AM to PM noise conversion in a cross-coupled quadrature harmonic oscillator

Djurhuus, Torsten; Krozer, Viktor; Vidkjaer, J.; Johansen, Tom K.

doi:10.1002/mmce.20129

Cited by 4 publications

(9 citation statements)

References 17 publications

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“…nonlinear flow , it follows that their respective tangent spaces are invariantly mapped by (8) (9) In the following, we let the set in (7) refer to the eigenvectors of the rank return map . State-space points contained in must contract, and we have (10) with being the contraction function for the th mode. The bundle is invariant under the linear response flow, and (10), together with the group property of the linear response , which follows from the group property of the nonlinear flow, yields (11) a group definition for the contraction function.…”

Section: Geometry Of a Limit Cycle Solutionmentioning

confidence: 99%

“…We then introduce the mapping operator along the th invariant manifold, which, according to (10), must have the form (37) where is the contraction function (see Section II, (12)- (16)) and is the time interval. The th component of the flow is then written as…”

Section: Decomposing the Oscillator Tangent Spacementioning

confidence: 99%

“…The aforementioned results can be extended to nonlinear coordinate transformations. 10 Here, we follow [1] and label the oscillator asymptotic phase (see also the discussion in Section VII).…”

Section: Coordinate-independent Representationmentioning

confidence: 99%

“…The two noise sources are uncorrelated Gaussian white noise sources with power , with being the single-sided available noise power in a 1-Hz bandwidth, and the extra factor two follows because we consider narrow-band noise sources [17]. We then interpret (52) and (53) as the noise-forced averaged state equations of a high-harmonic oscillator with resonator bandwidth (see, e.g., [9] and [10]). Repeating the calculations that lead to (50) in the previous section, we find the isochrone foliation for (52) and (53) (54) and the isochrone tangent bundle is then given as (55) where in the aforementioned equations represents the angle between the isochrone and radial, which is referred to here as the isochrone opening angle 11 .…”

Section: B Am-pm Noise Conversion (I): the Oscillatormentioning

confidence: 99%

“…We also offer a physical interpretation of the so-called perturbation projection vector (PPV) as a phase differential form. Then, in Section VI, we set out to discuss some interesting topics regarding oscillator noise response inspired by examples taken from the literature, including the validity of an orthogonal decomposition [8], AM-PM conversion [9], [10], and nonhyperbolic oscillator noise response [11]. Finally, Section VII includes a derivation of the asymptotic oscillator phase statistics.…”

mentioning

confidence: 99%

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Oscillator Phase Noise: A Geometrical Approach

Djurhuus

Krozer

Vidkjaer

et al. 2009

IEEE Trans. Circuits Syst. I

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Abstract-We construct a coordinate-independent description of oscillator linear response through a decomposition scheme derived independently of any Floquet theoretic results. Trading matrix algebra for a simpler graphical methodology, the text will present the reader with an opportunity to gain an intuitive understanding of the well-known phase noise macromodel. The topics discussed in this paper include the following: orthogonal decompositions, AM-PM conversion, and nonhyperbolic oscillator noise response.

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Section: Geometry Of a Limit Cycle Solutionmentioning

confidence: 99%

Section: Decomposing the Oscillator Tangent Spacementioning

confidence: 99%

Section: Coordinate-independent Representationmentioning

confidence: 99%

Section: B Am-pm Noise Conversion (I): the Oscillatormentioning

confidence: 99%

mentioning

confidence: 99%

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Oscillator Phase Noise: A Geometrical Approach

Djurhuus

Krozer

Vidkjaer

et al. 2009

IEEE Trans. Circuits Syst. I

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Phase Noise

Suárez¹

2008

Analysis and Design of Autonomous Microwave Circuits

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A generalized model of coupled oscillator phase‐noise response

Djurhuus

Krozer

2021

Circuit Theory & Apps

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Model frameworks, based on Floquet theory, have been shown to produce effective tools for accurately predicting phase-noise response of single (freerunning) oscillator systems. This method of approach, referred to herein as macro-modeling, has been discussed in several highly influential papers and now constitutes an established branch of modern circuit theory. The increased application of, for example, injection-locked oscillators and oscillator arrays in modern communication systems has subsequently exposed the demand for similar rigorous analysis tools aimed at coupled oscillating systems. This paper presents a novel solution in terms of a macro-model characterizing the phaseresponse of synchronized coupled oscillator circuits and systems perturbed by weak noise sources. The framework is generalized and hence applicable to all circuit configurations and coupling topologies generating a synchronized steady-state. It advances and replaces the phenomenological descriptions currently found in the published literature pertaining to this topic and, as such, represents a significant breakthrough w.r.t. coupled oscillator noise modeling. The proposed model is readily implemented numerically using standard routines.

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AM to PM noise conversion in a cross-coupled quadrature harmonic oscillator

Cited by 4 publications

References 17 publications

Oscillator Phase Noise: A Geometrical Approach

Oscillator Phase Noise: A Geometrical Approach

Phase Noise

A generalized model of coupled oscillator phase‐noise response

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