Stability analysis of wireless coupled-oscillator circuits

Distributed synchronization of sensor networks can be achieved by coupling the oscillator signals of the sensor nodes. Previous works describe the coupling effects in an idealized manner, with constant scalar coefficients. Here a realistic analysis of the coupled-system dynamics is presented for the first time to our knowledge, taking into account the antenna gains and propagation effects on the amplitude and phase values of the equivalent current sources, injecting the oscillator elements. The new formulation provides the synchronized oscillation frequency and amplitude and phase distributions of the coupled system. Distinct oscillation modes, with different phase shifts between the oscillator elements, are identified, associated with the system symmetry. The stability properties of these modes change with the distance between the oscillator elements. The possibility to impose in-phase operation by tuning of the oscillator elements is demonstrated. Good agreement is obtained between simulation and measurements.