Evaluating the Spectrum of Unlocked Injection Frequency Dividers in Pulling Mode

Abstract

Abstract:We study the phenomenon of periodic pulling which occurs in certain integrated microcircuits of relevant interest in applications, namely the injection-locked frequency dividers (ILFDs). They are modelled as second-order driven oscillators working in the subharmonic (secondary) resonance regime, i.e., when the self-oscillating frequency is close (resonant) to an integer submultiple n of the driving frequency. Under the assumption of weak injection, we find the spectrum of the system's oscillatory response in the unlocked mode through closed-form expressions, showing that such spectrum is double-sided and asymmetric, unlike the single-sided spectrum of systems with primary resonance (n1). An analytical expression for the amplitude modulation of the oscillatory response is also presented. Numerical results are presented to support theoretical relations derived.

Evaluating the spectrum of periodic pulling in subharmonic resonant LC circuits

“…We show that the frequency spectrum of the pulled oscillations is double‐sided and asymmetric, with respect to the injection frequency divided by n (as shown in Figure (f)), in contrast to the single‐sided spectrum (shown in Figure (d)) arising in systems with primary resonance. Finally, numerical and experimental results are presented (Section 4) to support the theoretical results presented, which are derived through a substantially different and more general approach than that in , where a special case n = 2 and a particular divider circuit are considered.…”