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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
Abstract
In this paper we present the uncertainty evaluation of a new cryogenic current comparator (CCC) bridge designed to compare two-terminal 1 Mȍ and 10 Mȍ standard resistors with the quantized Hall resistance (QHR) and then scale from these values to other values between 10 kȍ and 1 Gȍ.
Introduction
condition of balance, the bridge equations are:
I1N1 I2 N2 I F N F ',
(1)
I1
V ,
R1 rw1
I2
V .
R2 rw2
(2)
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
systematic contributions.
The CCC is used in many national metrology
laboratories to obtain high accuracy four-terminal
resistance measurements in the range of 1 ȍ to
10 kȍ. Some papers show that this traditional CCC
can be used to measure high value resistors with low
uncertainty [1]. 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 Mȍ and 100 Mȍ [2] resistors. The recent two-
terminal CCCs [3] developed to compare the QHR
Figure 1. Schematic diagram of the bridge, showing connections
with room-temperature resistors use resistive
for room-temperature resistors and the voltage source (VS).
windings. This paper presents a complete study of the uncertainty in the new CCC which provides new
Uncertainty components
capabilities in resistance scaling for high-value resistors.
Type A evaluation of standard uncertainty First, we describe components which produce
Two-terminal resistive-winding CCC
random errors in the result and can be eliminated by averaging or reduced by a correct design of the
Figure 1 shows a schematic diagram of the twoterminal 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
system.
x 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. x SQUID noise. The SQUID produces 1/f and white
interference device (SQUID) senses the total flux and
noise components. The first is reduced by alternating
drives a feedback winding of one turn to maintain the
the current polarity and by averaging. The white
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
noise is specified by the manufacturer in units of μɎ0/Hz1/2 where Ɏ0 is the flux quantum.
x Electromagnetic interference and vibration
and 31-turn windings are made of phosphor-bronze
noise. These types of interference are very difficult to
wire and these have nominal resistances at 4.2 K of
estimate but a good design can be used to eliminate
2500 ȍ, 250 ȍ and 25 ȍ, respectively. The internal
these effects. The CCC is surrounded by different
resistances of the windings decrease the effect of self-
levels of shielding. All the wires connecting the CCC
resonance in the CCC. This improves the sensitivity
with the electronics or the resistor are shielded and
[2] but the winding resistance must be measured to
twisted. Inside the CCC the interconnecting leads are
correct the value of each resistor. Since this bridge
twisted together and fixed rigidly to the CCC probe.
measures two-terminal resistors, we use the triple-
x Noise in CCC electronics: voltage source,
series connection technique to reduce errors in
feedback current and feedback sense. The voltage
measurements of the QHR, as described in [4]. In a
source and the feedback current source were designed
\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_
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.
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 voltage offset.
Type B evaluation of standard uncertainty These components produce systematic offsets in the result. x 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. x 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. x 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. x 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 μȍ/ȍ in 100 Mȍ. x 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 circuit. x 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. x Resistor time constant. The resistor under test should have a low settling time-constant relative to the current reversal rate. x QHR, triple-series connection. The relative change in the quantized Hall resistance using a tripleseries connection in DC can be calculated from a mathematical model of the QHR [4]. In that reference an offset of less than 0.001 μȍ/ȍ was found with
typical leads and longitudinal resistance.
Simulation
Relative Uncertainty [μȍ/ȍ]
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.
0.25 Primary wire resistance
Secondary wire resistance
0.2
Voltage
Feedback current
Primary Johnson-Nyquist Noise
0.15
SQUID 1/F Noise
Leakage current
0.1
Correlation 1
Standard uncertainty
0.05
0
Nominal ratio
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.
Conclusion
We estimate a combined standard uncertainty of order 0.25 μȍ/ȍ for resistors of 10 kȍ to 1 Gȍ with 10 V bridge voltage. The direct measurement of a 10 Mȍ or 1 Mȍ resistor with the QHR yields a combined standard uncertainty of 0.03 μȍ/ȍ with 1 V. This shows that the two-terminal CCC is a powerful tool for high resistance scaling.
References
[1] E. Pesel, B. Schumacher and P. Warnecke, “Resistance scaling up to 1 Mȍ at PTB with a cryogenic current comparator,” IEEE Trans. Instrum. Meas., vol. 44, no. 2, pp. 273-275, Apr. 1995.
[2] R. E. Elmquist, et. al., “Direct resistance comparisons from the QHR to 100 Mȍ using a cryogenic current comparator,” IEEE Trans. Instrum. Meas., vol. 54, no. 2, 525-528, Apr. 2005.
[3] R. E. Elmquist, et. al., “High resistance scaling from 10 kȍ and QHR standards using a cryogenic current comparator”, submitted to this conference.
[4] 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).
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