# Phase noise and timing jitter in oscillators with colored-noise sources

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##### Citations

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179 citations

### Cites background from "Phase noise and timing jitter in os..."

...A Lorentzian-like finite flat level of phase noise spectrum near the carrier frequency is well known [10], [11], [12], which originates from the fact that the total power of oscillation is invariant....

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177 citations

### Cites background or methods from "Phase noise and timing jitter in os..."

...[1], [2] proceeds without postulating that the phase noise in the oscillator can be modeled as the output of an ideal integrator....

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...For the spectrum of the oscillator away from the carrier, the white noise sources contribute a term that has a frequency dependence, and the colored noise sources contribute terms that have a frequency dependence as multiplied with the spectral density of the colored noise source [2], [4]....

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...We were able to make this observation based on the results obtained in [1], [2] summarized before....

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...The derivation of the above results and the numerical techniques for computing these coefficients have been covered extensively in [1] and [2]....

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...With timing noise characterized as above, the oscillator output with phase noise is a stationary process, and its spectral density is given by [2]...

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132 citations

### Cites background from "Phase noise and timing jitter in os..."

...While lacking the rigor of mathematically involved analyses [2]–[ 4 ], the linear-time variant (LTV) approach to analyzing noise in oscillators has gained the most traction in the circuit design community....

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122 citations

### Cites background from "Phase noise and timing jitter in os..."

...A true Wiener process does not take into account colored (correlated) noise sources [36] and cannot describe frequency and time-domain properties of PN properly [35], [37], [38]....

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...PN modeling has been investigated extensively in the circuits and systems community over the past decades [34], [36], [39]–[49]....

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117 citations

### Cites methods from "Phase noise and timing jitter in os..."

...This approach was adopted in [18] for the analysis of noise sources in the phase of an oscillator....

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##### References

5,597 citations

### "Phase noise and timing jitter in os..." refers methods in this paper

...The partial integro-differential equation (14) for the timevarying marginal PDF of is a generalization of a partial differential equation known as the Fokker‐Planck equation [4], [ 5 ] derived for the PDF of satisfying (10) when is a white-noise process, which is given as...

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4,717 citations

### "Phase noise and timing jitter in os..." refers background or methods in this paper

...The waveform for base‐emitter voltage is used in calculating the contribution of the and the burst noise source connected between the base and the emitter of the transistor in its noise model [ 6 ]....

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...The source of burst noise is not fully understood, although it has been shown to be related to the presence of heavy-metal ion contamination [ 6 ]....

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...where is a constant for a particular device, is the current through the device, is a constant in the range 0.5 to 2, and is the 3-dB bandwidth of the Lorentzian spectrum [ 6 ]....

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3,261 citations

2,383 citations

1,226 citations

### "Phase noise and timing jitter in os..." refers background or methods or result in this paper

...A brief review of previous work on phase noise is given in [ 1 ]....

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...We carried out a rigorous analysis of this case in [ 1 ] and obtained the following results....

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...In recent publications [ 1 ] and [2], we presented a theory and numerical methods for practical characterization of phase noise in oscillators with white-noise sources....

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...In [ 1 ], we concretized the above observation for white-noise perturbations, which we summarize in Section III....

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...We developed numerical methods [ 1 ], [2], both in time and frequency domain, for the efficient computation of the periodic Floquet vector in (3), which is sufficient to characterize both spectral spreading and timing jitter in oscillators....

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