Flicker noise measurement of HF quartz resonators

Rubiola, Enrico; Groslambert, J.; Brunet, Michel; Giordano, V.

doi:10.1109/58.827421

Cited by 45 publications

(31 citation statements)

References 15 publications

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“…The actual value depends on frequency, on the designer skill, and on the budget for implementation. A bunch of data are available from [GB85,Kro05,Wal95], and from our early attempts to measure the resonator frequency stability [RGBG00]. The oscillators we have analyzed exhibit the highest available stability, for we are confident about published data.…”

Section: Analysis Of the Oscillator Phase Noisementioning

confidence: 99%

“…This conclusion results from a set of selected articles, which includes the measurement of the frequency stability [WW75,RGBG00] and the interpretation of the flicker noise of crystal resonators [Kro98,Kro05]; the design fundamentals of the nowadays BVA resonators [Bes77]; some pioneering works on the low-frequency noise in quartz oscillators [BOM75,Dri75]; more recent articles focusing on specific design solutions for ultra-stable oscillators [Nor91, Nor96, CCG + 98, CCL + 03, TJA97]; and, as a complement, a thorough review of the SiO 2 crystal for the resonator fabrication is found in [Bri85]. Conversely, in everyday-life oscillators, which span from the low-cost XOs to the OCXOs used in telecommunications and instrumentation, the relative simplicity of the low-noise electronics required indicates that the frequency flicker is chiefly the 1/f fluctuation of the resonator.…”

Section: Introductionmentioning

confidence: 99%

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On the 1/f frequency noise in ultra-stable quartz oscillators

Rubiola

Giordano

2007

IEEE Trans. Ultrason., Ferroelect., Freq. Contr.

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The frequency flicker of an oscillator, which appears as a 1/f 3 line in the phase noise spectral density, and as a floor on the Allan variance plot, originates from two basic phenomena, namely: (1) the 1/f phase noise turned into 1/f frequency noise via the Leeson effect, and (2) the 1/f fluctuation of the resonator natural frequency. The discussion on which is the dominant effect, thus on how to improve the stability of the oscillator, has been going on for years without giving a clear answer. This article tackles the question by analyzing the phase noise spectrum of several commercial oscillators and laboratory prototypes, and demonstrates that the fluctuation of the resonator natural frequency is the dominant effect. The investigation method starts from reverse engineering the oscillator phase noise in order to show that if the Leeson effect was dominant, the resonator merit factor Q would be too low as compared to the available technology. Laplace transform of ψ(t) ω angular frequency Note: ω is used as a shorthand for 2πν or 2πf , and viceversa E. Rubiola, V. Giordano

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Section: Analysis Of the Oscillator Phase Noisementioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

On the 1/f frequency noise in ultra-stable quartz oscillators

Rubiola

Giordano

2007

IEEE Trans. Ultrason., Ferroelect., Freq. Contr.

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“…Usually, at room temperatures the phase noise of ultrastable quartz crystal resonators is measured with an inter- ferometric measurement system [18]. such a scheme is not possible for resonators working under cryogenic conditions because of a significant dispersion of resonator parameters at low temperatures.…”

Section: Open-loop Measurementsmentioning

confidence: 99%

Quartz resonator instabilities under cryogenic conditions

Goryachev

Galliou

Abbé

et al. 2012

IEEE Trans. Ultrason., Ferroelect., Freq. Contr.

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The phase noise of a quartz crystal resonator working at liquid helium temperatures is studied. Measurement methods and the device environment are explained. The phase noise is measured for different resonance modes, excitation levels, amount of operating time, device orientations in relation to the cryocooler vibration axis, and temperatures. Stability limits of a frequency source based on such devices are evaluated in the present measurement conditions. The sources of phase flicker and white noises are identified. Finally, the results are compared with previous works.

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“…for the spectrum [210,213]. Several researchers have suggested the constant h À1 % 10 À40 f 2 r for quartz resonators [175,214,215].…”

Section: Noise Sourcesmentioning

confidence: 99%

Survey of integrated‐circuit‐oscillator phase‐noise analysis

Pankratz

Sánchez-Sinencio

2013

Circuit Theory & Apps

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This tutorial distills the salient phase-noise analysis concepts and key equations developed over the last 75 years relevant to integrated circuit oscillators. Oscillator phase and amplitude fluctuations have been studied since at least 1938 when Berstein solved the Fokker-Planck equations for the phase/amplitude distributions of a resonant oscillator.The principal contribution of this work is the organized, unified presentation of eclectic phase-noise analysis techniques, facilitating their application to integrated circuit oscillator design. Furthermore, we demonstrate that all these methods boil down to obtaining three things: (1) noise modulation function; (2) noise transfer function; and (3) current-controlled oscillator gain. For each method, this paper provides a short background explanation of the technique, a step-by-step procedure of how to apply the method to hand calculation/computer simulation, and a worked example to demonstrate how to analyze a practical oscillator circuit with that method.This survey article chiefly deals with phase-noise analysis methods, so to restrict its scope, we limit our discussion to the following: (1) analyzing integrated circuit metal-oxide-semiconductor/bipolar junction transistor-based LC, delay, and ring oscillator topologies; (2) considering a few oscillator harmonics in our analysis; (3) analyzing thermal/flicker intrinsic device-noise sources rather than environmental/parametric noise/ wander; (4) providing mainly qualitative amplitude-noise discussions; and (5) omitting measurement methods/phase-noise reduction techniques.We categorize oscillators into one of three varieties, as illustrated in Figure 3: resonant, delay line, or relaxation. First, the resonant oscillator consists of a nonlinear amplifier and a lumped frequencyselective network or resonator, which typically has a band-pass frequency response with a single magnitude peak as indicated conceptually in the figure. This resonator can take the form of an LC tank circuit, dielectric puck, quartz crystal, SAW or bulk acoustic wave transducer, yttrium iron garnet resonator, or ceramic disk resonator to name a few [43,147,148]. IC resonant oscillators typically use LC tanks, although they are often designed to work in concert with an external 874 E. PANKRATZ AND E. SÁNCHEZ-SINENCIO ! ss t ð Þ correspond to the roughly circular trajectory in the figure called a limit cycle [150].Figure 4. Optoelectronic delay-line oscillator. 876 E. PANKRATZ AND E. SÁNCHEZ-SINENCIO For some subtleties of amplitude-noise behavior, see [50,143], where [50] also points out effects of not employing Floquet normalization (cf. Section 4.7).½ =fVoigt ð Þ 2(Gaussian) at small offsets [78,151,152,154]. Chorti also observed that, in general, noise processes with long correlation times tend to create such 'Gaussian' voltage spectra for small frequency offsets f m [151,152]. 4 Note well that, technically, defining spectra for f proves problematic, as it is not stationary and, what is worse, not bounded. This is in fact one reason why the ...

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Flicker noise measurement of HF quartz resonators

Cited by 45 publications

References 15 publications

On the 1/f frequency noise in ultra-stable quartz oscillators

On the 1/f frequency noise in ultra-stable quartz oscillators

Quartz resonator instabilities under cryogenic conditions

Survey of integrated‐circuit‐oscillator phase‐noise analysis

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