Evaluating the spectrum of periodic pulling in subharmonic resonant LC circuits.

We 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. [ABSTRACT FROM AUTHOR]