Download Introduction to low-level measurement techniques using short

Introduction to low-level
measurement techniques using
short segments of conducting wire
Bill Brandon
UNC-P
UNCP physics students investigated short segments
(length ~ 10-45 cm, resistance ~ 33-45 mW) of
copper wire (AWG 30, 24,22) to integrate
information using an exhaustive list of activities.
• Effects of 60 Hz and 120 Hz notch filters of the SR
830 lock-in amplifier (refutation of Keithley
“white paper”)
• Calculation of resistance (rl/a) with wire
diameter measured using diffraction pattern
• AC voltage characterization using SR 830 lock-in
amplifier (refutation of a previous AJP article)
Cannot be trusted for high accuracy constraints
Simplified block diagram of a lock-in amplifier setup
to measure the voltage of a DUT (e.g. a wire) at low
power.
The amplified voltage from the DUT is multiplied by both a
sine and a cosine wave with the same frequency and phase
as the applied source and then subject to a low pass filter.
In most cases, the multiplication and filtering is performed
digitally within the lock-in amplifier after the DUT signal is
digitized.
Extraction of signals
buried in noise
Our latest method of choice:
Function Generator
BNC 645
reference frequency
1 Hz – 100 kHz
monitor Supply Voltage
DMM
HP 3478
LIA
SR 830
VS = Vin: Supply Voltage
Vout ~ 1- 10mV
Rwire
~190 mV; 1Hz-100KHz
Rseries
Vin =190 mV; 1Hz-100KHz
Rseries ~ 1 kW
Voltage Divider
Vout ~ 1-10mV
Rwire ~ 30 mW
Rseries  Rwire   Rseries
Rwire 
our case :
Vout
Rwire
=
Rseries  Rwire
Vout
Rseries
Vin
Rseries  995 W ; Vin  190 mV
Rwire  5237  Vout
1
XC ~
; X L ~ L
C
Vout : from circuit
voltage across wire
1-10mV
Vimaginary
out of phase
Vreal
in phase
LIA as “vector voltmeter”
VS = Vin to circuit
~190 mV; 1Hz-100KHz
8.00E-06
In-phase voltage vs. frequency
The effect of line filtering: 10-200 Hz
7.00E-06
In phase voltage, Vreal
6.00E-06
5.00E-06
4.00E-06
3.00E-06
no line filter
60 Hz line filter
2.00E-06
120 Hz line filter
60+120 Hz line filter
1.00E-06
0.00E+00
10
60
110
frequency, Hz
160
1.0E-05
In-phase voltage vs. frequency
9.0E-06
no line filter
In phase voltage, Vreal
8.0E-06
7.0E-06
6.0E-06
5.0E-06
4.0E-06
3.0E-06
2.0E-06
1.0E-06
frequency, Hz
0.0E+00
0
50
100
150
200
6.8E-06
In-phase voltage vs. frequency
6.52 10 6 V
Rwire ( LIA) ~
995 W  34 mW
0.19 V
In phase voltage, Vreal
6.7E-06
Rwire ( AWG ) ~ 338.6 mW m  0.10m  34 mW
6.6E-06
6.5E-06
6.4E-06
frequency, Hz
6.3E-06
16.5
66.5
116.5
166.5
1.E-05
In-phase voltage vs. frequency
60 Hz line filter
In phase voltage, Vreal
8.E-06
34 mW
6.E-06
4.E-06
2.E-06
frequency, Hz
0.E+00
10
60
110
160
In-phase voltage vs. frequency
8.00E-06
120 Hz line filter
7.00E-06
34 mW
In phase voltage, Vreal
6.00E-06
5.00E-06
4.00E-06
3.00E-06
2.00E-06
1.00E-06
0.00E+00
10
60
110
frequency, Hz
160
In-phase voltage vs. frequency
8.00E-06
60+120 Hz line filter
34 mW
7.00E-06
In phase voltage, Vreal
6.00E-06
5.00E-06
4.00E-06
3.00E-06
2.00E-06
1.00E-06
0.00E+00
10
60
110
frequency, Hz
160
In-phase voltage vs. frequency
“choosing a frequency”
6.9E-06
Industry standard-differential inputs @ 30Hz
6.7E-06
no line filter
60 Hz line filter
120 Hz line filter
60+120 Hz line filter
6.5E-06
6.3E-06
Alternative--?
 single ended
@
6.1E-06
5.9E-06
f  60 Hz  120 Hz ~ 85 Hz
5.7E-06
5.5E-06
10
30
50
70
90
110
~30 Hz zoom
no line filter
precision, in this case
20
30
Industry standard:
use differential
inputs @ 30Hz
Better than 1% accuracy (0.5 sec constraint)
Suspect Claim 1: Keithley white paper
Tupta, "AC versus DC Measurement
Methods for Low-power Nanotech
and Other Sensitive Devices", 2007
40
6.60E-06
6.55E-06
6.50E-06
no line filter
6.45E-06
25
27
29
31
33
35
Tupta, "AC versus DC Measurement Methods for Low-power
Nanotech and Other Sensitive Devices", 2007
Next few slides:
Lock-in configuraiton
 1f+2f line filters
 “Sync” function
 Fixed frequency of 85 Hz
… perhaps a novel –
and potentially useful approach?
~80-95 Hz zoom
6.60E-06
34 mW
6.50E-06
The in phase signal, acquired utilizing a
single ended measurement, suffers
from an offset. The voltage should be
acquired with differential
measurement.
no line filter
6.40E-06
60+120 Hz line filter
6.30E-06
6.20E-06
1+2 line (60 + 120 Hz) filter appears to
provide an effective input offset
reduction and slight noise suppression.
32 mW
6.10E-06
6.00E-06
80
82
84
86
88
90
92
94
Out-of-phase voltage vs. frequency
Out-of-phase voltage, Vimaginary
3.E-06
2.E-06
1.E-06
3.E-07
-7.E-07 0
50
100
200
no line filter
60 Hz line filter
120 Hz line filter
60+120 Hz line filter
-2.E-06
-3.E-06
-4.E-06
150
frequency (Hz)
Out-of-phase voltage vs. frequency
60+120 Hz line filter
Out-of-phase voltage, Vimaginary
3.E-06
2.E-06
1.E-06
3.E-07
-7.E-07
0
50
100
-2.E-06
-3.E-06
-4.E-06
Note: Vy = 0
frequency (Hz)
150
200
Explanation of offset reduction
Out-of-phase voltage, Vimaginary
1.0E-06
Utilizing 1f+2f filter: Vy =0 at 86 Hz
5.0E-07
0.0E+00
80
-5.0E-07
85
90
The out-of phase voltage, Vy
goes to zero near
f theory  60 Hz 120 Hz ~ 85 Hz
-1.0E-06
frequency (Hz)
95
PHY 4200 final results of 1f+2f measurements at 85 kHz
Includes comparison to theoretical result.
internal ref
31.77+0.03 mW
external ref
31.81+0.07 mW
R = r l /a
31.6+0.8
mW
“expected”
Recall, from AWG table:
Rwire ( AWG ) ~ 338.6 mW m  0.10m  34 mW
How the “expected” result was obtained…
The expected resistance, R of a copper wire is
known to obey the relation:
l
Rr
a
 r : resitivity; l : length ; a : cross - sectional area
The resistivity, r is actually temperature, T dependent –
r T   r 0 1   T  T0 
 r 0  1.678 10 8 Wm;   0.003862 / oC ; T0  200 C
r T  20.5  0.2   1.682 10 8 Wm
 room temp  drift
r T  20.5  1.6815(15) 10 8 Wm
 resistivity
The cross sectional area, a was calculated from
measurements using optical interferometry. The
relation characterizing the fringe pattern generated
by diffraction when a laser beam, with wavelength, l,
is obstructed by a wire with diameter, d is given by:
L
d l
y
L : distance to fringe pattern
y : mean fringe spacing
a=pd2/4
2
 l   L   y 
 a  2a          5.E  4
 l   L  y
2
2
Measured at 4
points along the
length of wire
~ 50 fringes
“Expected” result




 r   l   a  
l
R  r 1           31.6  0.8 mΩ
a
r   l   a 

  
propagted uncertainty


internal ref
31.77+0.03 mW
external ref
31.81+0.07 mW
R = r l /a
31.6+0.8
mW
VR  Vx  Vy
2
2
2
Appears to arise
from inductive
reactance
Suspect Claim 2:
Simplified block diagram of a lock-in amplifier setup
to measure the voltage of a DUT at low power.
The amplified voltage from the DUT is multiplied by both a
sine and a cosine wave with the same frequency and phase
as the applied source and then put through a low pass
filter. In most cases, the multiplication and filtering is
performed digitally within the lock-in amplifier after the
DUT signal is digitized.
VR  Vx  Vy
RESISTANCE IS FUTILE
2
2
External Ref: 0.500 Vs
100
90
Wire resistance, R (mW
2
Z_real
80
Z_imag
70
Z_quad
VR
R_calc
60
R_ideal
50
40
30
Vx
20
Vy
10
Vx : real voltage
turns downward
0
10
100
1000
frequency (Hz)
10000
100000
VR  Vx  V y
RESISTANCE IS FUTILE
2
2
2
Internal Ref: 0.500 Vo
100
Z_real
Z_imag
Z_quad
R_calc
R_ideal
Wire resistance, R (mW)
90
80
70
60
VR
Vx : real voltage
turns upward
50
Vy
40
30
20
Vy
10
0
10
100
1000
frequency (Hz)
10000
100000
….and hence the mixed
internal/external method
--shown previously and in the next slide
Function Generator
BNC 645
reference frequency
1 Hz – 100 kHz
monitor Supply Voltage
DMM
HP 3478
LIA
SR 830
VS = Vin: Supply Voltage
Vout ~ 1- 10mV
Rwire
~190 mV; 1Hz-100KHz
Rseries
And for the inductance…
0.07
Vsupply
 995 W
Inductive Reactance, XL (W
XL 
Vy
XL (W) vs.  (rad/s) : 10 cm wire (AWG 30)
0.06
0.05
y = 1.019E-07x - 3.166E-04
R² = 9.999E-01
L = 102 nH
L (theory) = 133 nH
0.04
0.03
0.02
0.01
0.00
0.E+00
2.E+05
4.E+05
6.E+05
angular frequency,  (rad/s)
8.E+05
500
450
self inductance (nH)
400
350
300
X L  L
250
  2p f
200
Measurements:
Slopes of – XL vs. 
For l = 5,10,15,20 cm
compared to theory
150
100
50
0
0
5
10
15
length, l (cm)
20
25
30
XL (mW) vs.  (rad/s) : 45.5 cm wire (AWG 24)
400
350
300
Zi_int
Reactance, X (mW)
250
200
Ltheory ~ 668 nH
Lmeasured ~ 535 nH
Xi_int =  (5.477E-0 4 mH) - 1.915E-02
150
100
50
Zi_ext
Xi_ext =  5.232E-04 mH) + 2.176E-01
4
nonlinearities at low frequencies due to:
1) capacitive inductance and
2) lock-in noise floor
2
0
0.0E+00
5.0E+03
0
0.E+00 1.E+05 2.E+05 3.E+05 4.E+05 5.E+05 6.E+05 7.E+05
angular frequency,  (rad/s)
Conclusions
In spite of the Tupta (whitepaper) claim, a lock-in
amplifier, when utilized effectively, will indeed provide 1%
accuracy in the measurement of such a low resistance
(Rexp~31mΩ) acquired within the low power limit
(Pexp~30nW) ascribed therein.
The characterization of in-phase (real) and out-of-phase
(imaginary) voltage drops across the resistive wire as
functions of frequency show that inductive reactance, and
NOT capacitive reactance, is indeed the major contributor
to the complex impedance. This conclusion follows quite
naturally from using the lock-in amplifier as a vector
voltmeter, and is based primarily on elementary notions of
impedance.