Linear Oscillators

Parametric autoresonance

“…For concreteness we assume β > 0 (for a pendulum β = 1/6). Working in the limit of weak nonlinearity, dissipation and driving, we can employ the method of averaging [2,3,26,27], valid for most of the initial conditions [3,4]. The unperturbed oscillation period is the fast time.…”

“…Substituting this value into Eqs. (A2) and (A3) we obtain the final expressions (26) and (27) for δψ(t) and δI(t).…”

Linewidth of higher harmonics in a nonisochronous auto-oscillator: Application to spin-torque nano-oscillators

“…For the analytical model the non-linear parameters ν and Γ p of the auto-oscillator were extracted in each case independently from the phase and amplitude noise of the first harmonic (fundamental frequency) following [9,13], and the intrinsic linewidth ∆f 0 was calculated from Eq. (4) for ∆f 1 . Using the set of values Γ p , ν, ∆f 0 , obtained solely from the analysis of the signal at the fundamental frequency, we then calculated ∆f n from Eqs.…”

“…Auto-oscillating systems are ubiquitous in nature, and can be found in many branches of science, such as physics (electronics, optics, or mechanics), chemistry and biology [1]. Since auto-oscillators are nonlinear, they generate not only the main auto-oscillation frequency, but also higher harmonics of this frequency.…”

“…Since auto-oscillators are nonlinear, they generate not only the main auto-oscillation frequency, but also higher harmonics of this frequency. In an auto-oscillating regime, the external phase noise (or timing jitter) broadens the spectrum of all the generated frequencies and determines the finite generation linewidths [1][2][3].…”