Harmonic-balance analysis and synthesis of coupled-oscillator arrays

A new harmonic-balance technique for the analysis and synthesis of coupled-oscillator systems with adjustable phase progression is presented here. It allows an accurate determination of the phase-shift versus the tuning elements, since detailed models are used for the individual oscillator circuits. It is also possible to impose the synchronization frequency at which the in-phase oscillation takes place and calculate the values of the tuning elements for a pre-fixed phase distribution. The phase noise of the system is analyzed through the carrier modulation approach. The phase-change rapidity versus a control voltage is analyzed through the envelope-transient method. A four-element oscillator array at 5 GHz has been designed through this method and experimentally characterized obtaining very good agreement with the simulation results.