Stability analysis of oscillators driven with multi-harmonic sources

An investigation of the synchronization behavior of oscillators driven with multi-harmonic sources is presented. The occurrence of ultra-subharmonic synchronization is demonstrated, which gives rise to a multi-resonance behavior versus the fundamental input frequency. When this frequency decreases, instabilities arise in the low amplitude intervals of the multi-resonance curve, and both flip and Hopf bifurcation may delimit the stable synchronization intervals. The study provides a generalization of the theory of fundamentally locked oscillators to the case of oscillators driven with multi-harmonic signals. It is illustrated through application to an oscillator at 5.7 GHz.