LabView Rescues Tiny Signals from a Sea of Noise
Philip
F
Kromer
and
Roger Bengtson
Department of Physics
,
University of Texas at Austin
Category
R&D / Lab Automation
Products Used
LabView 6.0.2; PCI

MIO

16E

4
The Challenge
Measure an extremely small signal obscured by noise thousands of times greater in magnitude, at a minimum of added
expense
and
hardware, i
n order to determine the resistance of a high

temperature superconductor.
The Solution
Use the signal

processing capabilities of LabView
to implement a
technique known as lock

in amplification. Compared to
hardware
lock

in amplifiers, the LabView approach
yields excellent price/performance, increased functionality, superior
flexibility, and the ability to inspect the signal at all stages of processing
1
.
Measuring Small Signals is Difficult
An experiment
in our lab
determines
the resistance of a high

temper
ature superconductor
2
by direct measurement:
we
apply a
known current across the sample, and measure its re
sistive voltage drop. Th
is signal
varies from
~
1 mV
while
normally
conducting
to
<
1
0
n
V
while
superconducting.
Even under carefully controlled condit
ions, there are intractable sources of
noise, due to fundamental physical processes, that
obscure this signal
3
. What is worse, a significant
portion of this noise has a “1/
f
spectrum:” its intensity
increases at low frequencies and is worst at DC,
precisel
y where
the
signal
naturally resides
. Finally,
intransigent sources of measurement error, such as
offset drift, thermoelectric voltages, and common

mode
error,
act to
corrupt the signal
.
Figure
1
shows
a ty
pical
input amplitude spectrum
(note the log scale
)
. One can
see the DC offset,
the
60 Hz interference, and the
mixture of 1/
f
and
broadband noise.
A
verag
ing
over a long time
reduces
the noise
by
narrowing the
bandwidth
and
effectively trading
aw
ay
response
time
for improved noise rejection. However,
no a
mount of averaging can distinguish
our slowly
varying signal from
DC and low

frequency
components
of
the
noise and error sources.
The Lock

in Technique Provides an Answer…
Instead, we
will
use lock

in amplification
4
to recover the signal
.
Rather than apply
a constant (DC) current, we
generate a
purely
sinusoidal
(AC)
reference
signal
and apply
a scaled current
)
2
cos(
ref
ref
ref
t
f
I
i
across the sample
.
The resistive
voltage drop
has
the same frequency and phase as the applied current:
)
2
cos(
)
2
cos(
ref
samp
ref
ref
samp
samp
t
f
R
I
t
f
V
v
.
However,
our actual
input
contain
s
not only
the desired
v
samp
, but also
the
undesirable offset,
interference
,
and noise
(see
Figure 1
)
.
We can represent t
he noise and interference a sum of randomly varying signals at all frequencies and pha
ses
:
n
)
2
cos(
n
n
n
offs
samp
in
f
t
f
V
V
v
v
.
To
select
only the interesting
(matching the reference
in
phase and frequency) part
of the input signal, we
use
a simple trick
from trigonometry. Recall the
cosine
sum rules:
)
sin(
)
sin(
)
cos(
)
cos(
)
cos(
b
a
b
a
b
a
)
sin(
)
sin(
)
cos(
)
cos(
)
cos(
b
a
b
a
b
a
.
Add
and re
arrang
e; the product of two cosines
yields
a cosine at the difference
frequency
plus
a cosine at the sum
frequency
:
)
cos(
)
cos(
2
1
)
cos(
)
cos(
b
a
b
a
b
a
.
Figure 1: Log Amplitude versus Frequency (for F
ref
=1122 Hz)
M
ultiply
ing
the noisy input signal
in
v
by
)
2
cos(
2
ref
t
f
copies
the input
,
shifted
up a
nd down by
ref
f
:
n
)
2
cos(
)
2
cos(
2
)
2
cos(
2
)
2
cos(
)
2
cos(
2
2
n
n
n
ref
ref
offs
ref
ref
samp
in
ref
mult
f
t
f
V
t
f
t
f
V
t
f
t
f
V
v
u
v
n
)
2
]
cos([
)
2
cos(
)
2
2
cos(
n
ref
n
n
ref
offs
ref
samp
samp
f
t
f
f
V
t
f
V
t
f
V
V
,
T
he voltage drop has the same frequency as
the
reference,
so
their difference term has zero frequency (DC).
Therefore,
filter
out
all frequencies below a cutoff
freque
ncy
ref
filt
f
f
:
filt
n
)
2
]
cos([
n
ref
n
n
samp
lock
f
f
t
f
f
V
V
V
.
This is
the
desired voltage drop, with
a
small
remnant
of
noise
,
those components indistinguishable in frequency
and
phase
from the
reference.
… And LabView provides a Solution
L
ock

in amplification is
traditionally accomplished
with
expensive, monolithic hardware
.
Our LabView
implementation
achieve
s
reasonable performance at
greatly reduced price
,
with superior
flexibility
5
.
Besides
a
National Instruments
PCI

MIO

16E

4
data acquisition
board
6
,
t
he only
additional hardware
devices are
an input
amplifier
and
a
voltage

controlled current source, both
shop

built
7
.
Our LabView
program i
nstructs the
DAQ
board
to
generate
a
waveform
continuously
at the
arbitrarily
chosen
reference frequency
of 1122 Hz
.
This
re
ference
drives
a voltage

controlled
current source
connected
across the superconductor sample.
The
superconductor’s
bulk
resistance
causes a
proportional voltage drop, which
is
passed to
a high

gain
,
low

noise differential amplifier
.
T
he DAQ board
continuo
usly acquires
the
amplified voltage drop,
the voltage
from
a thermocouple on
the sample,
and other
signals of interest.
As each buffer is acquired, our program processes the signals
and
performs preliminary data analysis
.
The
input signal i
s
lock
ed

in
–
mu
ltipl
ied
by
the unit reference
, scale
d
, and filter
ed
–
giving
the
sample voltage
and t
he nominal
bulk resistance (sample voltage over applied current)
.
Since the temperature changes slowly and needs no special attention,
we
take
the average over each buffe
r (LabView automagically compensates and scales the thermocouple data).
The program interactively graphs the various waveforms and their Fourier transforms
(see
Figure 3
)
.
T
his ability to observe
the
signal as it proceeds through
the lock

in
is
a distinc
t advantage
of the
so
ftware
approach
. Furthermore, the plots display
the natural quantities of interest
:
resistance, time, temperature, etc
.;
no subsequent data analysis is required.
The
key to the extraordinary stability and accuracy of our
device
is th
a
t, once acquired, all signal processing is
accomplished
digitally
.
Since the reference
signal
is
internally
calculated
,
its
accuracy
is
limited only by the
floating

point resolution of the computer.
Reading and
amplifying the
input signal
introduces
a vari
ety of
physical and measurement
artifacts,
but once safely
within the computer
no further degradation
occurs
.
There are subtle signal

processing pitfalls that must be
avoided, such as
synchronization (phase error)
,
aliasing
(undersampling)
and
windowing ar
tifacts (discontinuities
at the buffer edges)
5
. We
align
acquisition
with
the
waveform generation trigg
er to
minim
iz
e
phas
e error, and
use continuous acquisition
to
prevent
window
ing
artifacts.
Continuous acqu
isition
allows reference frequencies up to
several kilohertz on our modest PC with a 250 kS/s DAQ
board. One may instead read non

continuous chunks
containing an exact number of waveforms
,
each
synchronous with the
waveform generation. This allows
referenc
e frequencies up to about ten percent of the
maximum sampling
frequency
.
Figure 2: Block Diagram for Lock

In Detector
Figure 3: LabView Front Panel
Results
Figure
4
shows a data set recorded as the sample
warmed up
from approximately 80 to 200 K using
an
applied current
of
10 mA at
1122
Hz. The input
was sampled at 72 kHz,
then
lock
ed

in
and
filter
ed
at 0.5 Hz.
The inset graph shows the initial portion of the
transition on an expanded
y

axis.
One can clearly
observe the shape and details of the transition near
115 K.
The transition is not sharp
,
a general
characteristic of high

t
ransition temperature
superconductors. Above the transition, we can see
that the resistance increases linearly with
temperature. Below the transition, we find
a
superconducting
resistance of
0 ± 0.02 microohms.
Conclusions
Using LabView, we have implemente
d a versatile,
low

cost digital lock

in amplifier
8
. The
device
shows negligible offset drift
and
is robust against
noise and interference
–
yet
it
requires
minimal
hardware
and may
be customized for
each task.
I
t
is capable of
10 nV sensitivity,
a
quality
factor of
Q
= Δ
f
/
f
= 10
5
or more
, and
noise rejection of ~
120 dB (
can extract
signals
from
noise up to ~10
6
times greater in
amplitude
).
1
For implementation details, circuit diagrams, and source code, please
see
http://w
ww.ph.utexas.edu/~phy453/lockin/
or
contact t
he authors:
Philip (Flip) Kromer (
flip@physics.utexas.edu
)
or
Roger Bengtson (
bengtson@physics.utexas.edu
).
2
Superconductivity:
G.C. Brown, J.O. Rasure, and W.A. Morrison,
American Journal of Physics
. 5
7(12), 1142

1144 (1989).
M.J. Pechan and J.A. Horvath,
American Journal of Physics
.
58(7), 642

644 (1990).
Semiconductor
kits are
available from
Colorado Superconductor
, 1623 Hillside Drive, Fort Collins, CO 80524.
3
Sources of, and defenses against, noise:
"Signal Enhancement"
(
http://www.srsys.com/html/a
pplicationnotes.html
, or
p.225
of their
catalog
).
Stanford Research
Systems, Sunnyvale, CA, 1999
.
A summary of fundamental noise sources.
S.J.
Shah,
“
Field Wiring and Noise Considerations
,”
National Instruments
,
Austin, TX, 1994
;
see
http://digital.natinst.com/appnotes.nsf/web/index
, #25
.
Low Level Measurements Handbook
, ed. J. Yeager and M.A.
Hrusch

Tupta.
Keithley Instruments
, Cleveland, OH, 1998.
An excellent introduction to precision measurement, and
freely available
up
on request
.
P. Horowitz and W. Hill, The Art of Electronics. Cambridge University Press, New York, 1980.
4
Lock

in detection:
M. Stachel, "
The Lock

in Amplifier: Exploring Noise Reduction and Phase
,
"
(
http://www.lockin.de/
)
.
An excellent web

based introduction to lock

in detection, complete with Java simulations.
P. Temple,
American Journal of Physics
43(9),
p
801
(1975).
"
About Lock

in Amplifiers
"
(
http://www.srsys.com/html/applicationnotes.html
).
Stanford Research Systems
, Sunnyvale,
CA, 1999. A functional de
scription of lock

in amplifiers
.
Lock

in Applications Anthology, ed. Douglas Malchow.
EG&G Princeton Applied Research
, Princeton, NJ, 1985. A
freely available guide to applic
ations of the lock

in analyzer.
D.W. Preston and E.R. Dietz, The Art of Experimental Physics
, pp 367

375
. Jo
hn Wiley & Sons, New York, 1991
.
5
Data Acquisition:
Data Acquisition Handbook
, ed. J. Yeager and M.A. Hrusch

Tupta.
Keithley Instruments
, Cleveland, OH, 1998. An
excellent introduction to data acquisition, and
freely available on request
.
6
We use
the
PCI

MIO

16E

4
(NI 6040E) multifunction I/O board; it has 16 12

bit, 250 kS/s analog inputs; two 12

bit, 1
MS/s analog outputs; and two 24

bit counters.
National Instruments
, 11500 N. MoPa
c Expressway, Austin, TX 78759
7
Our
front

end amplifier
is based on
Texas Instruments
'
INA114
precision instrumentation amplifier. Other suitable de
vices
include
Analog Devices
'
AD624
and Texas Instruments'
OPA111
.
A c
ircuit
d
iagram
is
available
on our website.
8
Our source code is freely available under the Gnu Public License; download at
http://www.ph.utexas.edu/~phy453/lockin/
.
0
2
4
6
8
10
12
14
16
18
50
70
90
110
130
150
170
190
Temperature (K)
Resistance (milliohms)
Liquid Nitrogen
Temperature 77 K
Onset of
superconductivity
Room Temperature
300K
Zeropoint Resistance
0.04
0
0.04
0.08
80
85
90
95
100
105
110
Normal conductivity:
graph is linear
Figure 4: Resistance versus Temperature for a High

Temperature Superconductor
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