| Abstract: | 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. |
