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TOPIC 2

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).

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TOPIC 2

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  1. TOPIC 2

  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.

  3. Josephson voltage standards Steps of constant voltage can be observed on the current-voltage characteristic of the junction: 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.

  4. 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.

  5. 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.

  6. 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.

  7. 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.

  8. S G D S D QHE devices Longitudinal resistance Rx = Ux / I Hall resistance RH = UH / I

  9. 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.

  10. 1400 1200 T = 2.2 K T = 1.6 K 1000 800 Longitudinal resistance [Ω] 600 400 200 0 0 1 2 3 4 5 6 7 8 9 10 11 Magnetic flux density [T] Longitudinal resistance as function of magnetic flux density Negligibly small longitudinal resistance indicates a dissipationless regime.

  11. 14 12 T = 2.2 K T = 1.6 K 10 8 Hall resistance [kΩ] 6 4 2 0 0 1 2 3 4 5 6 7 8 9 10 11 Magnetic flux density [T] Hall resistance as function of magnetic flux density

  12. 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, ...

  13. 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 RKbeginning 1 January 1990.

  14. Thompson-Lampard'scross-capacitor (TLC)

  15. Cross-capacitor 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

  16. Cross-capacitor The effect of possible unsymmetry:

  17. Cross-capacitor Cx C-bridge Measurement of l by means of a built-in Fabry-Perot interferometer.

  18. CSIRO-NMLcross-capacitor

  19. Equivalent circuits of resistance standards Rp Gp Rs j Xs j Xp j Bp

  20. Equivalent circuits of capacitance standards Cp Cp Rs Cs Rp Gp Dissipation (power, loss) factor

  21. Equivalent circuits of inductance standards Lp Rs Ls Rp Dissipation and quality factor

  22. 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.

  23. 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.

  24. 12 906 Ω octofilar resistor

  25. Frequency characteristics of the 12 906 Ω resistors QF: quadrifilar version OF: octofilar version AC-DC difference = relative change of the parallel equivalent resistance from the DC value

  26. C0 P0 C2 P2 Cn Pn R3 R2 Rn R1 C1 P1 C3 P3 Cn-1 Pn-1 Hamon transfer standards Interconnection by means of zero-resistance four-terminal junctions:

  27. Ca Pa Pb Cb Hamon transfer standards Conversion of the array to a parallel connection by adding four "terminal fans".

  28. Hamon transfer standards where

  29. Pa Ca Cb Pb A 1000 Ω / 10 ΩHamon transfer standard equipped with 2 shorting bars and two compensation networks Rnom = 100 Ω r of the order of 1 Ω

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