Bifurcation Method in the Theory of Three-Circuit Oscillators with Stabilizing Cavities: (Classification and Optimization of Oscillating Systems and Modes)

The article presents the research results on generalization of three-circuit oscillatory systems (OS) classification, including the case when the time constant of the intermediate circuit $\tau_{2}$ varies from finite values up to zero, which means that the coupling between the circuits is resistive. It is proved that the bifurcation diagram of the OS loci can be divided into 10 regions that are topologically similar for any $\tau_{2} > 0$. At $\tau_{2} =0$, there remains the only boundary of $\gamma$-type, which separates the loci of hysteresis and non-hysteresis types. In this case, as the whole diagram shows, the OS resonance points are locally stable if they are located to the left of the $\gamma$-boundary and globally stable to the right of the boundary. The results obtained are important at the OS parameters' choose with account contradictory requirements to the loading power, steady-state stability, frequency and phase stability, etc.