Quadrature Synchronization of a Pair of Van der Pol Oscillators Coupled by NEMS Varactor: A Theoretical Analysis - Singh, Aman Kumar; Yadava, R. D. S. (Journal of Applied Nonlinear Dynamics, 2026)
The paper analyses frequency synchronization characteristics of two Van der Pol oscillators coupled by a NEMS varactor. Equations of motion are derived by taking into account the voltage nonlinearity of the NEMS varactor. The synchronization conditions are obtained in the form of coupled algebraic equations between synchronization frequency, amplitude ratio and phase diﬀerence. The synchronization frequency in phase quadrature is controlled by amplitude ratio of the coupled oscillators. A comparative analysis of synchronization characteristics is also presented for coupling by a ﬁxed value capacitor. It is found that NEMS coupled system is tunable over an order of magnitude greater frequency range under identical conditions for quadrature tolerance. The NEMS varactor coupling does not require a master-slave like condition for attaining phase quadrature. The analyses for phase sensitivity and linear stability are performed. The stable synchronization occurs for the amplitude ratio being more than 0.7. The paper illustrates that NEMS capacitive coupling of Van der Pol oscillators facilitates amplitude ratio as controlling parameter for synchronization, and results in enhanced tunability and quadrature accuracy.