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One of the features of electrical metrology is the large number of quantities deriving from the SI base unit, the ampere. Additionally, electrical metrology takes various forms and its quantities are used in fields quite distinct from that of electricity.

Another feature, creating an additional difficulty, is the frequency band in which these quantities can be found. Consequently, instruments specific to each frequency range must be developed and built. In practice, this sector can be divided into four sections:

Although the SI base unit for electricity is the ampere, it is so difficult to implement that the ampere is generally produced from the ohm and the volt, using Ohm's law: I= U/R. Based on the DC standards, the various quantities will be produced in alternating current, and for each frequency range, specific standards will be required.

*In France, units are first determined with respect to the farad, then with respect to the ohm. In addition to these measurements, the ohm and the volt are maintained using macroscopic effects such as the quantum Hall effect and the Josephson effect.*

Using the principle of the calculable capacitor of Thompson- Lampard, the value of the capacitance can be linked directly to a measurement of length via a system of cylindrical conductors. It is based on the theorem established by Douglas Geoffrey Lampard in 1956. The LNE’s Thompson-Lampard standard is a novel system made up of five electrodes horizontally positioned and set at the five apexes of a regular pentagon. With these five electrodes and using a set of connections adapted to the electrodes, one can obtain more measurements and thus compensate for a certain number of standard defects. For effective length of 138,25 mm, rated variation of capacitance is equal to 0.375 pF. Two capacitance bridges are used to connect the capacitors to the Thompson-Lampard standard. A first bridge with two pairs of terminals allows comparing the standard capacitance variation against one 1pF, then 10 pF and 100pF capacitor. A second bridge with four pairs of terminals is used for calibrating 100 pF, 1 000 pF then 10 000pF capacitors.

Un nouvel étalon de Thompson-Lampard est en cours de réalisation au LNE.

Calculable capacitance standard of Thompson-Lampard with 5 electrodes

The ohm is maintained using the quantum Hall effect, a physical phenomenon discovered by Klaus von Klitzing in 1980; this phenomenon results from the quantum properties of two-dimensional gases carrying an electron charge observed in semiconductor junctions at very low temperature (typically 1.5 K) and in high magnetic field. This method, commonly used in the National Metrology Institutes, allows obtaining quantified resistance values with excellent reproducibilities. The quantum resistance standard implemented in the quantum Hall arrays generates values of ** R_{K}/2** and

Heterojunctions for setting up the quantum Hall effect

The volt is maintained using the Josephson effect, a physical phenomenon discovered in 1962 by the author of the same name. This effect provides a means of maintaining the volt, based on the quantum properties of a junction formed from two superconductors separated by a very narrow insulating gap. When this junction is subjected to microwave radiation at very low temperature a voltage, dependent on the radiation frequency, is generated across the terminals. The proportionality constant between the frequency and the voltage is Josephson constant *K _{J} = 2·e/h*

Josephson bench

*The references in this field are used to determine the multiples, sub-multiples and derived quantities for a frequency range generally extending up to 100 MHz. To allow traceability to quantities determined in DC, specific AC methods and instruments must be developed and implemented. Due to the frequency range and the number of derived quantities, the range of measurement in this field is extremely large and there are numerous references. The following list of references is therefore not exhaustive, simply providing an overview of the main standards in this field.*

AC voltage and AC current are connected to the matching continuous quantities through thermal transposition. Thermal transposition principle is based on location of heating produced by applying a measurement signal to a heating resistance, using one or more thermocouples placed on this resistance There are three types of thermal converters: monojunction, multijunction converters and the thin-layer multijunction thermal converters. At the LNE the primary low pressure reference standard in this field is constituted by thin-layer multijunction thermal converters. Converter manufacturing calls for photolithography techniques. Thermal converters are made up of a heating resistive structure and several hundred thermocouples deposited on a fine dielectric membrane. Thermal converters exhibit transposition deviations that are closely linked to the frequency of the signal applied. The LNE is currently covering in voltage the range extending from 1 mV to 1 kV, and covers also the range of 2,5 mA to 20 A for frequencies ranging from 10Hz to 100Hz.

AC DC transfer benches

The LNE has developed a novel power standard that allows measuring the monophase electric power, at 53 Hz for sinusoidal signals (or exhibiting a rate of harmonic distorsion lower than 0.1%). Standard is based on the development of on digital sampling wattmeter. The instrument principle is as follows: a source of power delivers voltage *u(t)* and current* i(t)* signals on two distinctive circuits. Signals are digitized then processed by the discrete Fourier transform for calculating their root mean square (RMS) values *U _{RMS}* and

*P* = *U _{eff} I_{eff}* cos

This primary standard allows measuring active power at 53 Hz , in sinusoidal regime, with a relative standard uncertainty (relative to the apparent power) lower than 13 µW/VA, for voltages comprised between 60 V and 480 V, and currents fluctuating between 0.1 A to 10 A for any power factor.

These studies come under the general objective of the definition of the fundamental constants of Von Klitzing **R _{K}** and the fine structure

**Direct determination of the ohm**

Direct determination of the farad and the ohm is based on the implementation of the Thompson-Lampard standard. At the LNE this standard is made up of a system with five cylindrical electrodes horizontally assembled. It allows generating five capacitance variations proportional to the displacement length of the electrostatic screen. Lampard theorem enables calculating these capacitance variations. The farad is thus directly related to the metre.

a first comparison bridge including two pairs of terminals allows comparing the capacitance variation of a capacitor with ranges extending from 1 pF then 10 pF and 100 pF. A second comparison bridge involving four pairs of terminals allows calibrating capacitors ranging from 100 pF, 1 000pF then 10 000pF.

Two pairs of resistances ranging from 10 kΩ, 20 kΩ and 40kΩ ("Vishay" type) are then calibrated by comparison against the transfer capacities of 10 000 pF using a frequencymeter bench including four pairs of terminals (quadrature bridge) with pulses ranging from 10 000 rad/s (1 600 Hz), 5 000 rad/s (800 Hz) and 2 500 rad/s (400 Hz) respectively. The ohm is then directly realised in relation to the metre and the second. Resistance values have their frequency adjusted to obtain their DC value by comparison to a resistance which frequency behaviour is calculable (modulus and phase). And then, resistance values are compared against the resistance quantum standard on the basis of the quantum Hall effect using a bridge fitted with a cryogenic current comparator. Von Klitzing constant **R _{K}** is deducted from this comparison.

**AC-DC calculable resistors**

We have seen earlier that the calculable resistors intervene in the experimental process for determining the Von Klitzing constant **R _{K}** and the fine structure

The LNE keeps calculable resistors. These are bifilar resistors, called "Haddad" type. Resistors are made up of a resistive wire placed in the axis of a coaxial conductor surrounding it. Resistive wire is realised in annealing evanohm (NiCrAlCu) and exhibits a 20 µm diameter to minimise the skin effect and therefore the frequency variation of the resistance. Evolution of the resistors impedance according to frequency is calculated from the resolution of the Maxwell equations. These resistors are then installed in a temperature-controlled enclosure.

Schematic diagram of a AC-DC calculable resistor

The demands for calibration in the field of high voltage generally concern the 1 kV to 250 kV frequency range, in DC or AC currents. Only the pulsed states (in AC), e.g. lightning shocks, involve voltages which can reach up to some 450 kV. The measurement method of high voltage consists in obtaining a reduced image of the signal at high voltage and converting it into a low voltage signal.

The main references in the field of high voltage are transformers, dividers and capacitors.

Divider for high voltage measurements

*The references in this field are used to determine the multiples, sub-multiples and derived quantities for a frequency range generally extending from 100 MHz up to 100 GHz. The two main base quantities are power and noise.*

**HF power**

HF power is generally measurable when converted into a AC signal. The power standards are sets of bolometric mounts associated with a resistor component (generally a thermistor) which resistance depends on temperature. The power to be measured is dissipated in this resistor component, generating heat that is compared with the DC power producing the same heat in this sensitive component. All the power references using calorimeters cover a frequency range extending from 100 kHz to 110 GHz (100 kHz to 26,5 GHz in a coaxial line, and 8 GHz to 110 GHz on waveguide).

LNE’s power standard

**Radio noise**

The noise factor is one of the main characteristics of active microwave components and devices. This quantity is measured using a calibrated source of noise. The principle of the standard source of noise is based on the black body theory, which indicates that all heated bodies emit electromagnetic radiation.

The noise standard consists of a load (generally made from silicon carbide) placed at the end of a transmission line (waveguide) inserted in an oven raised to a certain temperature. To a first approximation, the spectral density of the electromagnetic radiation is proportional to the temperature of the source.

The LNE holds standards on waveguides that are available for the following frequency ranges: 8,2 GHz - 12,4 GHz; 12,4 GHz - 18 GHz; 18 GHz - 26,5 GHz and 26,5 GHz - 40 GHz.

The source of unknown noise is compared by substitution to the noise standard, through attenuation measurements made using a noise radiometer.

Radio noise standard