Journal of IKEEE (전기전자학회논문지)

Institute of Korean Electrical and Electronics Engineers (한국전기전자학회)
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Analytical Proof of Equivalence of ISF, and Floquet Vector-Based Oscillator Phase Noise Theories

ISF와 Floquet 벡터에 기초한 발진기 위상잡음 이론의 등가성에 대한 해석적 증명

  • Jeon, Man-Young (Dept. of Information and Communications Engineering, Dongyang University)
  • Received : 2013.12.09
  • Accepted : 2013.12.26
  • Published : 2013.12.30
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Abstract

This paper analytically proves the equivalence between two main oscillator phase noise theories, which are based on the ISF, and Floquet vector, respectively. For this purpose, this study obtains the power spectral density matrix from the ISF-based phase noise theory. As a result, one can prove that the power spectral density matrix obtained from the ISF-based phase noise theory is essentially equivalent to the power spectral density matrix presented by the Floquet vector-based phase noise theory, which manifests the equivalence of the two main theories. This study is intended to provide deeper insight into the relations between the two main theories.

본 논문에서는 ISF와 Floquet 벡터에 각각 기초하는 두 개의 주요한 발진기 위상잡음 이론의 등가성을 해석적으로 증명한다. 이를 위해 본 연구에서는 ISF에 기초하는 위상잡음 이론으로부터 전력 스펙트럼 밀도 행렬을 구한다. 이렇게 함으로써 ISF에 기초한 위상잡음 이론의 전력 스펙트럼 밀도 행렬과 Floquet 벡터에 기초한 위상잡음 이론의 전력 스펙트럼 밀도 행렬이 같다는 사실을 해석적으로 증명할 수 있으며 이는 두 이론이 본질적으로 등가임을 증명한다. 본 연구의 목적은 현재까지 널리 알려진 상기 두 위상잡음 이론사이의 관계에 대한 보다 깊은 통찰력을 제공하는데 있다.

Keywords

References

  1. D. B. Leeson, "A simple model of feedback oscillator noise spectrum," Proc. IEEE, vol. 54, no.2, pp. 329-330, Feb. 1966. https://doi.org/10.1109/PROC.1966.4682
  2. M. Lax, "Classical noise-V: Noise in self-sustained oscillators," Phys. Rev., vol. 160, pp. 290-307, 1967. https://doi.org/10.1103/PhysRev.160.290
  3. U. L. Rohde, Digital PLL Frequency Synthesizers: Theory and Design. Englewood Cliffs, NJ: Prentice-Hall, 1983.
  4. A. A. Abidi and R. G. Meyer, "Noise in relaxation oscillators," IEEE J . Solid-State Circuits, vol. SC-18, pp. 794-802, Dec. 1983.
  5. F. X. Kaertner, "Determination of the correlation spectrum of oscillators with low noise," IEEE Trans. Microwave Theory Tech., vol. MTT-37, pp. 90-101, Jan. 1989.
  6. T. C. Weigandt, B. Kim, and P. R. Gray, "Analysis of timing jitter in CMOS ring oscillators," Proc. ISCAS, vol. 4, pp. 27-30, June 1994.
  7. J. McNeil, "Jitter in ring oscillators," Proc. ISCAS, vol. 6, pp. 201-204, June 1994.
  8. B. Razavi, "A study of phase noise in CMOS oscillators," IEEE J . Solid-State Circuits, vol. SC-31, pp. 331-343, Mar. 1996.
  9. A. Hajimiri and T. H. Lee, "A general theory of phase noise in electrical oscillators," IEEE J . Solid-State Circuits, vol. SC-33, pp. 179-194, Feb. 1998.
  10. A. Hajimiri and T. H. Lee, The Design of Low Noise Oscillators. Boston, MA: Kluwer Academic, 1999.
  11. A. Demir, A. Mehrotra, and J. Roychowdhury, "Phase noise in oscillators: a unifying theory and numerical methods for characterization," IEEE Trans. Circuits Syst.-I, vol. 47, pp. 655-674, May 2000. https://doi.org/10.1109/81.847872
  12. A. Demir, "Phase noise and timing jitter in oscillators with colored-noise sources," IEEE Trans. Circuits Syst.-I, vol. 49, pp. 1782-1791, Dec. 2002. https://doi.org/10.1109/TCSI.2002.805707
  13. F. O'Doherty and J. P. Gleeson, "Phase diffusion coefficient for oscillators perturbed by colored noise," IEEE Trans. Circuits Syst.-II, vol. 54, pp. 435-439, May 2007. https://doi.org/10.1109/TCSII.2007.892203
  14. S. Sancho, A. Suarez, J. Dominguez, and F. Ramirez, "Analysis of near-carrier phase-noise spectrum in free-running oscillatorsin the presence of white and colored noise sources," IEEE Trans. Microwave Theory Tech. vol. 58, no. 3, pp. 587-601, Mar. 2010. https://doi.org/10.1109/TMTT.2010.2040326
  15. S. Sancho, A. Suarez, and F. Ramirez, "General phase-noise analysis from the variance of the phase deviation," IEEE Trans. Microwave Theory Tech. vol. 61, no. 1, pp. 472-481, Jan. 2013. https://doi.org/10.1109/TMTT.2012.2229713
  16. P. Vanassche, G. Gielen, and W. Sansen, "On the difference between two widely publicized methods for analyzing oscillator behavior," Proc. ICCAD, pp. 229-233. Nov. 2002.
  17. A. Papoulis, Probability, Random Variables, and Stochastic Processes. NewYork: McGraw-Hill, 1986.