PhD Abstract

The future International System of Units, based on fundamental constants, will allow to take full advantage of the quantum standards of resistance, current and voltage that are linked to the planck constant and the elementary charge only. In this thesis, we have developed and studied a resistance standard based on the quantum Hall effect in graphene obtained by chemical vapor deposition (propane/hydrogen) on silicon carbide substrate. For the first time we were able to show that a graphene resistance standard could operate at more practical experimental conditions than its counterpart in GaAs/AlGaAs, ie at higher temperatures (T = 10 K), weaker magnetics fields (B = 3,5 T) and larger measurement currents (I = 500 μA). From an understanding and improvement perspective, we have analyzed the fabrication process of the Hall bar and its reproducibility, tested a method to modify the electronic density, and investigated the quantum Hall effect dissipation mechanisms. In a second part, we have demonstrated that it was possible to realize a programmable and versatile quantum current source from the elementary charge, by combining the two quantum standards of voltage and resistance in a quantum circuit integrating a cryogenic current comparator. Currents were generated in the range from 1 μA to 5 mA, with a relative uncertainty never achieved before of 10⁻⁸. We have also showed that this current standard, realizing the new definition of the ampere, could be used to calibrate an ammeter.

Key words

metrology, quantum Hall effect

PhD abstract

Measuring high alternating currents over a wide frequency bandwidth is essential for many applications including the monitoring of the electrical distribution network and the development of electric vehicles. In the first case, current measurement is necessary to quantify the quality of the grid in the presence of harmonics from intermittent renewable energies with a large frequency spectrum (several hundred kilohertz). In the second case, current measurement (up to several tens of amperes) is used to quantify the efficiency of an electric motor's traction chain: in current measurement, it is essential to take into account a large number of harmonics (up to 1 MHz) to ensure an accurate knowledge of the motor's efficiency. Resistors of low values, called “shunt”, are then mandatory to measure high currents. Shunts are widely used as a resistance standard in metrology laboratories and precision instruments. Their use requires the preliminary knowledge of the following two parameters according to the frequency: Impedance phase shift; relative variation of the impedance magnitude according to its DC resistance value, this parameter is called “AC-DC difference”. For a current level of 10 A, the impedance of existing shunts shows strong variations in magnitude and phase for frequencies above 100 kHz. In addition, in National Metrology Institutes, to calibrate shunts beyond 1 A the measurement methods currently used are limited in magnitude up to 100 kHz and phase up to 200 kHz; and provide access to only one of the two parameters: magnitude or phase of impedance. The aim of this thesis is to extend the calibration capabilities of high current sensors up to 10 A and 1 MHz and thus improve the traceability of AC current measurements. Firstly, we developed a 10 A shunt standard whose electromagnetic (up to 10 MHz) and thermal responses are fully calculable: at 1 MHz the phase shift and transposition deviation are -0.01 mrad and 15 ppm respectively. Secondly, we developed a traceable calibration method to measure shunts up to 10 MHz. The measurement method, based on the use of a vector network analyzer, allows the AC-DC deviation and impedance phase of a shunt to be measured simultaneously with relative uncertainties less than 1×10⁻³ at 1 MHz.

PhD thesis

Key words

uncertainly, current measurement, calibration, current shunts, impedance, modeling

PhD abstract

Differential circuits are widely used in the design of high frequency components mainly because of their better noise immunity. These circuits can be characterized using mixed-mode S parameters (differential- and common-mode S-parameters and cross-mode terms). Furthermore, the trend toward miniaturization and integration of microwave devices increases the need for planar or coplanar microwave integrated circuits such as micro-strip lines or coplanar waveguides. The ungrounded coplanar waveguide structure with all the conductors located on the same side of the substrate eliminates the need for via-holes, and thus simplifies manufacturing and prevents the appearance of some parasitic elements. From the viewpoint of electrical metrology, it is necessary to establish the traceability of the mixed-mode S-parameter measurements to the International System of Units (SI). The Multimode Thru-Reflect-Line (TRL) calibration method, derived from the commonly-used TRL calibration for S-parameter measurements of single-ended circuits, is particularly well suited for this purpose as the standards are traceable via dimensional measurements. The characteristic impedance, which defines the reference impedance of the measurement system, can be achieved from the propagation constants determined during the Multimode TRL calibration and the capacitances per unit length of the transmission line.

We present the first design and realization of Multimode TRL calibration and verification kits using coupled coplanar lines in the “Ground - Signal - Ground - Signal – Ground” configuration on quartz (SiO2), the low-loss substrate, for on-wafer mixed-mode S-parameter measurements from 1 GHz to 40 GHz.

Measurements are performed using two methods: the “one-tier” technique, based on the Multimode TRL calibration procedure, determines and corrects all systematic errors. The “two-tier” approach, in which the Multimode TRL is applied at the second-tier, is applied to measurement data that were partially corrected by the first calibration. The feasibility and the validation of the methods are demonstrated by measurements of matched, mismatched and unbalanced lines and T-attenuators showing good agreement between simulated and measured results.

The propagation of uncertainty can be derived by the calculation of partial derivatives using the Metas.Unclib tool or by the numerical approach based on the Monte Carlo technique. The accuracy of on-wafer S-parameter measurements depends on sources of influence attributed to the measurements and to the imperfections of the standards such as the VNA noise and non-linearity, the cable stability, the measurement repeatability, and the sensitivity in calibration standards’ realization. We focus, first and foremost, on the propagation of uncertainties related to the repeatability of the standards and the device under test measurements to the corrected mixed-mode S-parameters of the mismatched line. The results show that the partial derivatives approach based on an approximation of the first-order Taylor series cannot be accurately used due to the significant influences of non-linear functions in the Multimode TRL algorithm. The Monte Carlo method is then more precise although it requires very long computation time.

Key words

four-port vector network analyzer, differential circuit, multimode TRL calibration, coupled coplanar waveguide, mixed-mode scattering parameters, measurement uncertainty

PhD abstract

As the worldwide concern for the climate change and its effects are growing, the governments are forced to make strong decisions in favour of the implementation of the smart electrical grids. However, the success of these actions strongly depends on meeting the certain requirements of the electricity system raised by the quality of the energy supplied and the means to assess it. The smart electrical networks have to tackle the challenges raised by the increasing uptake of the renewable energy sources, such as the photovoltaic (PV), wind, etc. and the equipment, such as photovoltaic inverters (PVI), electric vehicle chargers (EVC), etc. This introduces a complex dynamic operating environment for the distribution system. The distortions coming from the new generation and load equipment are generally larger and less regular than those due to the traditional generation and load equipment, making the power and energy measurements difficult to perform. In this context, the thesis aims to quantify and reproduce the supraharmonic emissions in the frequency range of 2 kHz to 150 kHz. Therefore, the existing literature on the supraharmonic emissions in the frequency range of 2 kHz to 150 kHz is studied. The 4-channel measurement system is designed and implemented for the measurement of the fundamental and supraharmonic components of the voltage and current waveforms in the frequency range of 2 kHz to 150 kHz in the electrical network. The measurements are carried out in the EDF’s Concept Grid platform. The individual equipment characterization and electrical network tests are carried out here. The waveforms acquired during the measurement campaigns are processed mathematically using the fast Fourier transform (FFT) algorithm and statistically using the analysis of variance (ANOVA) algorithm. The mathematical and statistical processing of the acquired waveforms helps to determine the individual effects and interactions of the different parameters in the generation of the supraharmonic emissions in the electrical network. The various parameters, such as the primary and secondary emissions, effects of the cable length, effects of the sudden addition and removal of the load equipment are also studied. The thesis describes the design of the complex waveform platform, which can be used for the laboratory testing and the characterization of the power quality analyzers (PQA) in the frequency range of 2 kHz to 150 kHz. In the electrical networks, the waveform platform can be used to measure the supraharmonic emissions in the frequency range of 2 kHz to 150 kHz. The software architecture of the waveform platform is described here. In addition, the paper explains the hardware design of the waveform platform. It also includes the laboratory and electrical network applications of the waveform platform. The laboratory setup for the characterization of the PQA and the measurement schema for the electrical network waveforms are also depicted here. The uncertainty budget for the waveform platform is calculated considering the various factors, such as the cable length, noise, etc. are discussed in the thesis. Finally, the PQA is characterized in the frequency range of 2 to 150 kHz with respect to the waveform platform for varying emission amplitudes.

Key words

power quality, renewable energy sources, smart grids, supraharmonic emissions, waveform platform

Abstract

We propose a method to determine the reference impedance of the TRA calibration technique for vector network analysers. This method was developed within the framework of our activity on traceability of on-wafer S parameters measurements. Starting from a modified TRA calibration procedure, we demonstrate the possibility to determine the calibration reference impedance, and leading to a significant reduction of the measurement uncertainties. In comparison with results obtained using the reference multiline TRL calibration technique, the results that we obtain show the efficiency of the present method.

Key words

vector network analyser
S parameters
on-wafer measurements
TRA calibration

Abstract

The LNE has recently developed a 1 V programmable Josephson voltage standard specially dedicated to its transfer activities such as calibration of DC voltage references (Zener diode reference and Weston saturated standard cells) and digital voltmeters of high precision. This new programmable Josephson voltage standard allows the LNE to propose new calibration capabilities with reduced uncertainties while taking advantage of the simplicity to operate programmable Josephson array. The 1.018 V output voltage of the Zener diode reference can then be calibrated with a typical relative uncertainty of 80 nV (k = 2) in the framework of routine calibration services (an improvement by a factor 7). This paper describes the design of the new system and its metrological performances.

Key words

DC volltage standard
josephson effect
programmable josephson junction array
voltage calibration

Abstract

This paper describes a new primary standard at LNE for precision measurement of RMS values and total harmonic distortion of periodic signals containing a fundamental frequency at 50 Hz and quasistationary harmonics which maximum order is 50. The method is based on the sampling of the signals and the analysis of the samples by discrete Fourier transform. The traceability to the SI units is ensured by comparing the measurements to those obtained using a thermal converter. The standard uncertainty for RMS value and total harmonic distortion are respectively 22 µV/V and 0,0025% for all the signals studied.

Key words

primary standard
quasi-stationnary harmonic
sampling technique
aperture time
thermal converter

Abstract

The article presents the new electrical power measurement capabilities at LNE. The primary standard is based on sampling techniques. The power is calculated with a discrete Fourier transform algorithm, which is used to process the quantised samples of the voltage and current signals. Up to now, this primary standard was characterised only to measure active power for sinusoidal signals in the 45 Hz–65 Hz frequency range. From now on, the reactive power can also be measured and the frequency range has been extended to 400 Hz.

Key words

digital wattmetter
active and reactive powers
uncertainty budget

Abstract

The RMS value of a signal is measured by averaging its squared value over an infinite duration, and similarly a power is measured by averaging the product of two signals (voltage and current). These computations of square, product and average are very easy when the signal has been digitised, but this digitisation carries three distinct sources of errors: truncation, sampling and quantification. These three error sources are studied independently of each others, as well as methods for reducing them, especially the use of a weighting window. With this “windowing”, a statistical study of the simultaneous effect of these three error sources has been made by simulation with a very large number of parameters values, and formulas are presented, which link the standard deviation to the resolution and the number of samples.

Key words

digitising
troncation
sampling
quantification
windowing

Abstract

This work explores MEMS (Micro-ElectroMechanical Systems) potentialities to produce flexible AC voltage references through mechanical-electrical transduction that could be used for high precision electrical metrology and for applications in miniaturized instrumentation. AC voltage references ranging from 2 V to 90 V have been designed and fabricated using the same Epitaxial Silicon On Insulator (SOI) Surface Micromachining process that permits an accurate control of both dimensions and material properties. The measured MEMS AC voltage reference values have been found in a good agreement with the calculations performed with Coventor software. These test structures have been used to develop the read-out electronics to drive the MEMS and to design a second set of devices with improved characteristics. Deep Level Transient Spectroscopy measurements carried out on the new MEMS showed resonance frequencies of about a few kilohertz, which makes it possible to have AC voltage references working from about tens of kHz. Moreover, the stability of the MEMS out-put voltage at 100 kHz has been found very promising for the best samples where the relative deviation from the mean value over almost 12 h showed a standard deviation of 6.3 × 10-6, which is a very good result.

Key words

ELECTRICAL METROLOGY
MEMS design
voltage reference
SOI process