Evaluating the Spectrum of Unlocked Injection Frequency Dividers in Pulling Mode

Entropy

Antonio Buonomo¹ 

关键词: Injection pulling;    analog frequency dividers;    injection-locked frequency dividers (ILFDs);    nonlinear oscillators;    synchronization;    averaging method;   

DOI  :  10.3390/e15104026

来源: mdpi

【 摘 要 】

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.

【 授权许可】

CC BY   
© 2013 by the authors; licensee MDPI, Basel, Switzerland.