Nonlinear effects of noise in electronic clocks

Grivet, P.

doi:10.1109/proc.1963.2633

Cited by 31 publications

(18 citation statements)

References 2 publications

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“…Since the active devices forming the positive feedback loop load the tank, in should be changed to in , which is taken care of by this factor. This validates of our earlier definition of the loaded tank quality factor in (24).…”

Section: Linewidth Compression Revisitedsupporting

confidence: 90%

“…The virtual damping assumes an exponential behavior and the virtual damping rate is identical to the phase diffusion constant , as we guessed earlier. From the mathematical perspective, (6) per se is not surprisingly new as it results from the standard probability calculation similar to the one shown in [24], which alone does not necessarily provide a physical meaning in conjunction with phase diffusion or its far-reaching implications. However, the virtual damping concept indeed has important impact, leading to an intuitive understanding of phase noise in a unified framework where resonators and oscillators are viewed from the same angle, as will be seen shortly.…”

Section: A Virtual Damping Conceptmentioning

confidence: 99%

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Virtual damping and einstein relation in oscillators

Ham

Hajimiri

2003

IEEE J. Solid-State Circuits

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Abstract-This paper presents a new physical theory of oscillator phase noise. Built around the concept of phase diffusion, this work bridges the fundamental physics of noise and existing oscillator phase-noise theories. The virtual damping of an ensemble of oscillators is introduced as a measure of phase noise. The explanation of linewidth compression through virtual damping provides a unified view of resonators and oscillators. The direct correspondence between phase noise and the Einstein relation is demonstrated, which reveals the underlying physics of phase noise. The validity of the new approach is confirmed by consistent experimental agreement.

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Section: Linewidth Compression Revisitedsupporting

confidence: 90%

Section: A Virtual Damping Conceptmentioning

confidence: 99%

Virtual damping and einstein relation in oscillators

Ham

Hajimiri

2003

IEEE J. Solid-State Circuits

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“…On the other hand, the most important step, consistently taken in all nonlinear analyses reported so far, is the application of the averaging principle [14] which involves smoothing of the instantaneous nonlinearity in the circuit [12]. I t is shown in the Appendix that this approximation is equivalent to replacing the actual nonlinear oscillator again by a linear oscillator with -AGC.…”

mentioning

confidence: 99%

The effects of noise in oscillators

Hafner

1966

Proc. IEEE

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An explicit expression for the output signal from an oscillator with several noise sources in the circuit is derived. This formula describes qualitatively and quantitatively the manner in which thermal and shot noise act to corrupt the performance of an ideal oscillator. The statistical properties of the signal are then evaluated, as it emerges from the oscillator stage, after passage through an output filter and after being operated on by an ideal n-times multiplier. Expressions are derived for *e short term frequency stability, the power spectral density, and the power spectrum of the signal, as well as for the spectra! density of the signal phase.* LYhen (6) is substituted into (3) with -F(t) = O and the principle of the harmonic balance [22] is applied, an infinite set of nonlinear algebraic equations results which can be solved by an iteration procedure. The effects of harmonic content on oscillator frequency have been studied extensively by Groszkowski [23].

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“…(10) and T is the inverse Fourier transform of Eq. (1) and Rhn(0) is the auto correlation function evaluated at zero, which is equivalent to the mean-squared value of the additive noise at the output of the passive cavity given by (13) The numerator of Eq. (12) (14) and substituting Eq.…”

Section: S(w) T*(w)/mentioning

confidence: 99%