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Simulation methods of oscillator circuits under weak excitation for circuit simulators

Keywords:

M.M. Gourary - Ph.D. (Eng.), Senior Research Scientist, Institute for Design Problems in Microelectronics of Russian Academy of Sciences (Moscow). E-mail: gourary@ippm.ru M.M. Zharov - Ph.D. (Eng.), leading Research Scientist, Institute for Design Problems in Microelectronics of Russian Academy of Sciences (Moscow). E-mail: zarov@ippm.ru S.G. Rusakov - Dr.Sc. (Eng.), Corresponding Member of RAS, Chief Research Scientist, Institute for Design Problems in Microelectronics of Russian Academy of Sciences (Moscow). E-mail: rusakov@ippm.ru S.L. Ulyanov - Dr.Sc. (Eng.), Head of Department, Institute for Design Problems in Microelectronics of Russian Academy of Sciences (Moscow). E-mail: ulyas@ippm.ru


The important problem of oscillator design is estimation of the impact of undesirable influence from other components of integrated circuits on oscillator behavior. A brief mathematical description of the principles of analysis of different modes of the oscillator behavior under weak excitation is given in the paper. The description is based on the harmonic balance (HB) technique. The set of methods providing the analysis of arbitrary excited oscillators is presented. The methods are based on transformations of small-signal Harmonic Balance equations aimed to the elimination of the matrix singularity at the zero frequency offset. Approaches to the solutions of a number of practically important problems arising in the analysis of excited oscillators are obtained. The problems include phase noise evaluation, injection locking conditions, evaluation of the spectrum of a pulled oscillator, the analysis of mutually locked oscillators. The features of forming the model equations for small-signal analysis are considered for modes of phase modulation, injection pulling, injection locking. The algebraic system is derived for oscillator phases and common locking frequency of mutually locked oscillators. The smoothed form of phase macromodel is given. The general case is presented when the excitation frequency is close to the rational fraction of the oscillator fundamental.
References:

 

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