Transcript
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.
Athens Programme / Course CTU 1 - Metrology on Electrical Quantities / Topic 1
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Unit of length (metre, m):
The metre is the length of the path travelled by light in vacuum during a time interval of 1/299 792 458 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.
Athens Programme / Course CTU 1 - Metrology on Electrical Quantities / Topic 1
Athens Programme / Course CTU 1 - Metrology on Electrical Quantities / Topic 1
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Athens Programme / Course CTU 1 - Metrology on Electrical Quantities / Topic 1
Athens Programme / Course CTU 1 - Metrology on Electrical Quantities / Topic 1
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Unit of time (second, s):
The second is the duration of 9 192 631 770 periods of the radiation corresponding to the transition between the two hyperfine levels of the ground state of the caesium 133 atom.
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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 2 × 10-7 newton per metre of length.
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Unit of thermodynamic temperature (kelvin, K):
The kelvin, unit of thermodynamic temperature, is the fraction 1/273.16 of the thermodynamic temperature of the triple point of water.
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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 0.012 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.
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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 540 × 1012 hertz and that has a radiant intensity in that direction of 1/683 watt per steradian.
Athens Programme / Course CTU 1 - Metrology on Electrical Quantities / Topic 1
Derived units are expressed algebraically in terms of base units by means of mathematical symbols of multiplication and division.
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Quantity volume velocity mass density current density magnetic field strength luminance
Symbol m3 m/s kg/m3 A/m2 A/m cd/m2
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Quantity plane angle solid angle frequency force pressure energy, work quantity of heat power
Name radian steradian hertz newton pascal joule joule watt
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Symbol rad sr Hz N Pa J J W
Quantity Name electric charge coulomb electric potential volt electric resistance ohm electric conductance siemens electric capacitance farad inductance henry
Symbol C V Ω S F H
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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
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Sv
SI prefixes
Factor 1024 1021 1018 1015 1012 109 106
Prefix yotta zetta exa peta tera giga mega
Symbol Y Z E P T G M
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SI prefixes
Factor 103 102 101 10-1 10-2 10-3
Prefix kilo hecto deca deci centi milli
Symbol k h da d c m
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SI prefixes
Factor 10-6 10-9 10-12 10-15 10-18 10-21 10-24
Prefix micro nano pico femto atto zepto yocto
Symbol µ n p f a z y
Athens Programme / Course CTU 1 - Metrology on Electrical Quantities / Topic 1
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.
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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.
Athens Programme / Course CTU 1 - Metrology on Electrical Quantities / Topic 1
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.
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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.
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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.
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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.
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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. Athens Programme / Course CTU 1 - Metrology on Electrical Quantities / Topic 1
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The distance between neighbouring steps is approximately 145 µV for a typical microwave frequency of 70 GHz.
The term Josephson constant KJ is used for the quotient 2e/h . A conventional value of KJ-90 = 483 597,9 GHz/V has been adopted for it beginning 1 January 1990.
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By means of Josephson junctions, voltages can be reproduced with relative uncertainties of less than one part in 1010.
Large series arrays consisting of several tens of thousands of Josephson junctions are fabricated for voltages up to more than 10 V.
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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.
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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.
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S
G
D
Longitudinal resistance Rx = Ux / I Hall resistance RH = UH / I
S
D
Athens Programme / Course CTU 1 - Metrology on Electrical Quantities / Topic 1
In case of GaAs heterostructures, the insulator (SiO2) is replaced by a semiconductor with a large energy gap (e.g. Al0.3Ga0.7As).
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.
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as function of magnetic flux density Longitudinal resistance [Ω]
1400 1200
T = 2.2 K T = 1.6 K
1000 800 600 400 200 0
0
1
2
3
4
5
6
7
8
9
10 11
Magnetic flux density [T]
Negligibly small longitudinal resistance indicates a dissipationless regime. Athens Programme / Course CTU 1 - Metrology on Electrical Quantities / Topic 1
as function of magnetic flux density
Hall resistance [kΩ]
14 12
T = 2.2 K T = 1.6 K
10 8 6 4 2 0
0
1
2
3
4
5
6
7
8
9
Magnetic flux density [T] Athens Programme / Course CTU 1 - Metrology on Electrical Quantities / Topic 1
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10 11
RH ( 1 ) 25 812.8 RH ( 2 ) 12 906.4 RH ( 3 ) 8 604.3 RH ( 4 ) 6 453.2 etc. i RH ( i ) = const, i = 1, 2, 3, ...
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where i is the plateau number, e is the electron charge and h is the Planck constant. A conventional value of RK-90 = 25 812.807 Ω has been adopted for RK beginning 1 January 1990.
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Athens Programme / Course CTU 1 - Metrology on Electrical Quantities / Topic 1
In case of symmetry,
where the electric constant
Magnetic constant
0 = 4 x 10 -7 H/m (exactly),
speed of light in vacuum c0 = 299 792 458 m/s (exactly), and so C / = 1.953 549 043 ... pF/m
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The effect of possible unsymmetry:
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l Measurement of l by means of a built-in Fabry-Perot interferometer.
C-bridge C-bridge
Cx
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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.
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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.
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Athens Programme / Course CTU 1 - Metrology on Electrical Quantities / Topic 1
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QF: quadrifilar version OF: octofilar version
AC-DC difference = relative change of the parallel equivalent resistance from the DC value Athens Programme / Course CTU 1 - Metrology on Electrical Quantities / Topic 1
C0
P0
C2
P2
R2
R1
C1
P1
Cn
R3
C3
Pn
Rn
P3
Cn-1
Pn-1
Interconnection by means of zero-resistance fourterminal junctions:
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Ca
Cb
Pa
Pb
Conversion of the array to a parallel connection by adding four "terminal fans".
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where
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equipped with 2 shorting bars and two compensation networks
Pa Ca Cb Pb Rnom = 100 Ω r of the order of 1 Ω
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