1973
DOI: 10.1109/proc.1973.9292
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A study of locking phenomena in oscillators

Abstract: A paper reprinted from the June 1946 issue of the PROCEEDINGS OF THE IRE.Absfracf--Impreseion of an external signal upon an oscillator of similar fundamental frequency affects both the inetantaneow amplitude and instantaneorrs frequency. Using the assumption that time constants in the osdtlator circuit am small compared to the length of one beat cycle, a Merential equation is derived which gives the osdllator phase as a function of time. W i t h the aid of this equation, the transient process of "pull-in" as w… Show more

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Cited by 945 publications
(567 citation statements)
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“…(3.80) describes the linear increase of the locking range with the injection strength K that we have already observed in the numerical evaluation of the bifurcation structure. Under the assumption of constant electricfield amplitude and α = 0, the above equation would reproduce the phase-locking behavior known from Adler's equation [ADL73], showing the connection between the optically injected quantum-laser and simple driven phase oscillators.…”
Section: Im G(t) ≡ −α Re G(t)mentioning
confidence: 58%
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“…(3.80) describes the linear increase of the locking range with the injection strength K that we have already observed in the numerical evaluation of the bifurcation structure. Under the assumption of constant electricfield amplitude and α = 0, the above equation would reproduce the phase-locking behavior known from Adler's equation [ADL73], showing the connection between the optically injected quantum-laser and simple driven phase oscillators.…”
Section: Im G(t) ≡ −α Re G(t)mentioning
confidence: 58%
“…Here, the master laser "enslaves" the injected laser, i.e., the injected signal is strong enough to force the slave laser to assume the same wavelength. The frequency detuning interval for which this phase-locking is possible is in first order proportional to the injection strength K [ARN65,ADL73]. This phenomenon shows the similarity between the optically injected quantum-dot laser and harmonically driven oscillators, from which such locking and synchronization effects are known [MUR05b].…”
Section: Injection Locking Of Quantum-dot Lasersmentioning
confidence: 69%
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“…The theoretical analysis of such oscillator arrays has traditionally been based on Adler's formulation of injection locking among oscillators modeled in the manner of Van der Pol [Adler, 1973;Van der Pol, 1934]. The inter-oscillator coupling is characterized by a coupling strength and a coupling phase and represented in the formulation by a complex coupling coefficient.…”
Section: Introductionmentioning
confidence: 99%