Abstract
Time synchronization of multiple elements of a wireless network can be achieved through the wireless coupling of their oscillator circuits. Most previous works on wireless locking of oscillators analyze the system in an idealized manner, representing the oscillator elements with phase models and describing the propagation effects with constant scalar coefficients and time delays. Here, a realistic analysis of the wireless system is presented, which relies on the extraction of the oscillator models from harmonic-balance (HB) simulations and takes into account the antenna gains and propagation effects. The most usual network configurations, corresponding to ring, fully connected, and star topologies, are investigated in detail. In symmetric conditions, the oscillation modes are detected through an eigenvalue/eigenvector calculation of an equivalent coupling matrix. For each particular mode, the system is analyzed in the following manners: by means of an analytical formulation, able to provide all the coexistent solutions, and through a circuit-level HB simulation of an equivalent system with a reduced number of oscillator elements. The stability properties are determined by means of a perturbation system of general application to any coupled structure. A specific formulation is also derived to predict the impact of discrepancies between the oscillator elements. All the results have been validated with independent circuit-level simulations and measurements.
Highlights
T IME synchronization between different devices is a usual requirement in engineering systems, such as computer networks, measurement systems, sensor networks and other [1]-[10]
In the phase-locked loops (PLL) case [2], the antenna signals enter the phase-detector of each oscillator and there is no clear solution to use a single antenna for both transmission and reception
Connected topology with N = 5 oscillator elements. It is based on the use of an Agilent 90804A Digital Storage Oscilloscope and two E4446A PSA spectrum analyzers in order to visualize the oscillator waveforms, the synchronized spectrum and the phase noise simultaneously
Summary
T IME synchronization between different devices is a usual requirement in engineering systems, such as computer networks, measurement systems, sensor networks and other [1]-[10]. In the PLL case [2], the antenna signals enter the phase-detector of each oscillator and there is no clear solution to use a single antenna for both transmission and reception This is achieved in the case of injection-locked operation, which should enable a simple testing of different network topologies. The first one is based on an analytical formulation that depends on the linearized HB models of the oscillator elements and the eigenvalue associated with each particular mode This formulation will allow an efficient tracing of the complete solution curves (including multi-valued sections) versus any relevant parameter, such as the distance between the oscillator elements or the antenna gain.
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