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The General Nature of Fundamental 1/f Noise in Oscillators and in the High Technology Domain

  • Peter H. Handel
Conference paper
Part of the Lecture Notes in Physics book series (LNP, volume 550)

Abstract

The ubiquitous fundamental 1/f noise spectrum is derived ontologically from quantum electrodynamics for any current, cross section or process rate as a universal macroscopic quantum fluctuation process, and as the most important infrared divergence phenomenon. It is present both in space and in time and is described in both the frequency and time domains. For small and ultrasmall devices and solid state samples the conventional quantum 1/f effect is introduced, and for larger sizes the coherent quantum 1/f effect applies. This new aspect of quantum mechanics is described by simple practical relations and by a general interpolation formula. The connection with numbers of harmonics and subharmonics characterizing the basic non-linearity of the particle-field interaction as well as other nonlinearities, is elucidated. Finally, the general epistemological explanation of the ubiquitous 1/f phenomenon is derived in the form of a sufficient 1/f noise criterion, and is applied to various nonlinear systems, including the particle-field system of quantum-electrodynamics as a particular example. Application of the frequency mixing 1/f frequency noise experiments of Planat and collaborators is considered as an equivalent way to understand the derivation of the fundamental 1/f spectrum. This new approach could reveal how our earlier qualitative interpretation of lattice-dynamical quantum 1/f effects below the lowest transversal acoustic phonon frequency of the sample in terms of subharmonics can be verified.

Keywords

Spectral Density Coherent State Surface Acoustic Wave Scattered Beam Quartz Resonator 
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.

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References

  1. 1.
    Johnson J. B. (1925) The Schottky effect in low frequency circuits. Phys Rev 26:71–85CrossRefADSGoogle Scholar
  2. 2.
    Press W. H. (1978) Comments astrophysics. Space Physics 7:103Google Scholar
  3. 3.
    Handel P. H. (1975) 1/f noise— an “infrared” phenomenon’. Phys. Rev. Lett. 34:1492–1494 (1975); Nature of 1/f noise. Phys. Rev. Lett. 34:1495-1498CrossRefADSGoogle Scholar
  4. 4.
    Handel P. H. (1980) Quantum Approach to 1/f Noise. Phys. Rev. 22A: 745ADSGoogle Scholar
  5. 5.
    Handel P. H. and Wolf D.(1982) Characteristic Functional of Quantum 1/f Noise. Phys. Rev. A26: 3727–30ADSGoogle Scholar
  6. 6.
    Handel P. H. (1989) The Quantum 1/f Effect and the General Nature of 1/f Noise. Archiv für Elektronik und Übertragungstechnik (AEÜ) 43:261–270Google Scholar
  7. 7.
    Handel P. H. (1982) Starting Points of the Quantum 1/f Noise Approach, Submitted to Physical Review B. Fundamental Quantum 1/f Fluctuation of Physical Cross Sections and Process Rates, submitted to Phys. Rev. Letters.Google Scholar
  8. 8.
    Sherif T. S. and Handel P. H.(1982) Unified Treatment of Diffraction and 1/f Noise. Phys. Rev. A26:596–602ADSGoogle Scholar
  9. 9.
    van der Ziel A. (1988) Unified Presentation of 1/f Noise in Electronic Devices; Fundamental 1/f Noise Sources (Review paper). Proc. IEEE 76: 233–258; The Experimental Verification of Handel’s Expressions for the Hooge Parameter, Solid-State Electronics 31:1205-1209 (1988) Semiclassical Derivation of Handel’s Expression for the Hooge Parameter. J. Appl. Phys. 63:2456-2455 (1988); 64:903-906 (1988); Birbas A.N. et al., J. Appl. Phys. 64:907-912 (1988); van der Ziel A. et. al., Extensions of Handel’s 1/f Noise Equations and their Semiclassical Theory, Phys. Rev. B 40:1806-1809 (1989); Tacano M., Proc. XI. Int. Conf. on Noise in Physical Systems and 1/f Fluctuations, Musha T., Sato S. and Mitsuaki Y. Editors, Ohmsha Publ. Co., Tokyo 1991, pp. 167-170; M. Tacano, Proc. Fifth van der Ziel Conference Quantum 1/f Noise and other Low Frequency Fluctuations, AIP Conference proceedings Vol. 282, Handel P. H. and Chung A. L. Editors, 1992; see also Quantum 1/f Bibliography by Handel P. H., unpublished.Google Scholar
  10. 10.
    Handel P. H. (1983), Any Particle Represented by a Coherent State Exhibits 1/f Noise in Noise in Physical Systems and 1/f Noise, (Proceedings of the VIIth International Conference on Noise in Physical Systems and 1/f Noise) edited by Savelli M., Lecoy G. and Nougier J. P. (North-Holland, Amsterdam), p. 97.Google Scholar
  11. 11.
    Handel P.H. (1986), Coherent States Quantum 1/f Noise and the Quantum 1/f Effect in Noise in Physical Systems and 1/f Noise (Proceedings of the VIIIth International Conference on Noise in Physical Systems and 1/f Noise) edited by D’Amico A. and Mazzetti P., Elsevier, New York, p. 469.Google Scholar
  12. 12.
    Handel P. H. (1966), Instabilities, Turbulence and Flicker-Noise in Semiconductors I, II and III, Zeitschrift für Naturforschung 21a: 561–593; Handel P. H. (1971) Turbulence Theory for the Current Carriers in Solids and a Theory of 1/f Noise, Phys. Rev. A3:2066.ADSGoogle Scholar
  13. 13.
    Zwanziger D. (1973) Phys. Rev. D7: 1082; Phys. Rev. Lett. 30:934; Phys. Rev. D11:3481 and 3504 (1975); T.W.B. Kibble, Phys. Rev. 173:1527; 174:1882; 175:1624 (1968); J. Math. Phys. 9: 315 (1968).ADSGoogle Scholar
  14. 14.
    Zhang Y. and Handel P.H. (1992), Proc. Fifth van der Ziel Conference. Quantum 1/f Noise and other Low Frequency Fluctuations. AIP Conference proceedings Vol. 282, P.H. Handel and A.L. Chung Editors.Google Scholar
  15. 15.
    Gradshteiyn J.S. and Ryzhik I.M. (1965) Table of Integrals, Series and Products Sec. 3.761, No. 9 and No. 7, Academic Press, New York.Google Scholar
  16. 16.
    Handel P. H. (1991), Proc. XI. Int. Conf. on Noise in Physical Systems and 1/f Fluctuations, Musha T., Sato S. and Mitsuaki Y. Editors, Ohmsha Publ. Co., Tokyo, pp. 151–157.Google Scholar
  17. 17.
    Walls F.L., Handel P.H., Besson R. and Gagnepain J.J. (1992), A New Model relating Resonator Volume to 1/f Noise in BAW Quartz Resonators, Proc. 46. Annual Frequency Control Symposium, pp.327–333.Google Scholar
  18. 18.
    Musha T., Borbely G. and Shoji M. (1990), Phys. Rev. lett. 64:2394.CrossRefGoogle Scholar
  19. 19.
    Handel P.H., Sherif T., van der Ziel A., van Vliet K.M. and Chenette E.R.: Towards a More General Understanding of 1/f Noise, submitted to Physics Letters.Google Scholar
  20. 20.
    Handel P.H. and Zhang Y. (1993), Proc. XII. Int. Conf. on Noise in Physical Systems and 1/f Fluctuations, Handel P., and Chung A. Editors, Amer. Inst. of Phys. Conf. Proceedings Vol. 285, St. Louis, pp. 172–175.Google Scholar
  21. 21.
    Handel P.H. (1979), Nature of 1/f Frequency Fluctuations in Quartz Crystal Resonators, Solid State Electron. 22:875–876.CrossRefADSGoogle Scholar
  22. 22.
    Hellwig H. (1993), A Look Into the Crystal Ball, the Next 25 Years in 25th Annual Precise Time and Time Interval Applications and Planning Meeting, NASA Conference Publ. 3267.Google Scholar
  23. 23.
    Hellwig W. (1975), Atomic Frequency Standards: a Survey, Proc. of IEEE 63:212–229.Google Scholar
  24. 24.
    Walls F.L. and Hellwig H. (1976), A New Kind of Passively Operating Hydrogen Frequency Standard, Proc. 30th Annual Frequency Control Symposium, Ft. Monmouth, NJ, June 1976, pp. 473–480.Google Scholar
  25. 25.
    Handel P.H. and Walls F.L. (1994): Analysis of Quantum 1/f Effects in Frequency Standards, Proc. 1994 IEEE Frequency Control Symp., Boston, MA, L. Maleki Editor, IEEE Press, IEEE Catalog No. 94CH3446-2, pp. 539–540.Google Scholar
  26. 26.
    Planat M., Dos Santos S., Ratier N., Cresson J. and Perrine S. (1988), Close to Resonance Interaction of Radiofrequency Waves in a Schottky diode Mixer, AIP Proc. Vol. 466, VII. van der Ziel Symp. on Quantum 1/f Noise and Other Low Frequency Fluctuations in Electronic Devices, Aug. 7–8, 1998, Univ. of Missouri, St. Louis, MO, P.H. Handel and A.L. Chung, Editors, pp. 177–187.Google Scholar
  27. 27.
    Planat M. and Eckert C. (2000) On the frequency and amplitude spectrum and the fluctuations at the output of a communication receiver. IEEE Trans. Ultrason. Ferroelect. Freq. Contr. (to appear in the Special Issue on Frequency Control and Precision Timing)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2000

Authors and Affiliations

  • Peter H. Handel
    • 1
  1. 1.Department of Physics and AstronomyUniversity of MissouriUSA

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