TOPIC 2
Josephson voltage standards
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.
Josephson voltage standards
Steps of constant voltage can be observed on the current-voltage characteristic of the junction:
fe
hnU
2n
where f is frequency of the microwaves,n = 1, 2, 3, ... is the step number, h is the Planck constant and
e ist the elementary charge.
Josephson voltage standards
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.
Josephson voltage standards
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.
Quantum Hall effect
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.
Quantum Hall effect
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.
QHE devices
S G D
S D
Longitudinal resistance Rx = Ux / I
Hall resistance RH = UH / I
QHE devices
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.
Longitudinal resistanceas function of magnetic flux
density
T = 2.2 K T = 1.6 K
0 1 2 3 4 5 6 7 8 9 10 110
200
400
600
800
1000
1200
1400
Long
itudi
nal r
esis
tanc
e [Ω
]
Magnetic flux density [T]
Negligibly small longitudinal resistance indicates a dissipationless regime.
Hall resistanceas function of magnetic flux
density
0 1 2 3 4 5 6 7 8 9 10 110
2
4
6
8
10
12
14
T = 2.2 K T = 1.6 K
Hal
l res
ista
nce
[kΩ
]
Magnetic flux density [T]
Quantized Hall resistance
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, ...
Von Klitzing constant
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.
RK = i RH ( i ) = h / e2
Thompson-Lampard'scross-capacitor (TLC)
Cross-capacitor
In case of symmetry,
2ln0//2
/1
CCC
where the electric constant
Magnetic constant0 = 4 x 10 -7 H/m (exactly),
speed of light in vacuumc0 = 299 792 458 m/s (exactly),
and so
C / = 1.953 549 043 ... pF/m
200
0c
1
Cross-capacitor
The effect of possible unsymmetry:
Cross-capacitor
l /CΔC
Measurement of l by means of a built-in Fabry-Perot interferometer.
C-bridge Cx
CSIRO-NMLcross-capacitor
Equivalent circuits of resistance standards
Rs j Xs
Rp
j Xp
Gp
j Bp
Equivalent circuits of capacitance standards
Rs Cs
Cp
Rp
Cp
Gp
Dissipation (power, loss) factor
Equivalent circuits of inductance standards
Rs Ls
Lp
Rp
Dissipation and quality factor
Lp
p
s
sL
1tan
QR
L
L
R
L2
sp
L2
L2
sp
tan1
tan
tan1
LL
RR
Calculable resistors
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.
12 906 Ω quadrifilar resistor
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.
12 906 Ω octofilar resistor
Wire radius 10 μm
Distance betweenadjacent wire elements
15 mm
Folded length ofresistive element
358 mm
Inside shield radius 51 mm
Shield thickness 2.6 mm
Frequency characteristics of the 12 906 Ω resistors
QF: quadrifilar versionOF: octofilar version
AC-DC difference = relative change of the parallel equivalent resistance from the DC value
Hamon transfer standards
C0 P0 C2 P2 Cn Pn
C1 P1 C3 P3 Cn-1 Pn-1
R1 R2
R3 Rn
Interconnection by means of zero-resistance four-terminal junctions:
Hamon transfer standards
Ca Pa
CbPb
Conversion of the array to a parallel connection by adding four "terminal fans".
Hamon transfer standards
where
A 1000 Ω / 10 ΩHamon transfer standard
Pa
Ca
Cb
Pb
equipped with 2 shorting barsand two compensation networks
Rnom = 100 Ω
r of the order of 1 Ω
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