| Features of the application of envelope methods for the analysis of autonomous oscillators |
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| Authors |
| | Gourary M.M. |
| | Rusakov S.G. |
| Date of publication |
| | 2020 |
| DOI |
| | 10.31114/2078-7707-2020-2-9-15 |
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| Abstract |
| | The paper proposes new approaches to the application of well-known versions of envelope methods for solving problems of accelerated simulation of autonomous oscillator circuits.
The process of slow variations of high-frequency oscillations in the electronic circuit is presented as a system of ordinary differential equations in the form of a charge model. Such an approach allows one to use the well-known step and order selection algorithms within the framework of the integration methods in the envelope transient analysis.
It is shown that a feature of simulation algorithms for oscillator circuits based on envelope methods is the need to take into account changes in the period of high-frequency oscillations in the integration process.
To take into account such changes in the Envelope Following Method, it is proposed to determine the initial and final points of the current oscillation period through the maxima of the charge variable. The advantages of this approach over the known methods of fixing the level of a system variable or its derivative are shown.
In the framework of the Transient Harmonic Balance method, the period’s initial point is defined by the zero phase value of one of the nodal harmonics, and the period value is determined by the instantaneous oscillation frequency. The phase and the instantaneous frequency are additional variables of the system. Corresponding additional equations are the zero phase condition and the expression presenting the instantaneous frequency as the phase derivative.
For each of the considered methods, the paper presents for the residual and the Jacobi matrix of the system of equations at the envelope integration step. |
| Keywords |
| | circuit simulation, shooting method, envelope following, transient harmonic balance, oscillator |
| Library reference |
| | Gourary M.M., Rusakov S.G. Features of the application of envelope methods for the analysis of autonomous oscillators // Problems of Perspective Micro- and Nanoelectronic Systems Development - 2020. Issue 2. P. 9-15. doi:10.31114/2078-7707-2020-2-9-15 |
| URL of paper |
| | http://www.mes-conference.ru/data/year2020/pdf/D001.pdf |
