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Analyzing oscillators using multitime PDEs

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2 Author(s)
Narayan, O. ; Tata Inst. of Fundamental Res., Bangalore, India ; Roychowdhury, J.

Oscillators are often difficult to analyze or simulate, because they generate waveforms that can span a range of widely separated time scales. We present a general oscillator formulation that separates slow and fast dynamics without approximations, and captures amplitude and frequency modulation in a natural and compact manner. To handle frequency-modulation effectively, we make use of a novel concept, warped time, within a multitime partial differential equation framework. The equations incorporate an explicit time-varying frequency variable that matches intuitive notions of changing frequency in a frequency-modulated signal. The formulation is useful for both hand analysis and numerical simulation.

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Circuits and Systems I: Fundamental Theory and Applications, IEEE Transactions on  (Volume:50 ,  Issue: 7 )