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https://doi.org/10.1109/TIM.2008.2006967

Uncertainty Evaluation in a Two-Terminal Cryogenic Current Comparator

M. E. Bierzychudek and R. E. Elmquist, Senior Member, IEEE



Abstract— We present an uncertainty evaluation of a new cryogenic current comparator (CCC) bridge designed to compare two-terminal 1 MΩ and 10 MΩ standard resistors with the quantized Hall resistance (QHR) and scale from these decade values to other decade values between 10 kΩ and 1 GΩ. Use of the bridge over a wide range of resistance values results in a spectrum of dominant contributions to the uncertainty budget, and this analysis helps to determine the optimum parameters of the measurements. Our theoretical analysis is compared with experimental data.



Index Terms—Uncertainty, Current Resistance measurement, SQUIDs, Noise





comparators,



I. INTRODUCTION

THE CCC bridge is used widely in metrology to obtain high accuracy resistance ratios, typically in the range of 1 Ω to 10 kΩ. The CCC can also be used to measure high value resistors [1] and small currents [2]; however the traditional bridge design in some ways is less than ideal for high resistance. Uncertainty due to electrical leakage currents in these bridges [3] can be largely eliminated by using a CCC that compares two-terminal high-value resistance standards. In particular, the effect of leakage current is greatly reduced by using a single voltage source, instead of two isolated current sources. This also simplifies the electronics design and can reduce instability in the critical bridge feedback circuit, which is based on a superconducting quantum interference device (SQUID).

Two-terminal CCC bridges have been described in [4] that compare the QHR standard directly with 1 MΩ and 100 MΩ resistors. One of these used resistive wire for the ratio winding with the largest number of turns, giving a reduced quality factor (Q) in that winding. Since high-Q



Manuscript received June 3, 2008. M. E. Bierzychudek is with the Instituto Nacional de Tecnología Industrial, San Martín, B1650KNA, República Argentina (54-11-47246200, marcosb@inti.gov.ar). R. E. Elmquist is with the National Institute of Standards and Technology, Gaithersburg, MD, USA (301-975-6591, elmquist@nist.gov). Official contribution of the National Institute of Standards and Technology, not subject to copyright in the United States.



windings provide no benefit at dc and can produce resonances [5] that destabilize the SQUID, the resistivewinding technique is adapted here for use in a CCC with multiple ratio windings. This paper presents a complete study of the uncertainty in a two-terminal CCC with multiple ratios, which provide new capabilities in resistance scaling for high-value resistors [6-7].

II. CCC BRIDGE OVERVIEW

Figure 1 shows a schematic diagram of the two-terminal CCC described in this work. The source voltage is applied directly to the two resistors under test, in parallel. Each resistor is in series with a winding in one arm of the bridge, and these two windings have opposite directions and are tied together at a superconducting point connected to the low of the source, which is grounded. A dc SQUID magnetic flux detector senses the net flux produced in the CCC when the voltage is applied, and drives a feedback winding of one turn to maintain a constant flux balance in the bridge. This feedback current is measured, and then measured again after the source voltage is ramped to a similar dc output level with the opposite sign. The known ratio of the CCC windings allows the resistance ratio of the two bridge arms to be calculated from the change in the feedback current between the two dc voltage states and the applied voltage difference.

This bridge uses six major windings. The four-turn winding is superconducting and is used with the QHR standard. The 3100-turn, 310-turn and 31-turn windings used with room-temperature standard resistors are made of phosphor-bronze wire and have nominal resistance values



Current High potential

Voltage



QHR 4



3100



Current



310



Low potentia



310



Voltage



31



SQUID



1



R3



Fig. 1. Diagram of the two-terminal CCC showing connections of the QHR and standard resistors. Note that only two of the five ratio arms are used simultaneously and the CCC windings in those arms must have opposite directions, and only the 3100-turn or upper 310-turn winding can be used in the primary bridge arm.



at 4.2 K of 2500 Ω, 250 Ω and 25 Ω, respectively. The



internal resistances of the windings greatly decrease the



effect of self-resonance in the CCC and this makes it



possible to use windings of high inductance that improve



the sensitivity without introducing excess noise. Since this



bridge measures two-terminal resistors, the winding



resistances must be measured separately to obtain a



correction to the measured value of each room-temperature



resistor.



The bridge can be connected to measure a 1 MΩ or



10 MΩ room-temperature resistor against the QHR



standard on the i = 2 plateau (12906.4035 ) with a



winding ratio of 310-to-4 or 3100-to-4. We use the triple-



series connection technique to reduce errors due to lead



resistance in measurements with the QHR, as described in



[4], and the triple series connection is made at the two



bridge superconducting junctions in the cryogenic



environment of the CCC.



In a condition of balance, the bridge equations are:



I1N1  I 2 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. We can solve the bridge equations above to



find the resistance R1,



R1







VN2 /R2



VN1

  rw2  I F NF















rw1.



(3)



III. UNCERTAINTY COMPONENTS

A. Type A evaluation of standard uncertainty. First, we describe components which produce random errors in the result and can be reduced by averaging. This



2



set of noise components contributes to the standard



deviation of measurements closely spaced in time, and is



calculated as the standard deviation within a set of data.



 Johnson-Nyquist noise. The noise current produced by a



resistor Rj, with a temperature T and a bandwidth BW is



In 



4 kB T BW , Rj



(4)



where kB is the Boltzmann constant. The standard deviation of the Johnson noise is multiplied by the number of turns Nj in the winding and divided by a current sensitivity factor



fCCC to obtain the flux in the SQUID loop produced by the Johnson current,



u In 



4



kB T Rj



BW







Nj f CCC



 .



(5)



The Johnson noise does not produce correlation among the



samples so when we average samples we can decrease the



effect of this noise. In the system described here, the factor



fCCC is approximately 3.81× 10–6 Aturn/Φ0, where Φ0 is the flux quantum.



 Electromagnetic interference (EMI) and vibration



noise. These types of interference are very difficult to



estimate and a well-tested design is necessary to minimize



these effects. The liquid-helium cooled region of the CCC



is surrounded by several levels of superconductive



shielding. All the wires connecting the CCC with the



electronics or the resistors are shielded and twisted. The



interconnecting leads inside the CCC cryostat are isolated



by fine tubing as necessary but are twisted together and



fixed to the CCC probe.



 CCC electronics: voltage source and feedback current.



The voltage source and the feedback current source were



designed using low pass filters and low noise components.



We made all the ground connections with very low



impedance paths to reduce noise between grounds. Inside



the cabinet the interconnecting wires and circuit boards



were shielded from other nearby components.



 SQUID and electronics. The dc SQUID system produces



1/f and white noise components specified by the manufacturer in units of Ф0/Hz1/2. The current reversal technique helps to eliminate the slowly changing offset in



the SQUID, but the 1/f noise is not totally eliminated with



this technique. The white noise of the SQUID magnetic flux detector is specified to be below 5 µФ0/Hz1/2, with a 1/f noise corner near 0.4 Hz and an output gain of 0.77 V/Ф0.

We measured the SQUID output voltage to characterize



the SQUID and semi-isolated CCC system noise. In these



measurements the cryostat was only connected to the



SQUID electronics, and the output of the SQUID



electronics was measured with a digital multimeter (DMM).



A histogram of voltage readings from the SQUID are



shown in Fig. 2. This data is typical for measurement



integration periods of 5 s, with delay times between



measurements of 4 s to 30 s, and shows that the noise in the



SQUID signal can be modeled with a Gaussian probability



density function with a mean value of 0 V and a standard



deviation of 30 µV. The excess contribution of EMI and



Frequency [%]



150 120 90 60 30 0 -30 -60 -90 -120 -150



vibration-induced noise is probably evident here, and is also seen as noise peaks at frequencies between 1 Hz and 500 Hz in power spectral density measurements.

18 16 14 12 10

8 6 4 2 0

SQUID residual voltage noise [µV]

Fig. 2. Histogram showing the distribution of noise voltage measurements made at the output of the dc SQUID. We eliminate the slowly changing voltage offset by taking a difference of three samples: the first is the average value of N readings, the second is the average value of 2*N readings and the last sample is the average value of N readings. The plotted data consists of 399 samples with 30 s of delay between samples with N = 5 seconds integration time. We obtained a mean of 0.59 µV and a standard deviation of 30 µV.

B. Type B evaluation of standard uncertainty.

This type of component can produce a systematic offset in the result. The physical process that causes an offset can sometimes be modeled and a calculated correction can be applied to reduce the uncertainty.  Winding and lead resistance. The uncertainty produced by the correction of the winding and lead resistance has three components: the measurement device, the current coefficient of resistance and the dependence on helium level. For the windings and connecting leads that are made of phosphor-bronze wire the change of resistance is in the range of one or two milliohms when the helium level changes from 100% to 10%. This effect is due mainly to the leads that connect the windings with the connectors in the top of the cryostat. This error can be eliminated if the resistance is measured each day.

We have compared several different methods of measuring the resistance of the connecting leads and windings, and found that high-resolution DMMs provide good sensitivity and accuracy using the four-terminal resistance function. A settling delay of up to 10 s is necessary before each reading for the 3100-turn winding and lead resistance. The estimated total relative uncertainty (1 ) of the resistance corrections is 10 µΩ/Ω for the 31 turn arm of the bridge, 10 µΩ/Ω for the 310 turn arm and 20 µΩ/Ω for the 3100-turn arm.

The uncertainty of the 31-turn lead and winding resistance is critical when it is connected to a 10 k resistance standard. Here, potentiometer measurements may be more accurate than the resistance function of the DMM. In this method the standard resistor’s four-wire terminations provide taps for measuring the voltage drops produced in the connecting wiring, using the voltage source as in a



3

normal CCC measurement. The DMM measures the voltage drop from the appropriate potential point of the bridge to the unused high and low potential taps of the resistor for both current directions, and these are used to calculate the resistance correction of the bridge arm.

To estimate the current coefficient we measure each winding with different currents. We have found that the effect of the current is only important in the 3100-turn winding, and its relative current coefficient is 4 × 10–7 Ω /µA. Typically, we measure the 3100 winding with a current of 50 µA, and in use it carries currents lower than 10 µA, so this uncertainty is 20 µΩ/Ω. This winding is typically used with resistor values greater than 1 MΩ, so the systematic uncertainty produced by the current

coefficient is approximately 0.005 Ω/Ω or less.

 Measurement of the feedback current. To measure the feedback current we use a 200 k sense resistor and two buffers, one at each resistor terminal, and a multimeter that measures the difference voltage between the outputs of the buffers. These buffers produce errors due to their bias currents, as well as high frequency voltage noise and 1/f noise due to the temperature dependence of the voltage offset. These last two produce a very small error but the buffer bias current limits the uncertainty in some high resistance measurements where both the measurement currents and feedback current are small. One of these buffers is between the sense resistor and the feedback current source and the other is between the resistor and the 1-turn feedback winding. The first does not produces an error because it is before the sense resistor, however the bias current of the second buffer changes the sensed current, and it produces an error that we estimate like a flux error. The sense resistor is a stable, card-type wire-wound resistor with a temperature coefficient of less than 1 (Ω/Ω)/°C and its value has a negligible uncertainty contribution. Thus, the uncertainty of the feedback current measurement is calculated as the uncertainty produced by the DMM and the buffer bias current.  Voltage source and thermal EMF. This type of bridge does not use a feedback loop with a third winding to balance the voltage across each resistor; instead the voltage balance is created at the two superconducting junctions linking the arms of the bridge. The stability of the bridge voltage is best when using the voltage compensation technique, where the source output buffer senses the feedback voltage directly from the two superconducting junction points of the bridge.

Like the primary source in any current comparator bridge, the instability of the source produces an uncertainty that is proportional to the resistance ratio imbalance. In addition, the voltage across each resistor can be affected by the thermal electromotive forces (EMF) in the arms of the bridge. These effects are reduced by the bridge voltage reversals if the voltage source and thermal EMF are constant or drift linearly. We have found a stability of 5 nV in the EMF of the bridge connections which produces less

than 0.001 Ω/Ω uncertainty at 10V bridge voltage. The



Fig. 3a. Fig. 3b.



R2



N2



V



RL



R1



N1



RL



V



R



N



Fig. 3c. Fig. 3d.



V



RL



N



RL



V



R



N



voltage source stability is better than 25 V after an initial

warm-up of 45 minutes, which produces a similar level of

uncertainty.

 Leakage current. In this CCC the leakage current can affect only in four different situations. The first two are different to a traditional superconducting CCC and more similar to a Direct Current Comparator since some windings are resistive.

a) The first situation is for a leakage current IL between different windings (see Fig. 3a), which can be estimated as



IL







1 RL



 VRN1  R1  RN1







VRN 2 R2  RN2



 



,



(6)



where V is the source voltage, RN j is the resistance in the winding j plus the lead resistance and Rj is the resistance of the standard in the j bridge arm. The systematic error in the



ratio is then



er







I L N 1I L N VN1 R1 



2















RN1 RL







RN 2 RL



R1 R2



1 



N2 N1







.



(7)



A slightly different case is when one of the windings is



not used,



IL







1 RL



 



VRN1 R1  RN1



 



,



(8)



er







RN1 RL



1 



N2 N1



 .



(9)



In both case, the error is small because the point of leakage



is close to ground potential. This leakage current is limited



by grounded shields or polytriflouroethelene (PTFE)



insulation surrounding the bridge conductors in all regions



except in the contacts between the windings inside the



CCC. In this region the wires are at 4.2 K and we have



4



measured this isolation resistance using an electrometer and



found a minimun value of 10 TΩ.With a leakage resistance



of 10 TΩ the relative error is less than 0.001 µΩ/Ω.



b) Leakage through isolation resistance in parallel to a



winding (Fig. 3b) produces a current divider between the



winding resistance (RN j) and the leakage resistance.



IL



 Ij



RN j RL  RN j



,



(10)



er







RN j RL  RN j



.



(11)



The most likely location of this type of leakage current is



between the turns of the windings. We cannot measure this



isolation resistance but we know that it should be on the



order of the resistances isolation between windings. The



uncertainty increases with RNj and is greatest for RNj  2500 Ω, and this error is 0.00025 µΩ/Ω with an isolation



resistance of 10 TΩ. We use thick Formvar insulated wires



to wind the CCC, and the specification of resistivity for this material is 1·1017 Ωcm at ambient temperature. It is



important to note that this error is independent of the



resistor under test.



c) When a winding is not used, a leakage current could



flow from the positive terminal of the source to the positive



terminal of the winding (Fig. 3c) and produce an error as it



flows in the winding. Inside the CCC probe, all of the



Formvar-insulated wires used to connect the resistors are in



separate PTFE tubes giving very low leakage current. The



cable terminations of all of the decade-value windings are



shielded PTFE-insulated coaxial connectors on the top



flange of the CCC probe, eliminating any source of such



leakage. The three positive terminations that allow the QHR



standard to be connected to the CCC are made at a shielded,



multi-pin connector which also carries the source voltage.



Because of this construction difference, the leakage



problem is more important in the QHR coil (4-turn) and



also the feedback coil (1-turn). The relative error produced



by this current leakage can be estimated as the flux



produced in the 4-turn plus 1-turn windings by a current



that flows in the isolation resistance with due to the source



voltage,



er







5V RL



N 1V R1







R1 RL



5 N1



.



(12)



The insulation of the multi-pin connector is improved by



selected grouping the pins and is measured to be greater



than 10 T. Thus, this error is less than 0.2 Ω/Ω for ratios



involving a 1 G primary resistor. d) Leakage in parallel to the resistors under test (Fig. 3d)



can be caused by surface conduction of the resistor element,



with an uncertainty that can be made negligible by the



resistor’s construction, or conduction through insulators



used in mounting the resistor. The second of these can be



intercepted by grounded or guarded conductors. Leakage



from the high resistor terminal to a grounded conductor is



in parallel to the source voltage and thus does not produce a



significant error.

Guarding is necessary with this design of CCC only for

high-resistance Hamon network devices [8, 9] with multiple

internal connections, where leakage through an isolation

resistance causes current to flow through a major part of the

resistor under test. Internal or external guard networks are

often used to decrease the effect of the leakage current. The

CCC voltage source provides a guard voltage output to

drive a guard network and reduce the leakage current

uncertainty, which can be of order 5 Ω/Ω for an

unguarded Hamon device of 1 G series resistance. The

residual error with a guard network matched to 1% would

be of order 0.05 Ω/Ω.

 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. To test this, the CCC solenoid was constructed with an additional five superconducting windings: two of 1-turn, two of 2-turn and one of 4-turn. A build-up procedure was used where currents from the reversing source were applied and the SQUID output voltage was measured. We used a resistor in series with the voltage source to limit the current to 5 mA or 10 mA. The estimated relative uncertainty was calculated as the flux mismatch divided by the total theoretical flux,

and was approximately 0.005 Ω/Ω or less.

 SQUID feedback null. Upon the reversal of the voltage source, the external feedback must maintain constant output voltage in the SQUID electronics. We can make the same measurement as for SQUID 1/f noise but with the feedback on, which tests the operation of the feedback integrator. It is important to note that with feedback on, the SQUID output voltage is more constant than without feedback. This means that the SQUID 1/f noise is cancelled by the feedback and it is transferred to the voltage in the current sense resistor. No difference upon current reversal greater than the

measurement uncertainty of 1.5 V was detected in the SQUID output. This is equivalent to an uncertainty of about

0.08 Ω/Ω in a 1-to-1 ratio at 100 M and 10 V, using 310-turn windings.

 Resistor under test. Resistors of value higher than 1 MΩ in particular can exhibit a time constant of resistance, due to dielectric absorption after the measurement voltage is applied. We have seen excellent results with no measurable

time constant in standard resistors up to 1 G constructed using metal film resistors [10, 11]. In this analysis we do not consider the effect of the temperature coefficient of resistance in the resistors under test, and this can increase the total uncertainty.

 QHR, triple-series connection. The relative change in the quantized Hall resistance using a triple-series connection for DC measurements, compared to a fourterminal resistance measurement, can be calculated from a mathematical model of the QHR [12, 13]. We estimate this difference to be less than 0.001 µΩ/Ω for this CCC when using typical QHR lead resistance and longitudinal



5



Ratio Standard Uncertainty (x 10-6)



1.0000 0.1000



Resistance (Rw1) Feedback (IF) SQUID 1/f noise Total



Resistance (Rw2) Johnson (R1) Leakage current



0.0100



0.0010



0.0001



1E+06



1E+07



1E+08



1E+09



Primary Resistance ()



Fig. 4. The seven most significant uncertainty contributions derived in the simulation, for 100-to-1 resistance ratios using the 3100-turn and 31-turn CCC windings. The contributions are derived for a 10 V source voltage and for sequences of 24 readings each having 4 s DMM integration time. The total uncertainty includes all factors described in the text.



1.0000 0.1000



Resistance (Rw1) Feedback (IF) SQUID 1/f noise Total



Resistance (Rw2) Johnson (R1) Leakage current



Ratio Standard Uncertainty (x 10-6)



0.0100



0.0010



0.0001



1E+05



1E+06



1E+07



1E+08



Primary Resistance ()



Fig. 5. Significant uncertainty contributions derived in the simulation, for 10to-1 ratios using the 310-turn and 31-turn CCC windings. The contributions are derived for a 10 V source voltage and for sequences of 24 readings each having 4 s DMM integration time. The total uncertainty includes all factors described in the text. Note the total uncertainty is a minimum at a primary

resistance of 1 M, while the minimum is at 10 M in Fig. 4.



resistance values. Calculations of the combined standard uncertainty for

the many combinations of windings, resistance values, and measurement parameters were condensed into spreadsheet form, which simplifies the calculation of uncertainty terms. Graphs of the largest contributions in the simulated uncertainty calculations are shown for two important cases in Fig. 4 and Fig. 5. Comparing these figures shows that for

resistance comparisons at values of 10 M and above, ratios which use the 3100-turn winding should yield the lowest uncertainty. For scaling involving only standard

resistors of 1 M and below, better results may be produced using the lower 10-to-1 ratio, with the 310-turn winding in the primary arm, because of smaller winding resistance uncertainty.

The QHR to 1 M and 10 M ratios eliminate the secondary arm resistance correction, but the voltage source output must be limited to about 1 V to maintain ideal contact resistance and longitudinal resistance in the QHR



6



Resistance ()



10000359

10000358

10000357

10000356

10000355

10000354 0.6 0.7 0.8 0.9 1 1.1 1.2

Bridge Voltage (V)

Fig. 6. Resistance values for a 10 M resistance standard measured using direct scaling from the QHR standard (solid squares) and by scaling from the QHR using an intermediate 1 M resistance standard (open triangles). The standard uncertainty for each point is approximately 1 .

standard. Calculations for these ratios yield combined standard uncertainties of approximately 0.07 Ω/Ω for 1 M and 0.07 Ω/Ω for 10 M with the same timing parameters as in Fig. 4 and Fig. 5.

IV. COMPARISON WITH EXPERIMENT Type A uncertainties obtained with the bridge for a variety of bridge parameters are between one and two times the estimated combined standard uncertainty for the SQUID and Johnson noise contributions. This range of values reflects typical laboratoy conditions and is reasonable given external noise sources. Measurement results for a 10 M resistor based on a direct scaling using the QHR standard agree with the 10-to1 scaling between 10 Mand a calibrated 1 Mresistor within the estimated standard uncertainty. Figure 6 shows resistance values obtained for a 10 M standard in direct ratio comparisons with the QHR standard at three voltage levels, and similar results based on a QHR-calibrated 1 M standard. In this low voltage range the uncertainty in 10-to1 scaling is dominated by 1/f noise in the DC SQUID detector. Results based on comparisons between 1 M and 10 M standards at a bridge voltage of 10 V agree with QHR-based comparison results to within the standard uncertainty of 0.05 Ω/Ω. Another test of the bridge type B uncertainty is to compare two scaling paths between resistors having a resistance ratio of 100-to-1. Direct ratios, using 100 M and 1 M standards, were compared to combined ratios based on two 10-to-1 ratios using an intermediate 10 M standard. No significant differences were seen between these scaling paths to 100 M, with a typical type A uncertainty of 0.15 Ω/Ω for a source voltage of 10 V. Similar results were obtained based on the 3100-to-310 winding ratio and the 310-to-31 ratio for the comparison of 1 M and 10 M standards, which agree at the level of



0.03 Ω/Ω ± 0.05 Ω/Ω.

V. CONCLUSIONS

At present, the dominant uncertainty component in most of the measurement range is the 1/f noise component. The uncertainty calculation is in good agreement with the most sensitive results of 100-to-1 and 10-to-1 scaling measurements, and the uncertainty estimate shows that this CCC can achieve a combined standard uncertainty of order 0.1 µΩ/Ω for resistors of 100 MΩ and 1 µΩ/Ω for resistors of 1 GΩ with 10 V bridge voltage. Comparing this new CCC with traditional methods its combined standard uncertainty is two or three times smaller. But the great advantage of the two-terminal CCC is its scaling power. While with a traditional method the total uncertainty in a scaling process to high value resistor is the quadratic sum of the uncertainty in each step. The two-terminal CCC can measure a 10 MΩ resistor directly with the QHR, and its uncertainty at 10 MΩ is approximately 10 times lower than the best uncertainties claimed in the CCEM-K2 key comparison [14]. In further scaling, it is possible with this new method in only one step to scale to a resistor between 100 kΩ and 1 GΩ.

ACKNOWLEDGMENT

The authors are indebted to several collaborators who have made significant contributors to the development of the high-resistance CCC, including B. Pritchard of the National Measurement Institute (Australia), F. HernandezMarquez of the Centro Nacional de Metrología (Mexico), and G. R. Jones, Jr. of the National Institute of Standards and Technology.

REFERENCES

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[7] M. E. Bierzychudek, R. E. Elmquist, “Uncertainty Evaluation in a Two-Terminal Cryogenic Current Comparator,” CPEM 2008 Digest, p. 152-153, Broomfield, Colorado, USA, June 2008.



[8] B. V. Hamon, “A 1-100  build-up resistor for the calibration of standard resistors,” J. Sci. Instrum., vol 31, pp. 450-453, 1954.

[9] D. G. Jarrett, “Evaluation of guarded high resistance hamon transfer standards,” IEEE Trans. Instrum. Meas., vol. 48, pp. 324-328, Apr. 1999.

[10] R. F. Dziuba, D. G. Jarrett, L. L. Scott, and A. J. Secula, “Fabrication of high-value standard resistors,” IEEE Trans. Instrum. Meas., vol. 48, pp. 333-337, Apr. 1999.

[11] M. E. Bierzychudek, R. Garcia, M. Real and A. Tonina, “Design and fabrication of high value standard resistors at INTI,” CPEM 2008 Digest, p. 396-397, Broomfield, Colorado, USA, June 2008.

[12] F. Delahaye, “Series and parallel connection of multiterminal quantum Hall effect devices,” J. Appl. Phys., vol 73, pp. 7915-7920, 1993.

[13] M. E. Cage, A. Jeffery, R. E. Elmquist and K. C. Lee, “Calculating the effect of longitudinal resistance in multi-series-connected quantum Hall effect devices,” J. Res. Natl. Inst. Stand. Technol. 103, 561 (1998).

[14] R. F. Dziuba and D. G. Jarrett, “CCEM-K2 Key Comparison of Resistance Standards at 10 MΩ and 1 GΩ,” July, 2001. Available



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online at http://kcdb.bipm.org/AppendixB/appbresults/ccemk2/ccem-k2\_final\_report.pdf

M. E. Bierzychudek received the electronics engineer degree from the Universidad de Buenos Aires, Argentina, in 2006.

In 2005, he joined the Electricity Division, Instituto Nacional de Tecnología Industrial, Argentina, and he has worked since then in the voltage and resistance laboratory; involved in measurements of the Josephson effect and the Quantum Hall effect.

R. E. Elmquist (M ’90, SM ’98) received the B. A. and Ph.D. degrees from the University of Virginia in Charlottesville, in 1979 and 1986, respectively.

In 1986, he joined the National Institute of Standards and Technology, in Gaithersburg, MD. His interests include development of cryogenic current comparator systems for resistance scaling, ac/dc calculable resistors, and SI measurements. He presently is the leader of the Metrology of the Ohm project in the Quantum Electrical Metrology Division of the Electronics and Electrical Engineering Laboratory.