Crystal Oscillators

Poddar, Ajay K.; Rohde, Ulrich L.

doi:10.1002/047134608x.w8154

Cited by 10 publications

(3 citation statements)

References 15 publications

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“…Otherwise, if according to the traditional explanation of Leeson model, f 0 /2Q L and Q L will be estimated at about 21 KHz and 254, and F = 2.8 dB will undoubtedly be obtained if we want to get a result similar to Fig. 4, which is inconsistent with the results of previous researches [6,14,15].…”

contrasting

confidence: 57%

“…Otherwise, if according to the traditional explanations of Leeson model, the corner frequency f c will be estimated as about 10 KHz when Q L is about 103000, and F = 3 dB will be inevitably obtained if we want to get a result similar to as shown in Fig. 3, which is inconsistent with the results of previous researches [6, 14, 15]. These false estimates also will make designers believe that the noise figure F of circuit is low enough and the major direction of improvement is to reduce f c or even consider that Leeson model would cause large error, and then gives oscillator designers’ improvement efforts wrong orientations.…”

Section: Verifications Of New Explanationsmentioning

confidence: 86%

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Reviews of leeson model of oscillator phase noise

Huang

Bai

et al. 2016

Electron. lett.

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Through theoretical deduction, two new explanations of Leeson model are presented: the corner frequency of high Q oscillators in the phase noise curve should be the frequency at the intersection of the f 0 curve segment after adding 3 dB and the f −1 curve segment; f 0 /2Q L of low Q oscillators in the phase noise curve should also be the frequency at the intersection of the f 0 curve segment after adding 3 dB and the f −2 curve segment. Moreover, these two new explanations were verified by the experimental data of a reported 80 MHz high Q quartz crystal oscillator and a reported low Q lithium tantalate (LiTaO 3) oscillator, respectively. The results could help researchers and engineers properly estimate the key parameters of oscillator phase noise.

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contrasting

confidence: 57%

Section: Verifications Of New Explanationsmentioning

confidence: 86%

Reviews of leeson model of oscillator phase noise

Huang

Bai

et al. 2016

Electron. lett.

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“…A crystal is a solid in which the constituent atoms, molecules, or ions are packed in a regularly ordered, repeating pattern extending in all three spatial dimensions [28,38]. Almost any object made of an elastic material could be used like a crystal, with appropriate transducers, since all objects have natural resonant frequencies of vibration.…”

Section: Crystal Oscillatorsmentioning

confidence: 99%

Symmetry-Breaking Bifurcations and Patterns of Oscillations in Rings of Crystal Oscillators

Buono¹,

Chan²,

Ferreira³

et al. 2018

SIAM J. Appl. Dyn. Syst.

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Symmetry is used to investigate the existence and stability of collective patterns of oscillations in rings of coupled crystal oscillators. We assume N identical crystal oscillators, where each oscillator is described by a two-mode nonlinear oscillatory circuit. We also assume the coupling to be identical and consider two different topologies, unidirectional and bidirectional, which lead to networks with Γ = ZN and Γ = DN symmetry, respectively. The whole system can be seen as an ε-perturbation of N uncoupled, two-mode oscillators. The spectrum of eigenvalues of the linearized system near the origin leads to expressions not amenable to analysis. To circumvent this problem, we apply the method of averaging and rewrite the model equations, via near identity transformations, in the socalled full-averaged equations. The truncation to the average part, expressed in complex coordinates, is O(2) × O(2) × Γ-equivariant. Then, we present new theoretical results linking symmetry and averaging theory to study the existence and stability of steady-states of the truncated averaged systems, and show that they persist as periodic solutions of the full-averaged system for small ε. A decomposition of the phase-space dynamics along irreducible representations of the symmetry groups ZN and DN leads to a block diagonalization of the linearized averaged equations. Direct computation of eigenvalues leads to the desired identification of periodic solutions that emerge via symmetry-preserving and symmetry-breaking steady-state bifurcations leading to the corresponding periodic solutions with spatio-temporal symmetries. Numerical simulations are conducted to show representative examples of emergent rotating waves. The motivation for this work is to aid future design and fabrication of novel precision timing devices.

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Continuous Models

Palacios

2022

Mathematical Engineering

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Crystal Oscillators

Cited by 10 publications

References 15 publications

Reviews of leeson model of oscillator phase noise

Reviews of leeson model of oscillator phase noise

Symmetry-Breaking Bifurcations and Patterns of Oscillations in Rings of Crystal Oscillators

Continuous Models

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