Study of Injection Locking With Amplitude Perturbation and Its Effect on Pulling of Oscillator

Ali, Ikbal; Banerjee, Abhijit; Mukherjee, A. S.; Biswas, Baidyanath

doi:10.1109/tcsi.2011.2161361

Cited by 29 publications

(23 citation statements)

References 17 publications

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“…In order to further compare the results from analytical expressions of the LR and the results from SPICE simulations, in Figure 3 we show the results obtained for different values of the parameters of the passive and active components. Results in Figure 3 confirm that the best analytical estimation of the LR is provided by (22). …”

Section: Journal Of Electrical and Computer Engineeringsupporting

confidence: 61%

“…Figure 2, where the results obtained by formulas and by SPICE simulations are reported, shows that the considered formulas are equivalent for small injection values; that is, < 0.2. By increasing the injection amplitude, the LRs in (9) and (12) are significantly smaller than the LR predicted by (22), while the LR in (10) is wider. Comparing these values with those obtained by numerical simulations, we deduce that the best estimation of the LR is provided by (22).…”

Section: Journal Of Electrical and Computer Engineeringmentioning

confidence: 76%

“…By increasing the injection amplitude, the LRs in (9) and (12) are significantly smaller than the LR predicted by (22), while the LR in (10) is wider. Comparing these values with those obtained by numerical simulations, we deduce that the best estimation of the LR is provided by (22). Moreover, we observe that the boundaries of the LR obtained by numerical simulations are not symmetric with respect to Δ = 0, but are different from the boundaries obtained by formulas, because they do not take into account the presence of harmonics.…”

Section: Journal Of Electrical and Computer Engineeringmentioning

confidence: 76%

“…It is interesting to observe that the frequency range in (20) is equal to the LR obtained by the Paciorek-like approach in (10), but the approach in [12] allows us to establish that the range with locked oscillations is stable and, thus, can be observed; that is, the LR is smaller than that in (20) and is equal to that in (22).…”

Section: Journal Of Electrical and Computer Engineeringmentioning

confidence: 85%

“…Outside the region which delimits the locked states in Figure 2, as a rule called Arnold's tongue, it is reasonable to expect that the result of the interaction of the oscillator with the forcing signal V in changes radically, as it happens in an LC oscillator driven by a signal at frequency near to that of the free oscillation [2,21,22]. It is known that, near the Arnold tongue, this interaction manifests as a periodically repeated and incomplete frequency entrainment process, known as periodic pulling.…”

Section: Operation Modes Near the Boundaries Of The Arnold Tonguementioning

confidence: 99%

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Investigation on Locking and Pulling Modes in Analog Frequency Dividers

Buonomo

Schiavo

2013

Journal of Electrical and Computer Engineering

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We compare the main analytical results available to estimate the locking range, which is the key figure-of-merit of LC frequency dividers based on the injection locking phenomenon. Starting from the classical result by Adler concerning injection-locked oscillators, we elucidate the merits and the shortcomings of the different approaches to study injection-locked frequency dividers, with particular emphasis on divider-by-2. In particular, we show the potential of a perturbation approach which enables a more complete analysis of frequency dividers, making it possible to calculate not only the amplitude and the phase of the locked oscillation, but also the region where it exists and is stable, which defines the locking region. Finally, we analyze the dynamical behaviour of the dividers in the vicinity of the boundary of the locking region, showing that there exists a border region where the occurrence of the locking or the pulling operation mode is possible, depending on the initial conditions of the system.

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Section: Journal Of Electrical and Computer Engineeringsupporting

confidence: 61%

Section: Journal Of Electrical and Computer Engineeringmentioning

confidence: 76%

Section: Journal Of Electrical and Computer Engineeringmentioning

confidence: 76%

Section: Journal Of Electrical and Computer Engineeringmentioning

confidence: 85%

Section: Operation Modes Near the Boundaries Of The Arnold Tonguementioning

confidence: 99%

See 3 more Smart Citations

Investigation on Locking and Pulling Modes in Analog Frequency Dividers

Buonomo

Schiavo

2013

Journal of Electrical and Computer Engineering

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References

2014

Wireless Transceiver Architecture

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Evaluating the spectrum of periodic pulling in subharmonic resonant LC circuits

Buonomo¹,

Schiavo²

2014

Circuit Theory & Apps

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SUMMARYWe analyze the features of the oscillations arising in forced inductor-capacitor (LC) oscillators when they operate in the periodic pulling mode, under the action of a weak injection signal. In radio frequency integrated circuits, both voltage-controlled oscillators subject to undesired couplings and injection-locked frequency dividers behave like forced LC oscillators. These are modeled as second-order driven oscillators working in the subharmonic (secondary) resonance regime. The analysis is based on the generalized Adler's equation, which we introduce to describe the phase dynamics of dividers of any division ratio and to derive closed-form expressions for the spectrum components of the system's oscillatory response. We show that the spectrum is double-sided and asymmetric, unlike the single-sided spectrum of systems with primary resonance. Numerical and experimental results are given to validate the presented results, which significantly generalize those available in the literature.

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Study of Injection Locking With Amplitude Perturbation and Its Effect on Pulling of Oscillator

Cited by 29 publications

References 17 publications

Investigation on Locking and Pulling Modes in Analog Frequency Dividers

Investigation on Locking and Pulling Modes in Analog Frequency Dividers

References

Evaluating the spectrum of periodic pulling in subharmonic resonant LC circuits

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