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.

The authors would like to thank to Spanish Ministry of Economy and Competitiveness for their financial support under the research project TEC2014-60283-C3-1-R and Juan de la Cierva Research Program IJCI-2014-19141 and by the Parliament of Cantabria under the project Cantabria Explora 12.JP02.64069.