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A novel approximated solution for the Van der Pol oscillator. Application to pulsed oscillations modeling in switched cross-coupled MOS oscillators

The operation of a periodically switched cross-coupled oscillator is considered in this work. First, it is shown that this architecture corresponds to a Van der Pol oscillator. Based on that, a novel analytical solution is proposed for the Van der Pol equation taking into account the time-dependent amplitude and frequency variation at the starting of oscillation. In addition, an original specific model for the pulsed oscillations is presented. Comparison with numerical simulations of the Van der Pol equation shows very good accuracy. Finally, it is shown that synchronization of the oscillations pulses on the input signal can be obtained under specific conditions.