Nonlinear Analysis of Oscillator Mutual Injection Locking Through Inductor Coupling

This work presents an in-depth investigation of the nonlinear behavior two mutually injection-locked oscillators through inductor coupling. An analytical formulation, solved innovative procedure, facilitates understanding qualitative transformations in system solutions when increasing coupling factor. The analysis demonstrates that, a manner similar to unilaterally oscillators, families disconnected/connected curves are obtained this factor, although patterns, associated with distinct operation modes, more complex. Then, accurate numerical method predict coupled transistor-based is presented, based on admittance models individual oscillators. Mathematical conditions derived solve two-level contour-intersection technique. In way, all coexisting for given set element and parameter values calculated simultaneously, exhaustive manner. cases at fundamental frequency 1:3 ratio considered. Possible applications include oscillator phase-noise reduction implementation sensors using phase shift between elements.