Analysis of Oscillation Modes in Free-Running Ring Oscillators

An in-depth investigation of oscillation modes in ring oscillators is presented. The small-signal stability is initially considered, demonstrating that the poles associated with the dc regime are uniformly distributed on a circle on the complex plane, with increasing density for a higher number of stages. The existence of multiple pairs of poles on the right-hand side of the complex plane gives rise to different oscillation modes, related here to the eigenvectors of the circulant active-device immitance matrix. This paper shows that the stability properties of detected modes depend on both the order of appearance from dc regime, in a sequence of Hopf bifurcations, and the bifurcations undergone by each steady-state mode until reaching the final operation point, when changing a bias voltage, for instance. Thus, the stability analysis must combine a bifurcation analysis from dc regime and a bifurcation analysis of each individual oscillation mode in large-signal regime. The large-signal stability analysis presented shows the possible stabilization mechanisms, which lead to the common physical observation of some of these modes. The stabilization of the desired mode, using concepts from bifurcation theory, is also presented. All techniques have been successfully applied to a ring oscillator at 12.6 GHz.