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The averaging perturbation method for the dominant behaviour analysis of adiabatic single‐controlled oscillators
Author(s) -
Sommariva Antonino M.
Publication year - 1993
Publication title -
international journal of circuit theory and applications
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.364
H-Index - 52
eISSN - 1097-007X
pISSN - 0098-9886
DOI - 10.1002/cta.4490210502
Subject(s) - adiabatic process , mathematics , control theory (sociology) , perturbation (astronomy) , linear differential equation , fourier series , topology (electrical circuits) , differential equation , signal flow graph , network analysis , narrowband , mathematical analysis , physics , computer science , quantum mechanics , control (management) , engineering , optics , combinatorics , artificial intelligence , electrical engineering
Electrical oscillators are called single‐controlled when their non‐linear elements depend on a unique variable, while they are termed adiabatic when their transient operation signal can be represented as a narrowband‐modulated Fourier series with only a finite number of dominant components, including the DC one. the novel method presented here allows one to analyse the dominant dynamics, steady state and dynamical stability of such oscillators. the approach devised is perturbative and is termed averaging, since it moves from the differential equation in the oscillator signal to provide a set of simultaneous differential equations in the complex envelopes of the dominant components of that variable. Owing to the treatment generality, investigable circuit topologies comprise a linear lumped time‐invariant network of any order with bias sources, and any number of non‐linear elements, with or without memory, with a common control variable. to illustrate the use of the method, formulae concerning a seventh‐order oscillator are derived.