Semi-analytical formulation for the stability analysis of coexisting solutions in coupled-oscillator systems

Coupled oscillator systems with constant interstage phase shift are used for beam steering and other applications. The aim of this work is the stability investigation of the multiple mathematical solutions that coexist with the constant-phase-shift one. This will be efficiently done by means of a semi-analytical formulation, based on a perturbation model of the oscillator elements, extracted with harmonic balance. The formulation is valid for the most practical situation of weak oscillator coupling. The stability of each of the coexisting solutions is determined from the linear perturbation system, associated to the semi-analytical formulation. The presented techniques allow an in-depth understanding of the global system behavior and a conclusive determination of the instability phenomena that delimit the stable constant phase-shift ranges. The techniques have been applied to a coupled system of FET-based oscillators at 5 GHz, with very good results.