Abstract:
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 oscill...Show MoreMetadata
Abstract:
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.
Published in: IEEE Transactions on Circuits and Systems I: Fundamental Theory and Applications ( Volume: 50, Issue: 7, July 2003)
Keywords assist with retrieval of results and provide a means to discovering other relevant content. Learn more.
- IEEE Keywords
- Index Terms
- Time Scale ,
- Differential Equations ,
- Modulation Frequency ,
- Amplitude Modulation ,
- Time Warping ,
- Time-scale Separation ,
- Frequency Modulation Signal ,
- Time-variant ,
- Changes In Frequency ,
- Numerical Methods ,
- Large Systems ,
- Set Of Equations ,
- Periodic Boundary Conditions ,
- Fourier Series ,
- Voltage Control ,
- Periodic Function ,
- Local Frequency ,
- Compact Representation ,
- Phase-locked Loop ,
- Fourier Coefficients ,
- Differential-algebraic Equations ,
- Instantaneous Frequency ,
- Harmonic Balance ,
- Slow Variables ,
- Varactor ,
- Bivariate Function ,
- Warping Function ,
- Transient Simulation ,
- System Dynamics ,
- Time Axis
Keywords assist with retrieval of results and provide a means to discovering other relevant content. Learn more.
- IEEE Keywords
- Index Terms
- Time Scale ,
- Differential Equations ,
- Modulation Frequency ,
- Amplitude Modulation ,
- Time Warping ,
- Time-scale Separation ,
- Frequency Modulation Signal ,
- Time-variant ,
- Changes In Frequency ,
- Numerical Methods ,
- Large Systems ,
- Set Of Equations ,
- Periodic Boundary Conditions ,
- Fourier Series ,
- Voltage Control ,
- Periodic Function ,
- Local Frequency ,
- Compact Representation ,
- Phase-locked Loop ,
- Fourier Coefficients ,
- Differential-algebraic Equations ,
- Instantaneous Frequency ,
- Harmonic Balance ,
- Slow Variables ,
- Varactor ,
- Bivariate Function ,
- Warping Function ,
- Transient Simulation ,
- System Dynamics ,
- Time Axis