Open AccessStudy of injection‐locked non‐harmonic oscillators using Volterra series
Author(s) -
Zhou Yushi,
Yuan Fei
Publication year - 2015
Publication title -
iet circuits, devices and systems
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.251
H-Index - 49
eISSN - 1751-8598
pISSN - 1751-858X
DOI - 10.1049/iet-cds.2013.0424
Subject(s) - harmonic , mathematics , harmonic oscillator , topology (electrical circuits) , control theory (sociology) , injection locking , relaxation oscillator , series (stratigraphy) , ring (chemistry) , lock (firearm) , voltage , physics , engineering , computer science , voltage controlled oscillator , acoustics , quantum mechanics , paleontology , control (management) , artificial intelligence , mechanical engineering , laser , chemistry , organic chemistry , combinatorics , biology
This study presents a Volterra series approach to analyse injection‐locked non‐harmonic oscillators. We show that by depicting the voltage transfer characteristics of comparators using hyperbolic tangent functions, non‐harmonic oscillators can be analysed analytically using a set of Volterra circuits that are linear, have the same topology and element values but different inputs. We further show that the larger lock range of non‐harmonic oscillators as compared with that of their harmonic counterparts is because of the harsher non‐linear characteristics of these oscillators and the lower‐order attenuation of the high‐order frequency components of the oscillators. The reduced non‐linear characteristics of ring oscillators because of the absence of positive feedback also gives rise to a smaller lock range as compared with relaxation oscillators. These theoretical findings are validated using both the simulation results of relaxation oscillators and ring oscillators designed in IBM 130 nm complementary metal oxide semiconductor technology and the measurement results of ring oscillators implemented using commercial ICs.