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LabView Rescues Tiny Signals from a Sea of NoisePhilip 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 addedexpense and hardware, in 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 tohardware 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 processing1.

Measuring Small Signals is Difficult

An experiment in our lab determines the resistance of a high-temperature superconductor2

by direct measurement: we apply a

known current across the sample, and measure its resistive voltage drop. This signal varies from ~1 mV while normally

conducting to

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Multiplying the noisy input signal inv by )2cos(2 reftf copies the input, shifted up and down by reff :

+++==n

)2cos()2cos(2)2cos(2)2cos()2cos(22 nnnrefrefoffsrefrefsampinrefmult ftfVtftfVtftfVvuv

++++=n

)2]cos([)2cos()22cos( nrefnnrefoffsrefsampsamp ftffVtfVtfVV ,

The 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 frequency reffilt ff

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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 inputwas sampled at 72 kHz, then locked-in and filteredat 0.5 Hz.

The inset graph shows the initial portion of the

transition on an expandedy-axis. One can clearly

observe the shape and details of the transition near115 K. The transition is not sharp, a general

characteristic of high-transition temperature

superconductors. Above the transition, we can see

that the resistance increases linearly withtemperature. Below the transition, we find a

superconducting resistance of 0 0.02 microohms.

Conclusions

Using LabView, we have implemented a versatile,

low-cost digital lock-in amplifier8. 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. Itis capable of 10 nV sensitivity, a quality factor ofQ = ?f/f= 10

5or more, and noise rejection of ~120 dB (can extract signals from noise up to ~10

6times greater in

amplitude).

1For implementation details, circuit diagrams, and source code, please see http://www.ph.utexas.edu/~phy453/lockin/ orcontact the authors: Philip (Flip) Kromer (flip@physics.utexas.edu) or Roger Bengtson (bengtson@physics.utexas.edu).

2Superconductivity:

G.C. Brown, J.O. Rasure, and W.A. Morrison, American Journal of Physics. 57(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/applicationnotes.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 upon 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), p801 (1975).

"About Lock-in Amplifiers" (http://www.srsys.com/html/applicationnotes.htm l). Stanford Research Systems, Sunnyvale,

CA, 1999. A functional description of lock-in amplifiers.

Lock-in Applications Anthology, ed. Douglas Malchow. EG&G Princeton Applied Research, Princeton, NJ, 1985. A

freely available guide to applications of the lock-in analyzer. D.W. Preston and E.R. Dietz, The Art of Experimental Physics, pp 367-375. John Wiley & Sons, New York, 1991.

5Data Acquisition:

Data Acquisition Handbook, ed. J. Yeager and M.A. Hrusch-Tupta. Keithley Instruments, Cleveland, OH, 1998. Anexcellent introduction to data acquisition, and freely available on request.

6We 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. MoPac Expressway, Austin, TX 787597

Our front-end amplifier is based on Texas Instruments' INA114 precision instrumentation amplifier. Other suitable devices

include Analog Devices' AD624 and Texas Instruments' OPA111. A circuit diagram 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(milliohm

s)

Liquid Nitrogen

Temperature 77 K

Onset of

superconductivity

Room Temperature

300K

Zero-point 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

http://www.ph.utexas.edu/~phy453/lockin/http://www.srsys.com/html/applicationnotes.htmlhttp://digital.natinst.com/appnotes.nsf/web/indexhttp://www.lockin.de/http://www.srsys.com/html/applicationnotes.htmlhttp://www.ph.utexas.edu/~phy453/lockin/http://www.ph.utexas.edu/~phy453/lockin/http://www.srsys.com/html/applicationnotes.htmlhttp://www.lockin.de/http://digital.natinst.com/appnotes.nsf/web/indexhttp://www.srsys.com/html/applicationnotes.htmlhttp://www.ph.utexas.edu/~phy453/lockin/