SI units are divided into 2 classes: base units (7) and derived units. Athens Programme Course CTU 1 - Metrology of Electrical Quantities.
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1 Athens Programme Course CTU 1 - Metrology of Electrical Quantities The 11th CGPM (1960) adopted the name Système International d'unités (International System of Units, abbreviation SI), for the recommended practical system of units of measurement. SI units are divided into 2 classes: base units (7) and derived units.
2 Unit of length (metre, m): The metre is the length of the path travelled by light in vacuum during a time interval of 1/ of a second. Unit of mass (kilogram, kg): The kilogram is the unit of mass; it is equal to the mass of the international prototype of the kilogram.
3
4 Unit of time (second, s): The second is the duration of periods of the radiation corresponding to the transition between the two hyperfine levels of the ground state of the caesium 133 atom. Unit of electric current (ampere, A): The ampere is that constant current which, if maintained in two straight parallel conductors of infinite length, of negligible circular cross-section, and placed 1 metre apart in vacuum, would produce between these conductors a force equal to newton per metre of length.
5 Unit of thermodynamic temperature (kelvin, K): The kelvin, unit of thermodynamic temperature, is the fraction 1/ of the thermodynamic temperature of the triple point of water. Unit of amount of substance (mole, mol): The mole is the amount of substance of a system which contains as many elementary entities as there are atoms in kilogram of carbon 12. When the mole is used, the elementary entities must be specified and may be atoms, molecules, ions, electrons, other particles, or specified groups of such particles.
6 Unit of luminous intensity (candela, cd): The candela is the luminous intensity, in a given direction, of a source that emits monochromatic radiation of frequency hertz and that has a radiant intensity in that direction of 1/683 watt per steradian. Derived units are expressed algebraically in terms of base units by means of mathematical symbols of multiplication and division.
7 Quantity Symbol volume m 3 velocity m/s mass density kg/m 3 current density A/m 2 magnetic field strength A/m luminance cd/m 2 Quantity Name Symbol plane angle radian rad solid angle steradian sr frequency hertz Hz force newton N pressure pascal Pa energy, work joule J quantity of heat joule J power watt W
8 Quantity Name Symbol electric charge coulomb C electric potential volt V electric resistance ohm Ω electric conductance siemens S electric capacitance farad F inductance henry H Quantity Name Symbol magnetic flux weber Wb magnetic flux density tesla T luminous flux lumen lm illuminance lux lx activity becquerel Bq absorbed dose gray Gy dose equivalent sievert Sv
9 SI prefixes Factor Prefix Symbol yotta Y zetta Z exa E peta P tera T 10 9 giga G 10 6 mega M SI prefixes Factor Prefix Symbol 10 3 kilo k 10 2 hecto h 10 1 deca da 10-1 deci d 10-2 centi c 10-3 milli m
10 SI prefixes Factor Prefix Symbol 10-6 micro µ 10-9 nano n pico p femto f atto a zepto z yocto y Material measures, measuring instruments, reference materials or measuring systems intended to define, realize, conserve or reproduce a unit or one or more values of a quantity to serve as a reference.
11 International standard is a standard recognized by an international agreement to serve internationally as the basis for assigning values to other standards of the quantity concerned. National standard is a standard recognized by a national decision to serve, in a country, as the basis for assigning values to other standards of the quantity concerned. Primary standard is a standard that is designated or widely acknowledged as having the highest metrological qualities and whose value is accepted without reference to other standards of the same quantity. Secondary standard is a standard whose value is assigned by comparison with a primary standard of the same quantity.
12 Reference standard is a standard, generally having the highest metrological quality available at a given location or in a given organization, from which measurements made there are derived. Working standard is a standard that is used routinely to calibrate or check material measures, measuring instruments or reference materials. Transfer standard is a standard used as an intermediary to compare standards. Travelling standard is a standard, sometimes of special construction, intended for transport between different locations.
13 are based on an effect predicted in 1962 by Brian D. Josephson, a 22-year-old British student (Nobel prize in 1973). This effect can be observed if a so called Josephson junction (two weakly coupled superconductors, e.g. two superconductors separated by an insulating layer of a few nanometers in thickness) is irradiated with microwaves. Steps of constant voltage can be observed on the current-voltage characteristic of the junction: 2 where f. is frequency of the microwaves, n = 1, 2, 3,... is the step number, H is the Planck constant and e is the elementary charge.
14 The distance between neighbouring steps is approximately 145 µv for a typical microwave frequency of 70 GHz. The term Josephson constant K J is used for the quotient 2e/h. A conventional value of K J-90 = ,9 GHz/V has been adopted for it beginning 1 January By means of Josephson junctions, voltages can be reproduced with relative uncertainties of less than one part in Large series arrays consisting of several tens of thousands of Josephson junctions are fabricated for voltages up to more than 10 V.
15 has been discovered in 1980 by Klaus von Klitzing (Nobel prize 1985) as a result of a study of the behaviour of field effect transistors at helium temperatures and in high magnetic fields. In contradistinction to the discovery of the Josephson effect, for which a theoretical prediction existed, the discovery of the quantum Hall effect was a triumph of experimental physics. At the European High Magnetic Field Laboratrory in Grenoble, K. v. Klitzing used water-cooled copper coils with a power supply of 10 MW to generate magnetic flux densities up to 25 T. At present, superconducting solenoids are routinely used for generating such fields at many laboratories worldwide.
16 S G D Longitudinal resistance R x = U x / I Hall resistance R H = U H / I S D In case of GaAs heterostructures, the insulator (SiO 2 ) is replaced by a semiconductor with a large energy gap (e.g. Al 0.3 Ga 0.7 As). Ionized donors in this semiconductor act as a positive gate voltage, so that a 2DEG may be present in the structure even if no external gate voltage is applied.
17 as function of magnetic flux density Longitudinal resistance [Ω] T = 2.2 K T = 1.6 K Magnetic flux density [T] Negligibly small longitudinal resistance indicates a dissipationless regime. as function of magnetic flux density 14 Hall resistance [kω] T = 2.2 K T = 1.6 K Magnetic flux density [T]
18 R H ( 1 ) R H ( 2 ) R H ( 3 ) R H ( 4 ) etc. i R H ( i ) = const, i = 1, 2, 3,... where i is the plateau number, e is the electron charge and h is the Planck constant. A conventional value of R K-90 = Ω has been adopted for R K beginning 1 January 1990.
19 In case of symmetry, where the electric constant Magnetic constant 0 = 4 x 10-7 H/m (exactly), speed of light in vacuum c 0 = m/s (exactly), and so C / = pf/m
20 The effect of possible unsymmetry: l Measurement of l by means of a built-in Fabry-Perot interferometer. C-bridge C x
21 are resistors constructed in such a way that frequency dependences of their values can be calculated, with a sufficient accuracy, from the knowledge of their constructional parameters. In these calculations, changes in resistance due to parasitic inductances and capacitances, as well as changes due to eddy currents have to be evaluated.
22 Resistive element made of bare Nikrothal wire, 20 μm in diameter. Distance between adjacent parts of the wire 10 mm, folded length 730 mm. Inner diameter of the copper shield 103 mm, its wall thickness 2.5 mm.
23 QF: quadrifilar version OF: octofilar version AC-DC difference = relative change of the parallel equivalent resistance from the DC value C 0 P 0 C 2 P 2 C n P n R 1 R 2 R 3 R n C 1 P 1 C 3 P 3 C n-1 P n-1 Interconnection by means of zero-resistance fourterminal junctions:
24 C a P a C b P b Conversion of the array to a parallel connection by adding four "terminal fans". where
25 equipped with 2 shorting bars and two compensation networks P a C a C b P b R nom = 100 Ω r of the order of 1 Ω
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