Precision tests of quantum hall effect device DC equivalent circuit using double-series and triple-series connections

Jeffery, Anne-Marie; Elmquist, Randolph E.; Cage, Marvin E.

doi:10.6028/jres.100.050

Cited by 28 publications

(31 citation statements)

References 18 publications

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“…However, when nonadjacent terminals are short-circuited together, the resulting resistance value can be a multiple or a fraction of R H . Fang [6, figure 1(a DC analytical modelling of double-and triple-series connections of single and twin devices was performed in [2] and [3]; in [5] the analysis was extended to the ac regime. The modelling process is based on the Ricketts-Kemeny model [7] of the quantum Hall device, or on its derived ones [2,5].…”

Section: Introductionmentioning

confidence: 99%

“…In this section we analyse the effect of contact resistances on several examples of single device connections (table 1, first column). These examples, which were already analysed using other methods by Delahaye[2] and by Jeffery et al[3], have been chosen for their practical interest. For each connection, the second column of table 1 shows a suitable choice of port voltages and the third column shows the corresponding matrix A.…”

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confidence: 99%

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Matrix method analysis of quantum Hall effect device connections

Ortolano

Callegaro

2011

Metrologia

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The modelling of electrical connections of single, or several, multiterminal quantum Hall effect (QHE) devices is relevant for electrical metrology: it is known, in fact, that certain particular connections allow i) the realization of multiples or fractions of the quantised resistance, or ii) the rejection of stray impedances, so that the configuration maintains the status of quantum standard. Ricketts-Kemeny and Delahaye equivalent circuits are known to be accurate models of the QHE: however, the numerical or analytical solution of electrical networks including these equivalent circuits can be difficult. In this paper, we introduce a method of analysis based on the representation of a QHE device by means of the indefinite admittance matrix : external connections are then represented with another matrix, easily written by inspection. Some examples, including the solution of double-and triple-series connections, are shown.

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Section: Introductionmentioning

confidence: 99%

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confidence: 99%

Matrix method analysis of quantum Hall effect device connections

Ortolano

Callegaro

2011

Metrologia

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“…The two-terminal resistance of this device connection differs from R H by a relative error of order (R C /R H ) M where M is the number of external leads connected to discrete high or low device contacts. 20,21 For M = 3, R C ≤ 10 , and R H = R K /2, the resulting resistance value differs from the conventional four-terminal QHR resistance value by less than one part in 10 9 .…”

Section: Minimizing Qhr Lead Resistance Errormentioning

confidence: 96%

Precision high-value resistance scaling with a two-terminal cryogenic current comparator

Hernandez-Marquez

Bierzychudek

Jones

et al. 2014

Review of Scientific Instruments

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We describe a cryogenic two-terminal high-resistance bridge and its application in precision resistance scaling from the quantized Hall resistance (QHR) at RH = RK/2 = 12 906.4035 Ω to decade resistance standards with values between 1 MΩ and 1 GΩ. The design minimizes lead resistance errors with multiterminal connections to the QHR device. A single variable voltage source and resistive ratio windings are utilized to achieve excellent dynamic stability, which is not readily obtained in low-current measurements with conventional cryogenic current comparators (CCCs). Prototypes of this bridge have been verified by a successful international comparison of high-resistance scaling using two-terminal CCCs in the national metrology institutes of Argentina, Mexico, and the United States.

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“…Therefore the indirectly measured acl/12.9QFI quadratic dependence is (-1.3 ± 1.4) x 10W81kHz2. Equivalent Circuit Model Jeffery, Etmquist, and Cage [4] showed that the Ricketts and Kemeny equivalent electrical circuit model [5] represents multi-series-connected dc QHR devices to 1 part in 109 accuracies. That Ricketts/Kemeny model [5] lies at the heart of the Cage/Jeffery/Matthews equivalent electrical circuit representation [3] of an ac QHR standard with two external quadruple-series connections when measured under 4TP balance conditions.…”

Section: Exderimentmentioning

confidence: 99%

Quadratic Frequency Dependence of an AC QHR Device

Cage

2004

2004 Conference on Precision Electromagnetic Measurements

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An equivalent electrical circuit model of an ac quantized Hall resistance device externally connected in quadruple series predicts a quadratic frequency dependence no more than 4 x 10-9/kHzt. This agrees with experiment when indirectly comparing that device with a calculable quadrifilar resistor in interchanged 1:1 ratios using a four-terminal-pair bridge.Introduction AC quantized Hall resistance (ac QHR) standards have linear and quadratic frequency dependences, as do the reference resistors with which they are compared, and the ac measurement bridges themselves [1]. This paper deals only with the quadratic dependences. The bridge quadratic dependence is dominant [1] and must be removed. Then either a reference resistor with a calculable quadratic dependence is required to extract its ac-dc difference [2] and thereby determine the quadratic dependence of the ac QHR standard, or the quadratic dependence of the ac QHR standard itself must be determined [3]. This experiment does all of the above. Quadrifilar (Gibbings) resistors [2] are often employed as calculable reference resistors to

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Precision tests of quantum hall effect device DC equivalent circuit using double-series and triple-series connections

Cited by 28 publications

References 18 publications

Matrix method analysis of quantum Hall effect device connections

Matrix method analysis of quantum Hall effect device connections

Precision high-value resistance scaling with a two-terminal cryogenic current comparator

Quadratic Frequency Dependence of an AC QHR Device

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