Evaluation of Oscillator Phase and Frequency Transfer Functions

Gourary, M.M.; Русаков, С. Г.; Ulyanov, S.L.; Жаров, М.М.; Mulvaney, B.J.

doi:10.1007/978-3-642-12294-1_24

Cited by 5 publications

(1 citation statement)

References 13 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…In this case, relation ( 5) is modified to (9) The extra jitter due to AM, denoted as , enters time relationship (6) as follows 1 (10) Since in (10) , the first term on the right hand side of ( 9) is well approximated by (11) The error introduced by this approximation is of the order of and thus it is negligible compared to . Thus, plugging (11) into ( 9) and exploiting the -periodicity of and of , we obtain (12) In Section IV, it will be proven that, for a harmonic interference, the amplitude waveform takes the form (13) where is a -periodic function (i.e., an element of a Floquet eigenvector) while is a slowly-varying coefficient oscillating with frequency . In this case, using the approximation and the periodicity of , the numerator of ( 12) can be simplified to (14) With this simplification, AM-induced period variation ( 12) is estimated by (15) where is the ratio of over at the crossing time point , which is almost constant over all cycles.…”

Section: Oscillator Macromodel and Timing Jittermentioning

confidence: 99%

A Study of Deterministic Jitter in Crystal Oscillators

Maffezzoni

Zhang

Daniel

2014

IEEE Trans. Circuits Syst. I

View full text Add to dashboard Cite

Crystal oscillators are widely used in electronic systems to provide reference timing signals. Even though they are designed to be highly stable, their performance can be deteriorated by several types of random noise sources and deterministic interferences. This paper investigates the phenomenon of timing jitter in crystal oscillators induced by the injection of deterministic interferences. It is shown that timing jitter is closely related to the phase and amplitude modulations of the oscillator response. A closed-form variational macromodel is proposed to quantify timing jitter as well as to qualitatively explain the interference mechanism. Analytical results and efficient numerical simulations are developed to explore how timing jitter depends on the frequency of the interfering signal. The methodology is tested by a crystal Pierce oscillator

show abstract