Analysis of Stability Stationary Modes of Quadrature Voltage Controlled Oscillations with Mutual Synchronization

During the study the QVCO with mutual synchronization, it was found that in this model, at the zero phase of the transconductance in BJT model, there are two stable stationary modes with the same self-excitation margin, but with self-oscillation frequencies that differ from the resonant one. For that the operation modes of QVCO are determined, under which single-mode oscillations are established. To analyze the stability, numerical values of the normalized frequency detuning of oscillations, the local slope of the normalized oscillatory characteristic, the normalized average slope of the differential active device (DAD) in the stationary mode at the corresponding values of the phase shift, and the normalized amplitudes of stationary oscillations are required for the research. The oscillatory-theoretical analysis of this problem is complex from the point of view of considering the processes of establishing oscillations in QVCO. This paper presents an in-depth analysis of this issue.