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**Electricity - Magnetism

With the view of a new definition of the SI that could be based only on fundamental constants, several studies have been undertaken by the LNE. In addition, in order to meet the growing needs of the industry and research laboratories in terms of uncertainty and also to allow traceability to better adapted and more performant national standards a certain number of studies have been launched.

Fundamental electric metrology

The quantum standard for electrical current

To date, the realization of the ampere is not made directly, but on the basis of resistance standards and of electromotive force by application of the Ohm’s law. That’s why in order to improve the uncertainty of the realization, the LNE is developing a quantum standard for electrical current based on devices involving the association of Single Electron Tunelling (SET) (Single Electron Tunneling) and of Coulomb’s blockade. To realize a quantum current standard, requires that the devices are capable creating a current I which, through a determined f, frequency, can control the passage of electrons one by one (I = e·f). These devices, called R-type electron pumps, comprise three tunnel junctions assembled into series, two grid capacitors allowing or not passage of one electron through control of the Fermi level, and one resistor positioned at each end of the device to reduce the errors associated with the concomitant cotunneling effect.

Since the Coulomb blockade disappears below 3 K, measurement of current generated is made by setting the R-type electron pump and the measuring cable on a dilution refrigerator. Current amplification is based on the use of current cryogenic comparator (CCC).

A new high performance, dilution refrigerator will allow testing new configurations of CCC.

LPN’s R-type electron pump
LPN’s R-type electron pump

Dilution refrigerator of the single electron tunneling effect
Dilution refrigerator of the single electron tunneling effect

The quantum metrological triangle

Increasing confidence given to the relationships between the constantsRK and KJ on one hand, and the Planck’s constant h and the electron charge e on the other hand, constitutes an indispensable step before anticipating a redefinition of the electric units based on the fundamental constants of physics.

The objective of the study called “quantum metrological triangle” is to verify with an uncertainty of 10-8, the consistency of the fundamental constants RK, KJ and QX which values should be h/e2, 2e/h, and erespectively. Experimentally, this amounts to verifying that the product RK.KJ.QX has 2 for value. Practical implementation consists of the realization of the Ohm’s law on the basis of the resistance quantum standard, electromotive force standard and current standard.

Single electron tunneling ; quantum Hall effect ; Schematic diagram of quantum metrological triangle (f1, f2 : HF frequency irradiation of Josephson junctions; n1, n2, i : numerical factors)
Schematic diagram of metrological triangle (f1, f2 : HF frequency irradiation of Josephson junctions ; n1, n2, i : numerical factors)

AC Quantum standards: programmable binary Josephson junctions arrays and pulse-driven Josephson junctions arrays.

The LNE has adopted two approaches for the realisation of quantum AC standards. Both approaches are based on the arrays of Josephson junctions which current-voltage characteristics are non hysteretic and the idea of transforming the Josephson junctions arrays into a high precision digital/analog converters.

These both approaches are on the one hand, the studies of programmable Josephson junctions arrays and on the other hand, studies of pulse-driven Josephson junctions arrays.

a. programmable Josephson junctions arrays

Programmable Josephson junctions arrays comprise several Josephson junctions connected in series and distributed over binary sequences (segments). Under the effect of hyperfrequency irradiation and polarization current, each segment can be individually biased on a determined voltage step. Output voltage of array is matching the sum of voltage delivered by each segment. Finally, each current source control is automated, its generates high precision alternative voltage.

Josephson junctions array
Josephson junctions array

b. Pulse-driven Josephson junctions arrays

Pulse-driven Josephson junctions arrays are based on the Delta-Sigma digital/analog conversion technique. By applying a high-speed pulse train to the Josephson junctions array, an arbitrary low frequency signal can be synthesized. Then this signal is filtered in order to provide the desired high precision low frequency signal.

Quantum resistance standards: QHARS

The quantum resistance standards are implemented in the Hall bars which generally limit the resistance values at RK/2 and RK/4. Associating several Hall bars in series or in parallel allows extending the resistance values, whilst maintaining low uncertainties. The LNE has devised these devices called QHARS (Quantum Hall Array Resistance Standards) and has validated resistances obtained which values are ranging between 100 Ω and 1,29 MΩ.

QHARS (Quantum Hall Array Resistance Standard) Réfrigérateur à dilution de l'effet tunnel mono-électron
QHARS(Quantum Hall Array Resistance Standard)

Low frequency metrology

AC-DC calculable resistors and resistance bridge

Knowing the frequency behaviour of unknown resistances implies that they were compared with known or calculable standards. This comparison requires an essential instrument that is the comparison bridge which main component is one double stage transformer.

The LNE is also developing AC-DC ultrathin layers coaxial calculable resistances. Resistances are made up of two concentric and conductive conductors. One of them is a cylindrical ceramic rod on which a resistive thin layer of about some nanometer is deposited. This thin layer allows to overcome the skin effect and thus the the resistance value change with frequency. In addition, the resistance values are adjusted at nominal values by depositing gold contact at each end and by laser writing the lines over the full length of the rod. The other one, the outer conductor, is made of low resistance copper and let current flow in opposite directions. The impedance parameters are deduced from electromagnetism calculations.

Ultra thin resistive layer rods used for making AC-DC calculable resistors
Ultra thin resistive layer rods used for making AC-DC calculable resistors

AC/DC transposition

Studies carried out regarding AC/DC transposition have allowed to widen the voltage ranges up to 100 V for frequencies ranging from 0,5 MHz to 100 MHz. The measurement bench is under characterization.

New thermal converters are being developed for the lowest frequencies (lower than some dozens of Hz).

Closed and open thermal converters
Closed and open thermal converters

Phase shift measurement

A new measuring bench for AC sinusoidal phase shift (ranges from 20 Hz to 20 kHz) based on sampling and digital processing techniques is currently under development. Several input stages essential for the AC connection of the resistances (ranges from mΩ to some MΩ) and high value capacities (from mF to some F) have been constructed.
The bench is undergoing characterisation.

Measurements of very low currents and high resistances values

A measuring bench for high resistances values and very low currents is undergoing finalisation. Said bench is based on the realization of one current integration bridge. The first characterisation tests of the current integration bridge have begun with standard capacities of values 1,1 pF and 1 pF. The first measurements of sensitivity have been carried out.

High frequency metrology

High frequency power

At the LNE the high frequency power standards used are wattmeters that comprise one temperature-dependent resistive component in which power to be measured is dissipated. High frequency power is then measured by taking the DC power value that generates the same heat as the wattmeter. Calibrating the wattmeter means defining its efficiency with a known and acceptable uncertainty, and this is done with the means of a microcalorimeter. The LNE is currently developing a calculable HF power standard that associates different technologies (microstripe, coplanar, RF diode, thermocouple probe).

PScattering parameters

LThe scattering parameters are wave ratios that indicates the reflection and transmission loss in the active and passive hyperfrequency components and devices. To characterize these parameters’ modulus and phase, laboratories and companies are using Vector Network Analysers (VNAs). The LNE has developed Vector Network Analysers, double six ports reflectometers to realize hyperfrequency standards within a frequency range extending from 90 MHz to 40 GHz (in fact distributed over 4 double six ports reflectometers: 90 MHz - 500 MHz, 500 MHz - 1GHz, 1 GHz - 18 GHz, 18 GHz - 40 GHz).
A new reflectometer covering the 75 GHz – 110 GHz frequency range is under realization. Moreover, vector network analysers must be calibrated before making any measurement by applying a procedure based on the consecutive measurement of the standard components coming from a calibration kit. The role of the National Metrology Institutes (NMIs) is to guarantee traceability to the SI through the connection of the calibration kits to the Vector Network Analyser. Thus the LNE is working on the design and the realization of standards components for the calibration kit, on the development of new suitable calibration methods (allowing obtaining high accuracy and low uncertainties). Works are also undertaken to develop methods for comparisons (between different types of propagation media in order to guarantee traceability of the users’ measurements), and also on the implementation of traceability of the scattering parameters measurements. These works will also focus on the planar lines as well as on the coaxial lines.

Double six ports reflectometer (18GHz-40 GHz)
Double six ports reflectometer (18GHz-40 GHz)