A two-level simulation methodology for coupled-oscillator systems is presented. The inner level corresponds to the harmonic-balance analysis of the elementary oscillator in free-running regime, so as to obtain a one-port reduced-order model. The outer level corresponds to the analysis of the coupled system, deriving a formulation that explicitly relates the oscillation-frequency deviation and the amplitude and phase distributions to magnitudes characterizing the coupling network and oscillator elements. A stability analysis based on this formulation is also carried out obtaining a mathematical condition that determines the stable phase-shift interval. The formulation provides valuable insight into the system behavior and allows the derivation of realistic criteria for an optimum coupled-system performance. The two-level analysis has been extended to injection-locked systems, which enables an investigation of the impact of the number of oscillator elements and relative position of the injection signal on the locking bandwidth.
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