Nonlinear analysis of ring oscillator and cross-coupled oscillator circuits

Xiaoqing Ge, Murat Arcak*, Khaled N. Salama

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

11 Scopus citations


Hassan Khalil's research results and beautifully written textbook on nonlinear systems have influenced generations of researchers, including the authors of this paper. Using nonlinear systems tech-niques, this paper analyzes ring oscillator and cross-coupled oscillator circuits, which are essential build-ing blocks in digital systems. The paper first investigates local and global stability properties of an n-stage ring oscillator by making use of its cyclic structure. It next studies global stability properties of a class of cross-coupled oscillators which admit the representation of a dynamic system in feedback with a static nonlinearity, and presents sufficient conditions for almost global convergence of the solutions to a limit cycle when the feedback gain is in the vicinity of a bifurcation point. The result are also extended to the synchronization of interconnected identical oscillator circuits.

Original languageEnglish (US)
Pages (from-to)959-977
Number of pages19
JournalDynamics of Continuous, Discrete and Impulsive Systems Series B: Applications and Algorithms
Issue number6
StatePublished - 2010

Bibliographical note

KAUST Repository Item: Exported on 2020-04-23


  • Cross-couple oscillators
  • Cyclic structure
  • Ring oscillators
  • Stability
  • Synchronization

ASJC Scopus subject areas

  • Applied Mathematics
  • Discrete Mathematics and Combinatorics


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