Stability and Noise Analysis of Coupled-Oscillator Systems

We present a simplified closed-form formulation for the optimized design of coupled-oscillator systems. It is based on admittance models for the oscillator elements, extracted from HB simulations. The formulation relates explicitly the coupled-system oscillation frequency and amplitude and phase distributions with the parameters of the coupling network and the oscillator elements. It allows anticipating and understanding the form of variation of the system variables and can be used for an insightful design. With a perturbation analysis based on the new formulation, we will generalize existing stability criteria to more complete oscillator models. A combined amplitude- and phase-noise formulation will enable the prediction of the phase-noise spectrum flattening near oscillator carrier, while taking into account the system resonances that affect the spectrum shape. The techniques have been successfully applied to a coupled-oscillator system at 5.2 GHz.