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Nonlinear analysis of quadrature LC–VCOs

We present a nonlinear approach based on the perturbation theory to analyze the synchronized oscillations in circuits made up of two coupled LC differential oscillators (LC-VCO), widely used in RF systems to generate quadrature oscillations. Closed-form expressions are derived to predict the amplitude and phase of oscillations and their orbital stability. The capabilities of the method are also briefly highlighted. Finally, the validity of presented formulae was validated by circuit simulations.