Mutual injection locking of oscillator circuits through inductor coupling

This work presents an investigation of mutual injection locking of oscillator circuits through inductor coupling. A realistic analytical formulation provides insight into the system behavior, with coexistent oscillation modes. The stability of these modes is determined through a perturbation analysis, extended to the calculation of the phase-noise spectral density. An analytical expression enables an understanding of the phase-noise reduction mechanism. The cases of two coupled oscillators at the fundamental frequency and two distinct oscillators at a 1/3 frequency ratio are considered. Possible applications include the oscillator phase-noise reduction and the implementation of sensors using the phase shift between the two oscillator elements.