Modelling and analysis of differential VCOs: Research Articles
International Journal of Circuit Theory and Applications
On the theory of quadrature oscillations obtained through parallel LC VCOs
IEEE Transactions on Circuits and Systems Part I: Regular Papers - Special section on 2009 IEEE custom integrated circuits conference
Modeling, analysis, and experimental validation of frequency dividers with direct injection
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.