0000000000543760
AUTHOR
A.m. Sommariva
Necessary and sufficient conditions for frequency entrainment of quasi-sinusoidal injection-synchonised oscillators
A method is presented which permits the first-approximation exact analysis of the dynamical stability of fundamental-mode injectionsynchronized oscillators (FISO's) characterized by a quasi-sinusoidal quasi-static behavior. By combining small parameter and stroboscopic transformation techniques, the phase-lock stability investigation of an nth-order system is reduced to the simple Hurwitz test on an nth degree polynomial easily obtainable from steady state describing quantities. On this basis, equations for critical locking are also derived, which demonstrate the existence of a pair of limit curves (Locus and Boundary) already conjectured and looked for in the past, but only with partial su…
A method for the investigation of high-order two-frequency asynchronous oscillators
A general method for analysing asynchronous high-order two-frequency oscillators is presented. the oscillator model is made up of a GC non-linear parallel group embedded in a linear lumped time-invariant network of any order. the approach devised rests on the identification of a pair of narrow-band impedance operators which permit one to derive first-approximation steady state and dynamic equations in the phasor domain—as well as stability criteria—in a simple and expressive manner. Previous results from averaging and perturbation treatments on fourth-order asynchronous oscillators are shown to be obtainable from this theory as particular cases. the sixth-order oscillator chosen as an appli…
Approach to the analysis of nonlinear feedback oscillators under large-signal injection
A method for the analysis of driven oscillators under high-level injection is presented. It applies to single-loop feedback systems with a memoryless nonlinear element and a second-order (high-Q) tank circuit. The analysis technique employed combines the classical block-diagram approach with an improved firstharmonic dynamic modelling to provide a couple of differential equations capable of accounting for the amplitude-dependence effects arising under large-signal operation. On this basis, first-and second-order approximate expressions are also derived, which allow a better understanding of the validity limits of previous theories on this subject. As an example of application, both the stea…
On the dynamical stability of negative conductance free running oscillators
For a class of weakly nonlinear autonomous systems exhibiting both resistive and reactive nonlinearities, asymptotic orbital stability is investigated through a new narrow-band differential approach. The main result is the derivation of the exact characteristic polynomial associated with the local dynamics of the amplitude and phase of the free-running oscillation to be tested. For an nth-order circuit, (n - 1) necessary and sufficient stability conditions are then obtained, in an analytical explicit form suitable for computer implementation, by resorting to conventional Hurwitz test algorithms. A comparison with other differential stability criteria available in the literature is also carr…
Subharmonic phase-lock criteria for a class of weakly non-linear high-order oscillators
Subharmonic frequency entrainment of high-order weakly non-linear oscillators is investigated. For the class of circuits considered, equations are first derived which provide the first approximation values for the amplitudes and phases of the two main spectral components of the steady-state waveform. Necessary and sufficient stability criteria are then derived in explicit from. The example worked out (a negative conductance double-tuned oscillator) shows the efficiency and ease of use of the proposed method.