Nonlinear Analysis of Ring Oscillator and Cross-Coupled Oscillator Circuits

Xiaoqing Ge, Murat Arcak*, Khaled Nabil Salama

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

10 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 techniques, this paper analyzes ring oscillator and cross-coupled oscillator circuits, which are essential building 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 su cient 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)
JournalDynamics of Continuous, Discrete and Impulsive Systems Series B: Applications and Algorithms
StatePublished - Dec 15 2010


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