Envelope Domain Formulation for the Analysis of the Nonlinear Transient Dynamics of Coupled Oscillators
- 24 November 2020
- journal article
- research article
- Published by Institute of Electrical and Electronics Engineers (IEEE) in IEEE Transactions on Microwave Theory and Techniques
- Vol. 69 (1), 566-577
- https://doi.org/10.1109/tmtt.2020.3037475
Abstract
A reduced-order envelope-domain formulation of coupled-oscillator systems based on realistic nonlinear models of the oscillator elements is presented for the first time to our knowledge. The formulation, based on numerical models of the transistor-based oscillators, enables an accurate prediction of the nonlinear dynamics of the coupled system, including the oscillation build-up, the locked and unlocked states, and the oscillator ON-OFF switching. To increase the applicability of the method, both admittance- and impedance-type models are extracted through harmonic balance simulations, under a voltage and current excitation, respectively, at the node/branch where the oscillator is connected to the coupled system. They are used to derive a nonlinear differential-equation system able to describe the transient dynamics of the entire structure. Because the oscillators are coupled through current injection, the impedance-based formulation is formally different from the admittance one, so it requires a dedicated derivation. For illustration, the method has been applied to exhaustively investigate the nonlinear dynamics of a system of three FET-based oscillators at 5 GHz. Very good agreement has been obtained with both circuit-level envelope transient (when applicable) and with measurements.Keywords
Funding Information
- Spanish Ministry of Economy and Competitiveness and the European Regional Development Fund (ERDF/FEDER) under the Research Project (TEC2017-88242-C3-1-R)
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