Investigation of Self-excitation Conditions of Multi-circuit Oscillators With Stabilizing Cavities

A goal of this paper is to compare peculiarities and application effectiveness of algebraic and frequency stability criteria of the complex polynomials on an example of the self-excitation condition analysis of two- and three-circuit oscillators with stabilizing cavities. Investigation is performed by two methods: the algebraic Hermite-Hurwitz criterion and by the frequency Neimark method. It is shown that during the D-fragmentation construction, the frequency method is preferable than the Hermite-Hurwitz criterion. At the same time, additional information containing in the lower determinants of the criterion, turns out to be useful at bifurcation studying in the multi-circuit oscillators and, as it is well known, the algebraic criteria are the universal way to construct D-fragmentations in the plane and the space of dynamic system’s parameters. It is shown that an oscillatory system with a resistive coupling between the stabilizing cavities and the first circuit is optimal. The optimal values of the communication parameters between the circuits are found.