|Título/s:||Uncertainty evaluation in two-terminal cryogenic current comparator|
|Autor/es:||Bierzychudek, Marcos E.; Elmquist, Randolf E.|
|Institución:||Instituto Nacional de Tecnología Industrial. INTI-Física y Metrología. Buenos Aires, AR |
National Institute of Standards and Technology. Gaithersburg, US
|Palabras clave:||Incertidumbre; Instrumentos de medición; Comparadores; Criogenia; Voltaje; Resistencia térmica; Metrología|
| Ver+/- |
1Quantum Electrical Metrology Division, Electronics and Electrical Engineering Laboratory, U.S. Department of Commerce. Official contribution of the
National Institute of Standards and Technology, not subject to copyright in the United States.
UNCERTAINTY EVALUATION IN A TWO-TERMINAL CRYOGENIC CURRENT COMPARATOR
M. E. Bierzychudek* and R. E. Elmquist**
*Instituto Nacional de Tecnología Industrial, San Martín, B1650KNA, República Argentina
**National Institute of Standards and Technology, Gaithersburg, MD, 20899-8171 USA1
In this paper we present the uncertainty evaluation of
a new cryogenic current comparator (CCC) bridge
designed to compare two-terminal 1 M and 10 M
standard resistors with the quantized Hall resistance
(QHR) and then scale from these values to other
values between 10 k and 1 G.
The CCC is used in many national metrology
laboratories to obtain high accuracy four-terminal
resistance measurements in the range of 1 to
10 k. Some papers show that this traditional CCC
can be used to measure high value resistors with low
uncertainty . Here we analyze a two-terminal CCC
that does not use a voltage detector and requires only
a single voltage source, making it much easier to use
than the traditional CCC. This type of bridge has
been used at NIST to compare the QHR directly with
1 M and 100 M  resistors. The recent two-
terminal CCCs  developed to compare the QHR
with room-temperature resistors use resistive
windings. This paper presents a complete study of the
uncertainty in the new CCC which provides new
capabilities in resistance scaling for high-value
Two-terminal resistive-winding CCC
Figure 1 shows a schematic diagram of the two-
terminal CCC. A source voltage is applied directly to
the two resistors under test, in parallel. Each resistor
is in series with a winding, and the two windings
have opposite directions. A superconducting quantum
interference device (SQUID) senses the total flux and
drives a feedback winding of one turn to maintain the
flux balance in the bridge. This bridge uses six major
windings. The four-turn winding is superconducting
and is used with the QHR. The 3100-turn, 310-turn
and 31-turn windings are made of phosphor-bronze
wire and these have nominal resistances at 4.2 K of
2500 , 250 and 25 , respectively. The internal
resistances of the windings decrease the effect of self-
resonance in the CCC. This improves the sensitivity
 but the winding resistance must be measured to
correct the value of each resistor. Since this bridge
measures two-terminal resistors, we use the triple-
series connection technique to reduce errors in
measurements of the QHR, as described in . In a
condition of balance, the bridge equations are:
,2211 FF NININI (1)
Here, Ij is the current in the resistor j, rwj is the
resistance in the connections of the j bridge arm, Nj is
the number of turns in the winding j, V is the source
voltage, IF is the feedback current and includes all
Figure 1. Schematic diagram of the bridge, showing connections
for room-temperature resistors and the voltage source (VS).
Type A evaluation of standard uncertainty
First, we describe components which produce
random errors in the result and can be eliminated by
averaging or reduced by a correct design of the
Johnson-Nyquist noise. The Johnson noise of the
resistor Rj is estimated from the flux produced by the
Johnson current which flows in the winding j.
SQUID noise. The SQUID produces 1/f and white
noise components. The first is reduced by alternating
the current polarity and by averaging. The white
noise is specified by the manufacturer in units of
µ0/Hz1/2 where 0 is the flux quantum.
Electromagnetic interference and vibration
noise. These types of interference are very difficult to
estimate but a good design can be used to eliminate
these effects. The CCC is surrounded by different
levels of shielding. All the wires connecting the CCC
with the electronics or the resistor are shielded and
twisted. Inside the CCC the interconnecting leads are
twisted together and fixed rigidly to the CCC probe.
Noise in CCC electronics: voltage source,
feedback current and feedback sense. The voltage
source and the feedback current source were designed
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using low pass filters and low noise components. To
measure the feedback current we use a sense resistor
and two buffers, one at each resistor terminal. These
buffers produce high frequency voltage noise and 1/f
noise due to the temperature dependence of the
Type B evaluation of standard uncertainty
These components produce systematic offsets in the
Winding and lead resistance. The uncertainty
produced by the correction of the winding and lead
resistance has three components: measurement
device, current coefficient and the dependence on
helium level. The first two are the most important
because the last can be eliminated if the resistances
are frequently measured.
Measurement of the feedback current. This is
calculated as the uncertainty produced by the
multimeter and the uncertainty in the calibration of
the sense resistor.
Voltage source and thermal EMF. This bridge
does not use a feedback loop to balance the voltage
across each resistor, so the stability of the source
produces an uncertainty in the result. For the same
reason, the voltage across each resistor can be
affected by the resistance of the winding or leads and
the thermal electromotive forces (EMF). The first can
be corrected and the second can be eliminated using
the voltage reversal measurement technique, if the
thermal EMF is constant.
Leakage current. Using the guard technique we
can eliminate the possibility of leakage in parallel to
the resistors, which can exist especially in Hamon
devices. Leakage current can affect only the positive
terminals of the windings, and produces an estimated
error of 0.02 µ/ in 100 M.
CCC current-linkage error. With effective
shielding, reversing the current passing through two
windings of equal number in series-opposition should
produce no change in the voltage output of the
SQUID, when it is not connected to the feedback
SQUID feedback null. The external feedback
must maintain constant output voltage in the SQUID
electronics. If it is different from zero and is not
constant it will produce an error.
Resistor time constant. The resistor under test
should have a low settling time-constant relative to
the current reversal rate.
QHR, triple-series connection. The relative
change in the quantized Hall resistance using a triple-
series connection in DC can be calculated from a
mathematical model of the QHR . In that reference
an offset of less than 0.001 µ/ was found with
typical leads and longitudinal resistance.
We performed some simulations of the effect of each
component in the measurement and the combined
standard uncertainty for different combinations of
resistors, as shown in Fig. 2.
] Primary wire resistanceSecondary wire resistance
Primary Johnson-Nyquist Noise
SQUID 1/F Noise
Figure 2. Standard uncertainty calculation and relative uncertainty
produced by the most important components in normal situation of
measurements. Correlation 1 represents the correlation between the
primary and the standard wire resistance.
We estimate a combined standard uncertainty of
order 0.25 µ/ for resistors of 10 k to 1 G with
10 V bridge voltage. The direct measurement of a
10 M or 1 M resistor with the QHR yields a
combined standard uncertainty of 0.03 µ/ with
1 V. This shows that the two-terminal CCC is a
powerful tool for high resistance scaling.
 E. Pesel, B. Schumacher and P. Warnecke,
“Resistance scaling up to 1 M at PTB with a
cryogenic current comparator,” IEEE Trans.
Instrum. Meas., vol. 44, no. 2, pp. 273-275, Apr.
 R. E. Elmquist, et. al., “Direct resistance
comparisons from the QHR to 100 M using a
cryogenic current comparator,” IEEE Trans.
Instrum. Meas., vol. 54, no. 2, 525-528, Apr.
 R. E. Elmquist, et. al., “High resistance scaling
from 10 k and QHR standards using a
cryogenic current comparator”, submitted to this
 M. E. Cage, et. al., “Calculating the effect of
longitudinal resistance in multi-series-connected
Quantum Hall Effect devices”, J. Res. Natl. Inst.
Stand. Technol. 103, 561 (1998).