SPECTRAL VOLTAGE NOISE DENSITY OF
DUT, PA vs R
S
vs 4kTR
S
FIGURE 10. TOOL FOR SELECTING R
S
RESISTANCE VALUE
At some point the product R
S2
I
n2
magnitude becomes
high enough to raise it above background noise and
make it a measurable signal. Preferably, the value of R
S
should be chosen in a way that R
S2
I
n2
≥
4kTR
S
, but
that is not always possible. There is an upper limit to the
value of R
S
upon which leakage resistance degrades
accuracy of the measurement. This typically occurs for
R
S
values greater than 5MΩ. To measure noise currents
in the 10’s of femto amps requires a large number of
averages to smooth out the data. The data presented in
this Application Note for the ISL28148 went through the
process of averaging each frequency measurement 500
times, then repeating this process 10 times and
averaging the corresponding measurements to obtain
one value per frequency plotted. The theory of this
process is not covered in this Application Note, and is the
subject of another Application Note.
Based on empirical results, the value of the R
S
resistor
depends upon the Bias current (I
b
) of the device. For
Bipolar input devices with I
b
in the µA range, R
S
is 10kΩ
and 100kΩ for I
b
in the pA range. For MOS input devices,
R
S
is 5MΩ with I
b
in the f
A
range. The following two
graphs further demonstrate the signal to noise
improvement in both e
n
and i
n
as R
S
is increased.
Figure 11 shows the spectral voltage noise (e
n
) of the
DUT (HA-5147, A
V
= 1) and PA (HA-5147, A
V
= 101)
with different values of R
S
. The 4kTR
S
is also plotted to
show when the voltage noise level is above the
background noise of the 4kTR
S
value. From this
spectrum, the 1kΩ value of R
S
cannot resolve voltage
noise from the 4kTR
S
, where as the 100kΩ R
S
generates
very clean and accurate results for voltage noise.
i
n
(R
S
= 1k)
i
n
(R
S
= 10k)
i
n
(R
S
= 100k)
FIGURE 12. SPECTRAL CURRENT NOISE DENSITY OF
DUT, PA vs R
S
Figure 12 shows the calculated current noise (i
n
) for
three different R
S
values. The current noise was
calculated using Equation 10. From this spectrum, we
see the same results as with the voltage noise spectrum
in Figure 11. The 1kΩ value of R
S
cannot resolve current
noise from the 4kTR
S
, where as the 100kΩ R
S
generates
very clean and accurate results for current noise.
Measurement Algorithm
Now that our Test Platform’s noise floor is optimized for
our DSA, PA and DUT, it’s time to discuss the Test
Platform’s algorithm. Back in the “Basic Equations For
Calculating Noise” section, Equations 3 was used
calculate the total noise voltage referenced to the output
for the basic Op Amp in Figure 2. The total voltage noise
of a basic Op Amp is made up of three components: (A)
Internal voltage noise of the DUT, (B) External voltage
noise as a result of the current noise through the
resistors and (C) External Johnson noise of the resistors.
Equation 6 is the same as Equation 3 but with the three
components of noise replaced with “A”, “B” and “C”.
5
AN1560.1
January 19, 2011
微控制器 MCU
京公网安备 11010802033920号
Copyright © 2005-2026 EEWORLD.com.cn, Inc. All rights reserved
电子工程世界
