On Noise Analysis of Oscillators Based on Statistical Mechanics

• Autorzy: Thiessen T. , Mathis W.
• Języki publikacji: EN

Abstrakty

EN

In this paper a new approach of thermal noise analysis of electronic oscillators is presented. Although nonlinear electronic oscillators are one of the most essential subcircuits in electronic systems typical design concepts for these oscillators are based on ideas of linear circuits. Because the functionality of oscillators depends on nonlinearities, advanced design methods are developed where nonlinearities are an integral part. Since low voltage oscillator concepts have to be developed in modern IC technologies there is a need to include at least thermal noise aspects into the design flow. For this reason we developed new physical descriptions of thermal noise in electronic oscillators where we use ideas from nonequilibrium statistical mechanics as well as the Langevin approach. We illustrate our concepts by some examples.

Słowa kluczowe

EN

nonlinear oscillators; thermal noise; statistical mechanics

• Wydawca: Polish Academy of Sciences, Committee of Electronics and Telecommunication
• Czasopismo: International Journal of Electronics and Telecommunications
• Rocznik: 2010
• Tom: Vol. 56, No. 4
• Strony: 357--366
• Opis fizyczny: Bibliogr. 54 poz., wykr.

Twórcy

autor

Thiessen T.

autor

Mathis W.

• Institute of Theoretical Electrical Engineering, Leibniz University of Hannover, D-30167, Hannover, Germany,

Bibliografia

• [1] W. Mathis and P. Russer, Encyclopedia of RF and Microwave Engineering. John Wiley & Sons, 2005, vol. 4, ch. Oscillator Design.
• [2] W. Mathis and L. Weiss, Modeling, Simulation and Optimization of Integrated Circuits, ser. Series of Numerical Mathematics. Birkhäuser Verlag, 2003, vol. 146, ch. Noise Analysis of Nonlinear Electrical circuits and Devices, pp. 269-282.
• [3] W. Mathis, “Bifurcations in noisy nonlinear networks and systems, in Springer Proceedings Physics. Berlin-Heidelberg: Springer-Verlag, 2006.
• [4] D. B. Leeson, “A simple model of feedback oscillator noise spectrum,” Proceedings of the IEEE, vol. 54, pp. 329-330, 1966.
• [5] M. Lax, “Classical noise. V. Noise in self-sustained oscillators,” Physical Review, vol. 160, pp. 290-307, 1967.
• [6] F. Kärtner, “Analysis of white and f- noise in oscillators,” International Journal of Circuit Theory and Applications, vol. 18, pp. 485-519, 1990.
• [7] A. Demir and A. Sangiovanni-Vincentelli, Analysis and Simulation of Noise in Nonlinear Electronic Circuits and Systems. Kluwer Academic Publishers, 1998.
• [8] A. Hajimiri and T. H. Lee, The Design of Low Noise Oscillators. Kluwer Academic Publishers, 1999.
• [9] S.-M. Hong, C. H. Park, H. S. Min, and Y. J. Park, “Physics-based analysis and simulation of phase noise in oscillators,” IEEE Transactions on Electron Devices, vol. 53, no. 9, pp. 2195-2201, September 2006.
• [10] L. Weiss and W. Mathis, “A thermodynamical approach to noise in nonlinear networks,” International Journal of Circuit Theory and Applications, vol. 26, pp. 147-165, 1998.
• [11] W. Schottky, “Über spontane Stromschwankungen in verschiedenenElektrizit ätsleitern,” Annalen der Physik, vol. 57, pp. 541–567, 1918.
• [12] J. B. Johnson, “Bemerkungen zur Bestimmung des elektrischen Elementarquantums aus dem Schroteffekt,” Annalen der Physik, vol. 67, pp. 154-156, 1922.
• [13] W. Schottky and C. A. Hartmann, “Experimentelle Untersuchung des Schroteffektes in Glühkathodenröhren,” Zeitschrift für Physik, vol. 2, p. 206, 1920.
• [14] H. Nyquist, “Thermal agitation of electric charge in conductors,” Physical Review, vol. 32, pp. 110-113, 1928.
• [15] B. J. Johnson, “Thermal agitation of electricity in conductors,” Nature, vol. 119, p. 50, 1927.
• [16] B. J. Johnson, “Thermal agitation of electricity in conductors,” Physical Review, vol. 32, pp. 95-109, 1928.
• [17] A. Einstein, “Zur Theorie der Brownschen Bewegung,” Annalen der Physik, vol. 19, pp. 371-381, 1906.
• [18] G. L. de Haas Lorentz, Die Brownsche Bewegung und einige verwandte Erscheinungen. Braunschweig: Friedrich Vieweg & Sohn, 1913.
• [19] H. F. Mataré, “Brownsche Bewegung und Widerstandsrauschen,” Annalen der Physik, vol. 435, pp. 271-278, 1943.
• [20] A. Kolmogoroff, Grundbegriffe der Wahrscheinlichkeitsrechnung. Berlin: Springer-Verlag, 1933.
• [21] A. Khintchine, “Korrelationstheorie der station ären stochastischen Prozesse,” Mathematische Annalen, vol. 109, pp. 604-615, 1934.
• [22] N. Wiener, “Generalized harmonic analysis,” Acta Mathematica, vol. 55, pp. 117-258, 1930.
• [23] H. A. Kramers, “Brownian motion in a field of force and the diffusion model of chemical reactions,” Physica, vol. 7, pp. 284-304, 1940.
• [24] D. K. C. MacDonald, “Brownian movement,” Physical Review, vol. 108, pp. 541-545, 1957.
• [25] R. L. Stratonovich, Topics in the Theory of Random Noise I+II. Gordon & Breach Science Publishers, 1967.
• [26] N. G. van Kampen, “Thermal fluctuations in nonlinear systems,” Journal of Mathematical Physics, vol. 4, pp. 190-194, 1963.
• [27] N. G. van Kampen, Stochastic Processes in Physics and Chemistry, 2nd ed. North-Holland Personal Library, 1997.
• [28] R. L. Stratonovich, Nonlinear Nonequilibrium Thermodynamics I: Linear and Nonlinear Fluctuation-Dissipation Theorems: Linear and Nonlinear Fluctuation. New York: Springer-Verlag, 1993, vol. 1.
• [29] L. Weiss and W. Mathis, “Irreversible thermodynamics and thermal noise of nonlinear networks,” COMPEL, vol. 17, pp. 635–648, 1998.
• [30] L. Weiss and W. Mathis, “A thermodynamical approach to noise in nonlinear networks,” International Journal of Circuit Theory and Applications, vol. 26, pp. 147-165, 1998.
• [31] H. Haken, Synergetics. Berlin-New York: Springer-Verlag, 2004.
• [32] L. Arnold, “The unfoldings of dynamics in stochastic analysis,” Comput. Appl. Math., vol. 16, pp. 3-25, 1997.
• [33] N. G. van Kampen, “Ito versus Stratonovich,” Journal of Statistical Physics, vol. 24, pp. 175-187, 1981.
• [34] N. G. van Kampen, “The validity of nonlinear langevin equations,” Journal of Statistical Physics, vol. 25, pp. 431-442, 1981.
• [35] L. Weiss, Rauschen in nichtlinearen elektronischen Schaltungen und Bauelementen - ein thermodynamischer Zugang. Germany: University of Magdeburg, 1999.
• [36] H. B. G. Casimir, “On onsager's principle of microscopic reversibility,” Reviews of Modern Physics, vol. 83, pp. 34-40, 1951.
• [37] R. K. Brayton and J. K. Moser, “A theory of nonlinear networks - I and II,” Quarterly of Applied Mathematics, vol. 22, pp. 1-33, 81-104, 1964.
• [38] J. L. Wyatt and G. J. Coram, “Nonlinear device noise models: Satisfying the thermodynamic requirements,” IEEE Transactions on Electron Devices, vol. 46, pp. 184-193, 1999.
• [39] L. Weiss and W. Mathis, “A thermodynamic noise model for nonlinear resistors,” IEEE Electron Device Letters, vol. 20, pp. 402-404, 1999.
• [40] A. van der Ziel, “Thermal noise in field-effect transistors,” in Proceedings of the IRE, vol. 50, 1962, pp. 1808-1812.
• [41] D. W. Jordan and P. Smith, Nonlinear Ordinary Differential Equations, 4th ed. Oxford University Press, 2007.
• [42] W. Ebeling and I. M. Sokolov, Statistical Thermodynamics and Stochastic Theory of Nonequilibrium Systems. World Scientific, 2005.
• [43] E. S. Philippow and W. G. Büntig, Analyse nichtlinearer dynamischer Systeme der Elektrotechnik. Carl Hanser Verlag, 1992.
• [44] Y. L. Klimontovich, Turbulent Motion and the Structure of Chaos: The New Approach to the Statistical Theory of Open Systems. Berlin-New York: Springer-Verlag, 1991.
• [45] W. Ebeling, Stochastic Processes in Physics, Chemistry, and Biology (Lecture Notes in Physics). Springer-Verlag, 2000, ch. Problems of a Statistical Ensemble Theory for Systems Far from Equilibrium.
• [46] R. S. Langley, “Application of the principle of detailed balance to the random vibration of non-linear oscillators,” Journal of Sound und Vibration, vol. 125, pp. 85-92, 1988.
• [47] M. S. Miguel and S. Chaturvedi, “Limit cycles and detailed balance in Fokker-Planck equations,” Zeitschrift für Physik B - Condensed Matter, vol. 40, pp. 167-174, 1980.
• [48] A. Daffertshofer, “Effects of noise on the phase dynamics of nonlinear oscillators,” Physical Review, vol. 58, no. 1, July 1998.
• [49] P. E. Kloeden, E. Platen, and H. Schurz, Numerical Solution of SDE Through Computer Experiments. Berlin-Heidelberg: Springer-Verlag, 1994.
• [50] H. Risken, The Fokker-Plack Equation, 2nd ed. Springer-Verlag, 1989.
• [51] N. Bogoliubov and U. Mitropolski, Asymptotic Methods in the Non-Linear Oscillations. Gordon & Breach, 1961.
• [52] G. Dörfel and D. Hoffmann, Von Albert Einstein bis Norbert Wiener - frhe Ansichten und späte Einsichten zum Phänomen des elektronischen Rauschens, ser. Preprint/Max-Planck-Institut für Wissenschaftsgeschichte. Max-Planck-Institut für Wissenschaftsgeschichte, 2005, vol. 301.
• [53] W. Ebeling, E. Gudowska-Nowak, and I. M. Sokolov, “On stochastic dynamics in physics - remarks on history and terminology,” Acta Physica Polonica B, vol. 39, pp. 1003-1018, 2008.
• [54] S. K. Magierowski and S. Zukotynski, “CMOS LC-oscillator phasenoise analysis using nonlinear models,” IEEE Transactions on Circuits and Systems I: Regular Papers, vol. 51, pp. 664-677, 2004.