Circuit models and SPICE macro-models for quantum Hall effect devices

Quantum Hall effect (QHE) devices are a pillar of modern quantum electrical metrology. Electrical networks including one or more QHE elements can be used as quantum resistance and impedance standards. The analysis of these networks allows metrologists to evaluate the effect of the inevitable parasitic parameters on their performance as standards. This paper presents a systematic analysis of the various circuit models for QHE elements proposed in the literature, and the development of a new model. This last model is particularly suited to be employed with the analogue electronic circuit simulator SPICE. The SPICE macro-model and examples of SPICE simulations, validated by comparison with the corresponding analytical solution and/or experimental data, are provided

Electrical Resistance Tomography of Conductive Thin Films

The Electrical Resistance Tomography (ERT) technique is applied to the measurement of sheet conductance maps of both uniform and patterned conductive thin films. Images of the sheet conductance spatial distribution, and local conductivity values are obtained. Test samples are tin oxide films on glass substrates, with electrical contacts on the sample boundary, some samples are deliberately patterned in order to induce null conductivity zones of known geometry while others contain higher conductivity inclusions. Four-terminal resistance measurements among the contacts are performed with a scanning setup. The ERT reconstruction is performed by a numerical algorithm based on the total variation regularization and the L-curve method. ERT correctly images the sheet conductance spatial distribution of the samples. The reconstructed conductance values are in good quantitative agreement with independent measurements performed with the van der Pauw and the four-point probe methods.Comment: IEEE Transactions on Instrumentation and Measuremen

On the calibration of direct-current current transformers

Modern commercial direct-current current transformers (DCCT) can measure currents up to the kA range with accuracies better than 1E-5. We discuss here a DCCT calibration method and its implementation with commercial instruments typically employed in low resistance calibration laboratories. The primary current ranges up to 2 kA; in the current range below \SI{100}{\ampere} the calibration uncertainty is better than 3E-7. An example of calibration of a high-performance DCCT specified for primary currents measurement up to 900 A is discussed in detail.Comment: Accepted for publication in IEEE Trans. Instr. Meas. Copyright IEE

A quantum ampere

The revision of the International System of Units (SI), implemented since 20 May 2019, has redefined the unit of electric current, the ampere ( A), linking it to a fixed value of the elementary charge. This paper discusses the new definition and the realisation of the electrical units by quantum electrical metrology standards, which every year become more and more accessible, reliable and user friendly

A correlation noise spectrometer for flicker noise measurement in graphene samples

We present a high-resolution digital correlation spectrum analyzer for the measurement of low frequency resistance fluctuations in graphene samples. The system exploits the cross-correlation method to reject the amplifiers' noise. The graphene sample is excited with a low-noise DC current. The output voltage is fed to two two-stage low-noise amplifiers connected in parallel; the DC signal component is filtered by a high-pass filter with a cutoff frequency of 34 mHz. The amplified signals are digitized by a two-channel synchronous ADC board; the cross-periodogram, which rejects uncorrelated amplifiers' noise components, is computed in real time. As a practical example, we measured the noise cross-spectrum of graphene samples in the frequency range from 0.153 Hz to 10 kHz, both in two- and four-wire configurations, and for different bias currents. We report here the measurement setup, the data analysis and the error sources

A three-arm current comparator bridge, for impedance comparisons over the complex plane

We present here the concept of three-arm current comparator impedance bridge, which allows comparisons among three unlike impedances. Its purpose is the calibration of impedances having arbitrary phase angles, against calibrated nearly-pure impedances. An analysis of the bridge optimal setting and proper operation is presented. To test the concept, a two terminal-pair digitally-assisted bridge has been realized; measurements of an air-core inductor and of an RC network versus decade resistance and capacitance standards, at kHz frequency, have been performed. The bridge measurements are compatible with previous knowledge of the standards' values with relative deviations in the 10^-5 -- 10^-6 range

A simple algorithm to find the L-curve corner in the regularisation of ill-posed inverse problems

We propose a simple algorithm to locate the 'corner' of an L-curve, a function often used to select the regularisation parameter for the solution of ill-posed inverse problems. The algorithm involves the Menger curvature of a circumcircle and the golden section search method. It efficiently finds the regularisation parameter value corresponding to the maximum positive curvature region of the L-curve. The algorithm is applied to some commonly available test problems and compared to the typical way of locating the l-curve corner by means of its analytical curvature. The application of the algorithm to the data processing of an electrical resistance tomography experiment on thin conductive films is also reported

Calibration Setup for Ultralow-Current Transresistance Amplifiers

We describe a setup for the calibration of the transresistance gain of low-current amplifiers, based on the capacitance-charging method. The calibration can be performed in the current range of typical interest for electron-counting experiments. The setup implementation is simple and rugged, and is suitable to be embedded in larger experiments, where the amplifier is employed. The calibrated transresistance is traceable to the units of capacitance and time. Two different calibration modes were tested: with dc current (obtained using a custom-made piecewise linear ramp generator) and with low-frequency sinewave current (using a commercial generator). The relative base accuracy of the implementation is in the 10⁻⁵ range