Analysis of white and f^−α noise in oscillators

Abstract

SUMMARYIn this paper the general correlation spectrum of an oscillator with white and f -f f noise sources is derived from the Langevin equations describing the deterministic and stochastic behaviour of an oscillator by perturbation methods. The treatment off -a noise and the influence of the finite measuring time on the noise spectra are included in a time domain calculation. The theory is applied to a Van der Pol oscillator exhibiting parametric sideband amplification and to a realized oscillator demonstrating the applicability of the theory to technically relevant circuits,

Modelling and Discretization of Circuit Problems

“…(See also already [130,131] where a first start was made to treat the phase noise problem in the time-domain.) In [46,49] it is argued that, in first order, (20.37) has a solution of the form y(t) + z(t), with α determined by (20.42), and where the orbital deviation z(t) satisfies ||z|| ∞ < Const.||b|| ∞ (and even z(t) → 0 (t → ∞)).…”

Periodic AC and Periodic Noise in RF Simulation for Electronic Circuit Design

“…(See also [11,12] where a first start was made to treat the phase noise problem in the time domain.) Note that if bet) =0, for t~to, then a becomes a constant phase shift, and the phase shifted function yet) solves exactly (3.23) for t~to.…”

Rotary Traveling-Wave Oscillator With Differential Nonlinear Transmission Lines

“…This analysis will implicitly account for any near-critical circuit pole, with impact on the noise-analysis bandwidth. However, this method, due to its inherent linearity, cannot predict the effect of the perturbedoscillator nonlinearity in the common phase noise [26][27][28][29][30][31][32], associated to the carrier modulation, which affects the nearcarrier phase noise. Here a calculation of the phase-noise spectrum from the variance of the common-phase deviation is applied to RTWOs for the first time to our knowledge.…”