Abstract: This paper presents the stochastic characterization of the phase-noise spectrum of free-running oscillators in the envelope domain. The flicker-noise sources are modeled as an infinite summation of Ornstein-Uhlenbeck processes. Inputs of the formulation are parameters extracted with harmonic balance (HB) by means of the carrier-modulation approach. These parameters can be easily identified with commercial software packages without user access to the Jacobian matrix of the HB system. The presented envelope-domain formulation significantly reduces the complexity of the stochastic analysis in comparison with time-domain techniques. The phase-noise spectrum depends on the measurement time interval, instead of estimated cutoff frequencies for the colored noise sources. With the new formulation it has been possible to investigate the influence of the measurement time interval on the near-carrier phase-noise spectrum. The formulation will show that provided the measurement time fulfills some nonstrict mathematical conditions, typically accomplished in any practical measurement, the full phase-noise spectrum will be nearly the same, whatever the measurement time interval. Analytical expressions are provided for the full phase-noise spectrum. All the obtained expressions have been exhaustively validated by means of Monte Carlo simulations. In order to verify the generality of the results, the analysis method has been applied to various oscillator configurations. The simulated and measured phase-noise spectra have been compared, obtaining very good agreement in all cases.

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