New Techniques for the Analysis and Design of Coupled-Oscillator Systems

An in-depth analysis of the nonlinear dynamics of coupled-oscillator arrays is presented for a better understanding of their complex autonomous behavior. In one-dimensional arrays, the constant inter-stage phase shift is varied by simultaneously detuning the two outermost oscillators in opposite directions. Thus, the array can be considered as a two-parameter system. Here, a two-parameter stability analysis of the oscillator array is carried out, investigating the phenomena that limit the achievable values of constant inter-stage phase shift under both weak and strong coupling conditions. The gradual evolution of the system behavior with increasing coupling strength is studied. A semianalytical approach is presented for an efficient design of the oscillator array, avoiding the computational expensiveness of harmonic balance (HB) in systems with a high number of oscillator elements. The proposed method, valid for weak coupling, uses a perturbation model of the elementary oscillator obtained with HB so it is of general application to any oscillator topology with accurate descriptions of its linear and nonlinear components. Approaches for the stability and phase-noise analyses based on this formulation are also presented. The new techniques have been applied to the design of a coupled system of three oscillators at 6 GHz. The results have been successfully compared with full HB simulations and with measurements