Computation of the phase and amplitude noise in microwave oscillators and a simplified calculation method for far enough from the carrier offsets

Jahanbakht, Sajad; Farzaneh, Forouhar

doi:10.1049/iet-map.2009.0396

Cited by 14 publications

(24 citation statements)

References 14 publications

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“…Note that theoretically, the CMA approach gives infinite PSDs at very near to the carrier offsets. However, the CMA results of Figure become flat for these offsets, which is due to the ever present small numerical inaccuracies in computing the steady state of the oscillator . Furthermore, it seems that such numerical inaccuracies prevent the results of the new approach from producing a Lorentzian shape at very near to the carrier offsets.…”

Section: Resultsmentioning

confidence: 94%

“…The exact algorithm for computing the PPV of and the function g ( t ) of is completely addressed in , which is based on the eigenvalue decomposition of the HB Jacobian matrices. The method of this reference was implemented in MATLAB to extract the PPV and the function g ( t ) of .…”

Section: Resultsmentioning

confidence: 99%

“…It is assumed that Equation has a steady‐state periodic response x s ( t ) ∈ R n with fundamental angular frequency ω 0 that has orbital stability and asymptotic phase property . The steady‐state vector of the oscillator considering only the phase noise, neglecting the amplitude noise process, can be written as follows :

bold-italicx ((), t) = true \sum_{k = - H}^{H} X_{k} e^{i k ω_{0} ((), t + α ((), t))}

where X k is the vector containing the k th Fourier series component of x s ( t ) and α ( t ) is the common time‐delay process that is responsible for generating the major part of the phase noise process . The equation governing the common time‐delay process can be written as follows :

\frac{d α}{d t} = bold-italicg ((), t + α ((), t)) bold-italicξ ((), t)

where the row vector g ( t + α ( t )) is defined by

bold-italicg (() .) \overset{Δ}{=} v_{1}^{T} (() .) bold-italicD ((), x_{s} ((), .))

…”

Section: Phase Noise Characteristic Equationmentioning

confidence: 99%

“…However, based on the authors in , it is proved that for oscillators described by without the term

\tilde{h} ((), t)

and with only white noise sources being present, relations and are yet valid, but the parameter α ( t ) is to be interpreted as the slow‐varying portion of the common time‐delay process. However, it is proved that the fast‐varying portion of the common time‐delay process has much smaller influence on the phase noise at least at near‐carrier offset frequencies . The method of obtaining g (.)…”

Section: Phase Noise Characteristic Equationmentioning

confidence: 99%

“…where X k is the vector containing the kth Fourier series component of x s (t) and α(t) is the common time-delay process that is responsible for generating the major part of the phase noise process [12]. The equation governing the common time-delay process can be written as follows [3]:…”

Section: Phase Noise Characteristic Equationmentioning

confidence: 99%

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Phase noise characterization of oscillators through Ito calculus

Jahanbakht

Farzaneh

2014

Circuit Theory & Apps

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SUMMARYRecent phase noise analysis techniques of oscillators mainly rely on solving a stochastic differential equation governing the phase noise process. This equation has been solved in the literature using a number of mathematical tools from probability theory like deriving the Fokker-Planck equation governing the phase noise probability density function. Here, a completely different approach for solving this equation in presence of white noise sources is introduced that is based on the Ito calculus for stochastic differential equations. Time-domain analytical expressions for the correlation of the noisy variables of the oscillator are derived that in asymptotically large times give the steady-state stochastic correlations as well as the power spectral densities of the variables. The validity of the new approach is verified by comparing its results against extensive Monte-Carlo simulations. This approach is applied to an oscillator with a dielectric resonator at 4.127 GHz, and a very good agreement between its results with those of the Monte-Carlo simulations and the previous approaches is observed.

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Section: Resultsmentioning

confidence: 94%

Section: Resultsmentioning

confidence: 99%

bold-italicx ((), t) = true \sum_{k = - H}^{H} X_{k} e^{i k ω_{0} ((), t + α ((), t))}

\frac{d α}{d t} = bold-italicg ((), t + α ((), t)) bold-italicξ ((), t)

where the row vector g ( t + α ( t )) is defined by

bold-italicg (() .) \overset{Δ}{=} v_{1}^{T} (() .) bold-italicD ((), x_{s} ((), .))

…”

Section: Phase Noise Characteristic Equationmentioning

confidence: 99%

“…However, based on the authors in , it is proved that for oscillators described by without the term

\tilde{h} ((), t)

Section: Phase Noise Characteristic Equationmentioning

confidence: 99%

Section: Phase Noise Characteristic Equationmentioning

confidence: 99%

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Phase noise characterization of oscillators through Ito calculus

Jahanbakht

Farzaneh

2014

Circuit Theory & Apps

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Superposition properties of the phase noise based on the LTV model

Hashemi

Ghafoorifard

Abdipour

2012

Analog Integr Circ Sig Process

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Phase noise of electrical oscillators due to multi‐Lorentzian noise sources based on the LTV model

Hashemi

2017

IET Microwaves, Antennas & Propagation

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Using the general expression of the phase variance expressed by the linear time variant (LTV) phase noise model, phase variances due to multi‐Lorentzian and white noise sources of electrical oscillators have been extracted and phase noise expressions due to white and Flicker noises have been calculated. Despite the basic LTV model in which the expressed phase noise due to white noise is valid for offset frequencies larger than the −3 dB corner frequency of the output and it tends to infinity for small offset frequencies, in the proposed model, the extracted phase noises due to white and Flicker noises are valid for the entire spectrum and become limited for small offset frequencies. Comparison between the results of the proposed model by those of the harmonic balance technique shows the validity of the model. Also, the effects of the physical parameters of the oscillator circuit on the extracted phase noise can be observed in the expressions. The proposed model is applicable to calculate the phase noise of the oscillators with single perturbation source applied to the intended output node.

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Computation of the phase and amplitude noise in microwave oscillators and a simplified calculation method for far enough from the carrier offsets

Cited by 14 publications

References 14 publications

Phase noise characterization of oscillators through Ito calculus

Phase noise characterization of oscillators through Ito calculus

Superposition properties of the phase noise based on the LTV model

Phase noise of electrical oscillators due to multi‐Lorentzian noise sources based on the LTV model

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