Vol 54 No 1, February 2020
RAQ Issue 174:
Current Noise in FET
Input Amps
Kaung Win,Senior Field Applications Engineer
Question:
input amplifiers—for example, 1/f or flicker noise component and flat wideband
component, as shown in Figure 1. This is not the case in FET input amps; rather,
in Figure 2, it looks like a bizarre noise shape that is not well known and is
ignored in many simulation models.
Why is my design noisier at higher frequencies?
Input Current Noise (pA Hz)
1k
Answer:
100
10
1
Many semiconductor manufacturer data sheets, including ADI’s, specify the current noise of an amplifier in the specification tables, typically at a frequency of
1 kHz. It isn’t always clear where the current noise specifications come from. Is it
measured or is it theoretical? Some manufacturers are transparent in how they
come up with this number by providing an equation of
in = √2qib
(1)
known as the shot noise equation. Historically, ADI had provided most current
noise numbers this way. Does this calculated number hold up to 1 kHz for
every amplifier?
Over the past few years, there has been a growing interest regarding current
noise over frequency in amplifiers. Some customers—as well as manufacturers—
assume that current noise for FET input amps follows a similar shape as bipolar
VISIT ANALOG.COM
1
10
100
1k
10k
100k
1M
10M
100M
1G
Frequency (Hz)
Figure 1. Current noise of AD8099, a bipolar input amplifier.
1k
Current Noise (fA Hz)
The phenomenon of current noise increasing with frequency is well known to
IC design engineers and circuit designers, but it was elusive to many engineers
as a result of either too few articles in the field or incomplete information from
manufacturers.
100
10
1
0.01
0.1
1
10
100
Frequency (Hz)
Figure 2. Current noise of AD8065, a FET input amplifier.
1k
10k
100k
Linear Regulator
LT3045
Cookie Tin
DC417 Board
+20 V
Linear
Lab Supply
VCC
+ U1
GND
–20 V
Ohmite, HVC1206Z1008KET
Vout
SR785
DC to 100 kHz DSA
– DUT
VEE
10 GΩ
1 mHz Passive
High-Pass Filter
Cin
Cin_dut + Cstray
Linear Regulator
LT3094
Figure 3. Measurement setup.
The DC417B single amplifier evaluation board may be used. The power supplies
to the device under test (DUT) must be low noise and low drift. Linear supplies
are preferred over the switching supplies so that any supply variation, such as
switching artifacts, does not add to the measurement. The LT3045 and LT3094,
positive and negative ultrahigh PSRR, ultralow noise linear regulators, may be
used to further reduce the ripple from the linear supply. Using the LT3045 and
LT3094, a single resistor can be used to configure any output voltage necessary
up to +15 V and down to –15 V. These two parts are ideal bench top supplies for
low noise measurements.
A 10 GΩ SMT resistor from Ohmite (HVC1206Z1008KET) was used to convert
current noise to voltage noise at the noninverting pin of the DUT. Typical bias
current of FET input amps is about 1 pA, which equals 0.57 fA/√Hz
10k
1k
10
1
Ratio of Value 1 to Value 2
Table 1. RSS Addition Based on the Ratio of Two Numbers
Value 1
(2)
(3)
(4)
and it can be subtracted out in postprocessing. However, it becomes impossible to
measure accurately if the resistor current noise dominates the current noise of the
DUT. So, we would need a resistor value of at least 10 GΩ to see some of the noise.
100 MΩ source impedance thermal noise is about 1.28 µV/√Hz (= 12.8 fA/√Hz) and
it will not be enough to distinguish between DUT and resistor noise. The noise, if
uncorrelated, adds in root sum squared (RSS) fashion. Figure 4 and Table 1 show
the RSS impact on the ratio of two numbers. n:n adds about 41%, n:n/2 adds about
12%, n:n/3 adds about 5.5%, and n:n/5 about 2%. With enough averaging, we
might be able to extract about 10% (0.57 fA/√Hz and 1.28 fA/√Hz RSS).
2 RAQ Issue 174: Current Noise in FET Input Amps
1
0.1
n
This gives us the measurement current noise floor of
fA
in_R = 4kT = 1.28
R
√Hz
100k
Figure 4. RSS addition based on the ratio of two numbers.
if the equation
is correct. 10 GΩ source impedance thermal noise is
µV
en_R = √4kTR = 12.8
√Hz
10
Increase (%)
Before we get into why this is the case, let’s quickly look at the measurement
setup. Getting an easy-to-reproduce, reliable measurement method is required
so that the measurement can be repeated over many different parts.
in_dut = √2qib
1M
100
Increase (ppm)
Measurement Setup Is the Key
Value 2
RSS Sum
% Increase
n
1.414 n
41.42 %
n
n/2
1.118 n
11.80%
n
n/3
1.054 n
5.41%
n
n/4
1.031 n
3.08%
n
n/5
1.020 n
2.00%
n
n/6
1.014 n
1.38%
n
n/7
1.010 n
1.02%
n
n/8
1.008 n
0.78%
n
n/9
1.006 n
0.62%
n
n/10
1.005 n
0.50%
Why Are the Results So Strange?
100G
10G
Impedance Magnitude (Ω)
Figure 5 shows the voltage noise density of the setup with the AD8065, a 145 MHz
FET input op amp with a common-mode input impedance of 2.1 pF. The 10 GΩ
resistor thermal noise is 12.8 µV/√Hz until the input capacitance along with the
board and socket stray capacitance roll off the voltage noise. Ideally, this should
keep rolling off at –20 dB/dec, but the curve starts to change shape around
100 Hz and flattens around 100 kHz. What’s going on here? Our intuition tells
us that the only way to stop the –20 dB/dec roll-off and cause a flatness is to
provide a +20 dB/dec slope. The culprit is the current noise, increasing at higher
frequencies with +20 dB/dec slope.
1G
100M
10M
100k
RTO Voltage Noise Density (nV Hz)
1M
0.01
0.1
1
10
100
1k
10k
100k
Frequency (Hz)
10k
Figure 6. Total impedance magnitude of 10 GΩ resistor and 7.6 pF input capacitance in
parallel.
Taking the referred to output (RTO) voltage noise measured on the AD8065
(Figure 5) and dividing by the impedance vs. frequency (Figure 6) gives us the
equivalent current noise of AD8065 and the 10 GΩ resistor combined in RSS
(Figure 7).
1k
100
1000
10
0.01
0.1
1
10
100
1k
10k
100k
Figure 5. Output referred voltage noise density.
The SR785 dynamic signal analyzer or an FFT instrument can be used to measure
the output voltage noise; however, a noise floor of less than 7 nV/√Hz is preferred. When the output voltage noise of the DUT roll-off is close to 20 nV/√Hz
to 30 nV/√Hz, we want the analyzer noise floor to add as little noise as possible.
A ratio of 3 times only adds about 5.5%. We can live with a 5% error in the noise
domain (see Figure 4).
The Art Is in Back-Calculation
Let’s look at an example with this data in Figure 5. The 3 dB roll-off point is read
at 2.1 Hz, which corresponds to
1 = 7.6 pF
2πRf
capacitance at the input. The data sheet mentions that the common-mode input
capacitance is only about 2.1 pF, which means that there is about 5.5 pF of stray
capacitance. Differential-mode input capacitance is bootstrapped by negative
feedback, so it doesn’t really come into play at low frequencies. With 7.6 pF
capacitance, the impedance that the current noise sees is shown in Figure 6.
100
10
1
0.01
Measuring this way, the two main parameters necessary to plot current noise
were obtained in just one measurement. First, we got the total input capacitance—that is, stray capacitance and input capacitance—which was necessary
to back-calculate the roll-off. Even if there is stray capacitance, the information
was captured. The input capacitance dominates over the 10 GΩ resistance. This
total impedance converts the current noise into voltage noise. Therefore, knowing
this total input capacitance is important. Second, it shows where the current
noise starts to dominate—that is, where it starts deviating from the –20 dB/dec slope.
C=
Current Noise (fA Hz)
Frequency (Hz)
(5)
0.1
1
10
100
1k
10k
100k
Frequency (Hz)
Figure 7. RTI current noise of the AD8065 and a 10 GΩ resistor.
After removing the current noise of 10 GΩ, the input referred noise of the AD8065
looks as shown in Figure 8. Below 10 Hz, it was very fuzzy because we were trying
to fish out the 0.5 fA/√Hz to 0.6 fA/√Hz out of 1.28 fA/√Hz (10% on RSS scale) and
only 100 averages were done. Between 15 mHz to 1.56 Hz, there are 400 lines with
4 mHz bandwidth. That’s 256 seconds per average! 100 averages of 256 is 25,600
seconds, slightly more than 7 hours. Why is measurement down to 15 mHz required,
and why spend that much time? Input capacitance of 10 pF with 10 GΩ creates a
low-pass filter of 1.6 Hz. Low noise FET amplifiers have large input capacitances
that can be up to 20 pF, which puts the 3 dB point at 0.8 Hz. To measure the 3 dB
point correctly, we would need to see a decade before—that is, down to 0.08 Hz (or
80 mHz).
If we eyeball the fuzzy lines below 10 Hz, 0.6 fA/√Hz through
in_dut = √2qib
(6)
can be verified. This equation is not entirely false for current noise. In the firstorder approximation, it still shows the low frequency current noise behavior of the
part because this current noise density value was obtained through dc input bias
current. At high frequencies, however, current noise does not follow this equation.
VISIT ANALOG.COM
3
Is This All There Is to Current Noise in
FET Input Amps?
Input Current Noise (fA Hz)
1k
There are four major current noise sources that contribute to total input current
noise in high source impedance applications and, so far, we have covered two.
A simplified TIA amplifier with major noise sources is shown below in Figure 11.
MT-050 is a good reference for the op amp noise sources.
100
Note: Residual Noise After
Subtracting 10 GΩ Noise Source
10
R
1
Photodiode Model
0.1
0.01
0.1
1
10
100
1k
10k
100k
Rshunt
Frequency (Hz)
Csource
Cin
in_dut
en_Rshunt
At higher frequencies, the DUT current noise dominates the resistor current
noise significantly, and the resistor noise can be ignored. Figure 9 shows the
input referred current noise of various FET input amplifiers at 10 GΩ noise,
measured with the setup shown in Figure 3. It seems that 100 fA/√Hz at 100 kHz
is the typical performance that can be expected from most precision amplifiers.
1k
Figure 11. Simplified TIA amplifier with major noise sources.
Current Noise from the FET Input Amplifier (in_dut)
The shape of the current noise depends on the amplifier input stage topology.
Generally, the noise is flat in low frequencies, but gets larger as frequency gets
higher. See Figure 8. Eventually, the noise will roll off at –20 dB/dec as the amplifier runs out of gain at higher frequencies.
Current Noise from the Resistor (in_R)
100
Current Noise (fA Hz)
en_dut
isn
Figure 8. RTI current noise of AD8605.
en_R
This can be calculated from the thermal voltage noise of the resistor en_R divided
by the impedance of the resistor, R. 1 MΩ contributes roughly 128 fA/√Hz and
10 GΩ contributes 1.28 fA/√Hz.
en_R √4kTR
in_R =
=
= 4kT
(7)
R
R
R
10
AD8655
ADA4610
LTC6240HV
ADA4625
AD8065
1
0.1
0.01
0.1
1
10
100
1k
10k
100k
Frequency (Hz)
The thermal voltage noise of the resistor is ideally flat over frequency, until
it sees a capacitor and rolls off at –20 dB/dec. Figure 5 shows this behavior
between 10 mHz to 1 Hz range.
Current Noise from the Sensor (in_source)
Figure 9. RTI current noise of selected ADI amplifiers.
There are exceptions: LTC6268/LTC6269 current noise is 5.6 fA/√Hz at 100 kHz.
These parts are great for high speed TIA applications where high bandwidth, low
input capacitance, femtoampere-level bias current are required.
100
The sensor itself contributes current noise, and we have to live with it. It can
have any shape over frequency. For example: a photodiode exhibits shot noise,
Isn, from photocurrent, IP, and dark current, ID, as well as Johnson noise, Ijn, from
the shunt resistance.1
in_source = Isn + Ijn = √2q(IP + ID) +
VS = ±2.5 V
Vcm = 0.25 V
4kT
Rshunt
(8)
Current Noise (pA Hz)
Current Noise from the Amplifier Voltage Noise Itself
The current noise from the amplifier voltage noise is coined as enC noise and
is explained very well in The Art of Electronics by Horowitz and Hill.2 Similar to
resistor voltage noise being converted into current noise by the resistance, the
amplifier voltage noise en_dut is converted into current noise by the total input
capacitance, which includes the sensor capacitance, board stray capacitance,
and the amplifier input capacitance
10
1
Cin_total = Csource + Cstray + Cin_dut
0.1
1
10
100
Frequency (MHz)
Figure 10. Input referred current noise of LTC6268.
4 RAQ Issue 174: Current Noise in FET Input Amps
On first order, we get
en_dut
en_dut
in_enC =
=
= ωen_dutC = 2πf en_dutC
Zcin_total 1/ωC
(9)
(10)
photodiodes tend to be in the order of 100 pF to 1 nF, while high speed, small area
photodiodes can be 1 pF to 10 pF.
This equation tells us three things. First, the current noise gets larger with
increasing frequency—yet another current noise component that gets larger
with frequency. Second, the larger the input voltage noise of the amplifier, the
larger the current noise. Third, the larger the total input capacitance, the larger
the current noise. This results in the figure of merit enC where both the voltage
noise of the amplifier and the total input capacitance should also be considered
for a given application.
The shape of current noise for TIA applications, ignoring the DUT current noise,
is shown in Figure 12. The flat portion is mainly the resistor noise
in_R = 4kT
R
The phenomenon of current noise increasing with frequency, in both CMOS and
JFET input amplifiers, is well known to IC design engineers and seasoned circuit
designers, but it was elusive to many engineers as a result of either too few
articles in the field or incomplete information from manufacturers. The goal of
this article is to bridge the understanding of the current noise behavior toward
a higher frequency domain and to show a technique to reproduce the measurement on the op amp of choice.
Further Reading
(11)
Choosing op amps to get the best performance is not a simple task. Based on
the applications, trade-offs are performed between noise, bandwidth, gain, and
accuracy. References 1, 2, 3, 4, 5, 6, and 7, along with many amplifier data sheets,
detail how these trade-offs can be made.
(12)
References
and the capacitor induced current noise is
in_enC = 2πf en_dutC
Summary
increasing with 20 dB/dec. From the two equations, the crossover point can be
calculated as
√4kT
1
fx =
×
(13)
2π
en_dutC√R
in
in_enC
1
Photodiode Characteristics and Applications. OSI Optoelectronics, August 2007.
2
Paul Horowitz and Winfield Hill. The Art of Electronics, 3rd edition. Cambridge
University Press, April 2015.
3
ADA4530-1 Data Sheet. Analog Devices, Inc., November 2019.
4
CN-0407. Analog Devices, Inc., February 2019.
5
“ADA4530-1R-EBZ User Guide: UG-865.” Analog Devices, Inc., October 2015.
6
“MT-050: Op Amp Total Output Noise Calculations for Second-Order System.”
Analog Devices, Inc., February 2009.
7
Low Level Measurements Handbook: Precision DC Current, Voltage, and Resistance
Measurements. Tektronix, Inc., February 2016.
C Increase
fX
C Decrease
Brisebois, Glen. “Signal Conditioning for High Impedance Sensors.”
Analog Devices, Inc..
R Decrease
in_R
Brisebois, Glen. “Transimpedance Amplifier Noise Considerations.”
Analog Devices, Inc..
R Increase
f
Acknowledgements
Kaung would like to thank Glen Brisebois and Aaron Schultz for their support,
and Henry Surtihadi, Scott Hunt, Barry Harvey, Harry Holt, Philip Karantzalis, and
Jordyn Ansari for their input.
Figure 12. enC noise over frequency.
Depending on the Cin, enC noise can be larger or smaller than the DUT current
noise. For inverting configuration such as TIA applications, Cdm is not bootstrapped; that is,
Cin_dut = Ccm + Cdm
For instance, at 100 kHz, the LTC6244 with Ccm = 2.1 pF, Cdm = 3.5 pF, and
en = 8 nV/√Hz will have enC current noise of
nV
fA
× (2.1 + 3.5) pf = 28
in_enC = 2π × 100 kHz × 8
√Hz
√Hz
Appendix
(14)
(15)
This is much less than the DUT current noise of 80 fA/√Hz
However, when a photodiode is connected, an extra Csource or Cpd is added to the
equation and the current noise can be recalculated. It takes only 16 pF of extra
capacitance from Cpd to be equal to the DUT current noise. Low speed, large area
Measuring noise in a high impedance environment, 10 GΩ impedance with FET
input, doesn’t come without fighting with the environment and its subtleties.
In a typical single amplifier pin layout, Pin3 (Vin+) is next to Pin4 (V–). Layout of
the board matters significantly when there is no guard ring in place. There was
significant dc shift at the output as the supplies were swept. The 10 GΩ SMD
was originally soldered in parallel with the V– (R10 in Figure 13) and the leakage
from solder paste was unbearable. As a result, the 10 GΩ SMD was moved to
another location (R8) and the leakage disappeared. The data sheet of ADA4530-1
(electrometer-grade amplifier with 20 fA at 85°C) shows all the precautions
necessary regarding solder paste selection, contamination, humidity effects, and
other juicy details regarding high impedance measurements. The data sheet and
user guide UG-865, as well as circuit note CN-0407, are worth studying.
VISIT ANALOG.COM
5
1 × 10-2
Acoustic Power Spectrum
1 × 10-3
1 × 10-4
1 × 10-5
1 × 10-6
1 × 10-7
1 × 10-8
100
1k
10k
Frequency (Hz)
Figure 15. Phone booth acoustic noise.
Devices that are high impedance and not soundproof are prone to triboelectric, piezoelectric, or microphonic effects. One day, I accidentally dropped my
keys and saw the noise spiking up at audible frequencies (1 kHz and beyond in
particular). I did not think measurement with 10 GΩ at the high impedance FET
input amp would be this sensitive to sound. I whistled just to double check. And
there it was, a spike between 1 kHz and 2 kHz. Even with a significant amount of
averages, one sharp whistle would bring up a noise spike on the CRT screen of
the SR785. The hermetically sealed glass resistors mentioned in CN-0407 would
be a better choice for piezoelectric/triboelectric effects.
1 × 10-2
768.75, 0.002104
Acoustic Power Spectrum
1 × 10-3
1 × 10-4
1 × 10-5
1k
100
10
100
1k
10k
Frequency (Hz)
Figure 16. Output referred voltage noise density without acoustic shielding.
10k
RTO Voltage Noise Density (nV Hz)
To confirm, I measured the lab environment sound with a laptop microphone,
processed the data with MATLAB®, and found that the noise correlates well
with the measurement. A significant noise spike was seen at 768 Hz and other
frequencies as seen in Figure 14. The culprit was the large ac duct running a
few meters away from my bench. To make sure I was not picking up the noise
of the laptop itself, I went into one of the phone booths, the acoustically quietest
place, and took data. There was no 768 Hz measurement. Noise spikes at other
frequencies were at least 100 times lower.
10k
RTO Voltage Noise Density (nV Hz)
Figure 13. Measurement setup.
1k
100
1 × 10-6
10
100
1 × 10-7
1k
10k
Frequency (Hz)
1 × 10-8
100
1k
10k
Frequency (Hz)
Figure 14. Lab acoustic noise.
6 RAQ Issue 174: Current Noise in FET Input Amps
Figure 17. Output referred voltage noise density with acoustic shielding.
To attenuate the audible noise, a Temptronix box was used. The box seems to
be thermally isolated, meaning no significant air flow. All I needed was for it to
shield the acoustics enough so that the microphonic effects would not show up
in the measurements. And it did the job. See Figure 16 and Figure 17.
Instrument Specific Issue:
FET input amps have input bias currents in the order of pA. 10 pA going into
10 GΩ still reads about 100 mV of offset at the output of the amplifier. The SR785
has an ac coupling feature that works well to remove this offset and measure
the output noise with the best range of –50 dB V peak (3.2 mV peak). However,
the ac coupling features cuts into the frequency of interest less than 1 Hz, which
makes it hard to determine the flat 12.8 µV/√Hz and read 3 dB off of the point.
DC coupling must be used, but now the most sensitive range of the instrument
cannot be used. A 1 mHz passive filter, made with two 270 µF polarized caps in
series (135 µF cap) and 1 MΩ resistor, was put in between the output of the DUT
and the SR785. Due to the long leads in capacitor—that is, more loops—it tends
to pick up the magnetic field produced by the SR785 CRT screen at 20 kHz and
its harmonics. Because magnetic fields are three-dimensional in nature, angling
and rotating the passive filter box solved the issue. Notice the angled blue box in
Figure 18. E&M black magic!
Figure 18. Filter box rotated to be less sensitive to the magnetic fields.
About the Author
Kaung Win joined ADI in 2013 as a product evaluation engineer for the Linear Products and Solutions Group and transferred to
an application engineer position in 2019. He has a bachelor’s degree in electrical and computer engineering from Worcester
Polytechnic Institute and a master’s degree in electrical engineering from Santa Clara University. Kaung specializes in amplifier
signal chain solutions. He can be reached at kaung.win@analog.com.
For regional headquarters, sales, and distributors or
to contact customer service and technical support,
visit analog.com/contact.
Ask our ADI technology experts tough questions, browse
FAQs, or join a conversation at the EngineerZone Online
Support Community. Visit ez.analog.com.
©2020 Analog Devices, Inc. All rights reserved.
Trademarks and registered trademarks are
the property of their respective owners.
VISIT ANALOG.COM
