Phase-sensitivity analysis of injection-locked mutually coupled oscillators

Abstract

A system of two injection-locked mutually-coupled oscillators intended for sensing applications is analyzed with the aid of a semi-analytical formulation, based on realistic oscillator models, extracted from harmonic-balance simulations. Two different configurations are compared. In the first configuration, only one oscillator is connected to the synchronizing source, whereas the second oscillator is tuned by a capacitive element. Explicit expressions for the synchronization bandwidth and the phase sensitivity versus the tuning element are derived, which should be useful for an optimized design. The system stability properties and their dependence on the coupling-network elements and injection amplitude are also investigated. In the second configuration, the two oscillators are injection locked by the synchronizing source. Results are validated with costly harmonic-balance simulations at circuit level and with experimental measurements.