Journal of Low Temperature Physics

, Volume 92, Issue 5–6, pp 367–413 | Cite as

Self-consistent theory of a voltage-current characteristic and of intrinsic noise of hysteretic RF SQUID

  • Ya. S. Greenberg


As well known, in practical RF SQUIDs the electronic components (preamplifier, tank circuit, transmission line) contribute substantially to the output noise of the device. So the output noise of RF SQUID is mainly defined by the slope of its voltage-current characteristics (VCC). However the existing theory of the slope is of semi-empirical manner and does not account for the real VCC slope, i.e., for its fine structure. At the present study in virtue of careful computer simulation the self-consistent theory of VCC fine structure is developed. The simple analytical expressions for the slope which allow to analyze real VCC structure for the practically used parameter 1<1<6 have been obtained. The influence of intrinsic noise of interferometer and of electronic noise on VCC slope has been considered as well. In the frame of the self-consistent theory the contribution of intrinsic interferometer noise to the spectral power of output noise is found. The special attention has been paid to the problem of macroscopic quantum tunneling (MQT) in RF SQUIDs. The analytical expressions are derived which allow to compute the MQT contribution to the VCC slope and to the intrinsic noise of the interferometer.


Computer Simulation Fine Structure Magnetic Material Transmission Line Electronic Component 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    A. Barone and G. Paterno,Physics and Application of Josephson Effect (John Wiley & Sons, 1982).Google Scholar
  2. 2.
    C. S. Owen, E. K. Jaffe, and D. F. Wilson,Rev. Sci. Instr. 48, 1541 (1977).Google Scholar
  3. 3.
    C. D. Tesche, C. C. Chi, C. C. Tsuei, and P. Chaudhari,Appl. Phys. Lett. 43, 384 (1983).Google Scholar
  4. 4.
    W. M. Folkner, M. V. Moody, J.-P. Richard, K. R. Carroll, and C. D. Teche,J. Appl. Phys. 65, 5190 (1989).Google Scholar
  5. 5.
    V. L. Vvedenski and V. I. Ozhogin,High sensitive magnetometry and biomagnetism, (M. Nauka, 1986) (in Russian).Google Scholar
  6. 6.
    M. Odehnal,Fiz. nizkich. temper. 2, 5 (1985), (in Russian).Google Scholar
  7. 7.
    L. D. Jackel and R. A. Buhrman,J. Low Temp. Phys. 19, 201 (1975).Google Scholar
  8. 8.
    I. M. Dmitrenko, V. A. Khlus, G. M. Tsoi, and V. I. Shnyrkov,IEEE Transactions on Magnetics 19, 576 (1983).Google Scholar
  9. 9.
    I. M. Dmitrenko, D. A. Konotop, G. M. Tsoi, and V. I. Shnyrkov, Proc. 10th Int. Cryogenic Engineering Conf. Helsinki, Finland, 31 July–3 Aug., 1984, pp. 746–749.Google Scholar
  10. 10.
    N. V. Golyshev and S. V. Motorin,Measuring and Computing Systems. Novosibirsk Electrotechnical Institute p. 40 (1989), (in Russian).Google Scholar
  11. 11.
    J. Clarke,Low Frequency Application of Superconducting Quantum Interference Devices. In:Superconductive Applications: SQUIDs and Machines (eds. by S. Foner, B. B. Schwartz) Proc. of summer school (N.Y., Plenum Press, 1977) p. 67.Google Scholar
  12. 12.
    V. V. Danilov, and K. K. Licharev,Radiotechnika i elektronika 25, 1725 (1980) (in Russian).Google Scholar
  13. 13.
    J. Kurkijarvi J. and W. W. Webb, Applied Superconducting Conference, Annapolis, Maryland, May 1–3, 1972. (N.Y.: IEEE, 1973) pp. 581–587.Google Scholar
  14. 14.
    J. Kurkijarvi,Phys. Rev. B6, 832 (1972).Google Scholar
  15. 15.
    J. J. Kurkijarvi,Appl. Phys. 44, 3729 (1973).Google Scholar
  16. 16.
    M. B. Simmonds and W. H. Parker,J. Appl. Phys. 42, 38 (1971).Google Scholar
  17. 17.
    E. Ben-Jacob and D. Abraham,Appl. Phys. Lett. 39, 835 (1981).Google Scholar
  18. 18.
    Y. S. Greenberg, Y. V. Katruk, and B. M. Rogatchevski,Izmerit. technika 4, 38 (1988), (in Russian).Google Scholar
  19. 19.
    I. M. Dmitrenko, G. M. Tsoj, and V. I. Schnyrkov,Fiz. nizkich temper. 8, 660 (1982), (in Russian).Google Scholar
  20. 20.
    I. M. Dmitrenko, V. A. Khlus, G. M. Tsoj, and V. I. Schnyrkov,Fiz. nizkich temper. 11, 146 (1985), (in Russian).Google Scholar
  21. 21.
    K. K. Likharev and B. T. Ulrich,Systems with Josephson junctions (Moscow State University, 1978), (in Russian).Google Scholar
  22. 22.
    V. V. Danilov and K. K. Licharev,J. Techn. Phys. 45, 1110 (1975).Google Scholar
  23. 23.
    B. V. Vasiliev, V. V. Danilov, and K. K. Likharev,IEEE Transactions on Magnetics. 11, 743 (1975).Google Scholar
  24. 24.
    V. V. Danilov, K. K. Likharev, and O. V. Snigirev, SQUID-80 (Eds. H.-D. Hahlbohm, H. Lubbig, B. Lubbig, N.Y.: W. de Gruyter, 1980) p. 473.Google Scholar
  25. 25.
    Y. S. Greenberg,J. Techn. Phys. 57, 2392 (1987), (in Russian), Superconducting Devices and their Applications (H. Koch and H. Lubbig, eds.), Proc. 4-th Int. Conf., Berlin, 18–21 June, 1991. Springer Proc. in Physics, v. 64. Springer-Verlag, 1992, pp. 244–247.Google Scholar
  26. 26.
    P. J. Marcos,Low Temp. Phys. 81, 147 (1990).Google Scholar
  27. 27.
    A. V. Gusev and V. N. Rudenko,J. Exp. Theor. Phys. 88, 134 (1985) (in Russian).Google Scholar
  28. 28.
    L. D. Jackel, W. W. Webb, J. E. Lukens, and S. S. Pei,Phys. Rev. 9B,115 (1974).Google Scholar
  29. 29.
    G. M. Tsoi,Investigation of RF SQUIDs at temperatures 0.5-4.2 K,Cand. Phys. (Math. Sci. Thesis, Institute of Low Temperature Physics, Kharkov, USSR, 1984) (in Russian).Google Scholar
  30. 30.
    V. I. Shnyrkov,Interference and quantum phenomena in RF SQUIDs, Doctor Phys. (Math. Sci. Thesis, Institute of Low Temperature Physics, Kharkov, USSR, 1985) (in Russian).Google Scholar
  31. 31.
    J. J.,Low Temp. Phys. 45, 37 (1981).Google Scholar
  32. 32.
    N. V. Golyshevand Y. S. Greenberg,Superconductivity: physics, chemistry, technique,3, 943 (1990), (in Russian).Google Scholar
  33. 33.
    D. W. Bol, J. J. F. Scheffer, W. T. R. Giele, and R. de Bruyn,Ouboter, Physica 133, 196 (1985).Google Scholar
  34. 34.
    F. Thrum and W. Krech,Exp. Techn. der Physik 28, 311 (1980).Google Scholar
  35. 35.
    A. O. Caldeira and A. J. Leggett,Phys. Rev. Lett. 46, 211 (1981).Google Scholar
  36. 36.
    H. Grabert, U. Weiss, and P. Hanggi,Phys. Rev. Lett. 52, 2193 (1984).Google Scholar
  37. 37.
    A. A. Golub and V. P. Iordatij,J. Exp. Theor. Phys. Lett. 36, 184 (1982), (in Russian).Google Scholar
  38. 38.
    Handbook of Mathematical functions with formulas, graphs and mathematical tables, eds. M. Abramowitz and I. Stegun, NBS, 1964.Google Scholar
  39. 39.
    D. B. Schwartz, B. Sen, S. N. Archie, A. K. Jain, and J. E. Lukens, in:SQUID-85 (Eds. H.-D. Hahlbogm, H. Lubbig. B. N.Y.: W. de Gruyter, 1985)p. 337. D. B. Schwartz, B. Sen, S. N. Archie, and J. E. Lukens,Rev. Lett. 55, 1547 (1985).Google Scholar
  40. 40.
    J. Kurkijarvi, in:SQUID-80 (Eds. H.-D. Hahlbohm, H. Lubbig. B. Lubbig N.Y.: W. de Gruyter, 1980) p. 247.Google Scholar
  41. 41.
    E. de Wolf, M. H. Fogel, and R. de Bruyn,Ouboter Physica B160, 118 (1989); P. W. Bol and R. de Bruyn,Ouboter Physica B176, 113 (1992).Google Scholar
  42. 42.
    V. I. Shnyrkov, G. M. Tsoi, D. A. Konotop, and I. M. Dmitrenko,Single Electron Tunneling and Mesoscopic Devices (H. Koch and H. Lubbig, eds.), Proc. 4-th Int. Conf., Berlin, 18–21 June, 1991. Springer Series in Electronics and Photonics, v. 31, Springer-Verlag W1991, pp. 211–217.Google Scholar
  43. 43.
    P. G. Wolynes,Phys. Rev. Lett. 47, 968 (1981); V. I. Melnikov and S. V. Meshkov,Pisma Zh. Eksp. Teor. Fiz. 38, 111 (1983) (Sov. Phys. JETP Lett. 38, 130 (1983)); A. I. Larkin and Yu. N. Ovchinnikov,Zh. Eksp. Teor. Fiz. 86, 719 (1984) (Sov. Phys. JETP 59, 420 (1984)); H. Grabert and U. Weiss,Phys. Rev. Lett. 53, 1787 (1984).Google Scholar

Copyright information

© Plenum Publishing Corporation 1993

Authors and Affiliations

  • Ya. S. Greenberg
    • 1
  1. 1.Novosibirsk Electrotechnical InstituteNovosibirskRussian Federation

Personalised recommendations