Stability Analysis of Injection-Locked Multimode Oscillators

This paper presents an in-depth stability analysis of injection-locked multimode oscillators. The various types of bifurcations, or qualitative stability changes, occurring in these systems when varying the input power are studied in detail. It is shown that, for low injection power, each stable injection-locked oscillation coexists with as many two-fundamental quasi-periodic solutions as the number of stable periodic oscillations in the original free-running circuit. The mechanisms leading to the successive extinctions of these undesired stable quasi-periodic solutions are investigated in-depth, as well as the possible stabilization of periodic oscillation modes that were originally unstable in free-running conditions. The overall study enables a thorough understanding and anticipation of the complex nonlinear dynamics of these multimode systems. It is demonstrated that, by changing the injection frequency, together with control of the bias voltage, it is possible to switch between the various injection-locked oscillations, obtaining a reconfigurable system. The study is illustrated through application to a demonstrator, consisting of a ring oscillator in which six stable oscillation modes were measured at different operation points and frequencies comprised between 9.4 and 15.4 GHz.