A Study of Locking Phenomena in Oscillators

Adler, R.

doi:10.1109/jrproc.1946.229930

Cited by 1,423 publications

(375 citation statements)

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“…It is generally known that in self-sustained oscillators possessing phase degeneracy, large phase fluctuations can be suppressed by injecting a small, but frequency stable, signal in resonance with the oscillator [37]. This effect is explained by a violation of the symmetry of the phase degeneracy by external driving.…”

Section: Injection Lockingmentioning

confidence: 99%

“…Applying an input signal detuned from the oscillation frequency gives rise to the interesting and related phenomenon of frequency synchronization [37,39]. We introduce a detuning s between the injection signal and the parametric oscillations in mode 3 and study the output photon spectral densities of both modes as functions of s and n [see Figs.…”

Section: Synchronization and Secondary Idlersmentioning

confidence: 99%

“…8(a)-8(d) as a gap in frequency space where the oscillations have the same frequency as the locking signal. The gap size is proportional to the size of the synchronization detuning window, which in turn is proportional to the square root of the input power [37]. In Fig.…”

Section: Synchronization and Secondary Idlersmentioning

confidence: 99%

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Nondegenerate parametric oscillations in a tunable superconducting resonator

et al. 2018

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We investigate nondegenerate parametric oscillations in a superconducting microwave multimode resonator that is terminated by a superconducting quantum interference device (SQUID). The parametric effect is achieved by modulating magnetic flux through the SQUID at a frequency close to the sum of two resonator-mode frequencies. For modulation amplitudes exceeding an instability threshold, self-sustained oscillations are observed in both modes. The amplitudes of these oscillations show good quantitative agreement with a theoretical model. The oscillation phases are found to be correlated and exhibit strong fluctuations which broaden the oscillation spectral linewidths. These linewidths are significantly reduced by applying a weak on-resonant tone, which also suppresses the phase fluctuations. When the weak tone is detuned, we observe synchronization of the oscillation frequency with the frequency of the input. For the detuned input, we also observe an emergence of three idlers in the output. This observation is in agreement with theory indicating four-mode amplification and squeezing of a coherent input.

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Section: Injection Lockingmentioning

confidence: 99%

Section: Synchronization and Secondary Idlersmentioning

confidence: 99%

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Nondegenerate parametric oscillations in a tunable superconducting resonator

et al. 2018

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“…formulated for the first time by Adler [43]. Here, Ψ is the phase difference between the external field and oscillations of the system.…”

Section: The Time Required To Achieve the Synchronization Regime In Amentioning

confidence: 99%

Synchronization of Distributed Electron–Wave Self-Oscillatory Systems with a Backward Wave

Trubet︠s︡kov

Koronovsky

Храмов

2004

Radiophysics and Quantum Electronics

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621.385We present the results of studying the phenomenon of synchronization in distributed electronwave self-oscillatory systems with a counterpropagating wave. General laws governing the appearance of the classical synchronization in distributed systems are revealed. We propose methods for increasing the synchronization bandwidth by using the distributed input of a signal to the interaction space by means of coupled waveguide structures. Transient processes in nonautonomous self-oscillation regimes are studied. In particular, the effect of ultrafast synchronization is found. The possibility of chaotic synchronization in a gyro-oscillator with a counterpropagating wave under the action of a deterministic chaotic signal is shown. Mutual oscillation regimes in a system of two distributed oscillators with coupled waveguide systems are studied.

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“…For a qualitative analysis of the phenomenon of ultrafast synchronization of self-oscillations in an active distributed medium one can use the equation of phase synchronization, obtained for the first time by R. Adler in [20], to which analysis of the synchronization phenomenon is reduced for a variety of systems:…”

Section: Onset Of the Synchronous Oscillation Modementioning

confidence: 99%