Wireless-Coupled Oscillator Systems With an Injection-Locking Signal

Abstract

A detailed analysis of wireless-coupled oscillator systems under the effect of an injection-locking signal is presented. The injection source of high spectral purity is introduced at a single node and enables a reduction of the phase-noise spectral density. Under this injection source, the behavior of the coupled system is qualitatively different from the one obtained in freerunning conditions. Two cases are considered: bilateral synchronization, in which an independent source is connected to a particular system oscillator, coupled to the other oscillator elements, and unilateral synchronization, in which one of these elements is replaced by an independent source that cannot be influenced by the rest. The two cases are illustrated through the analysis of a wireless-coupled system with a star topology, such that the injection signal is introduced at the central node. The investigation involves an insightful analytical calculation of the coexisting steady-state solutions, as well as a determination of their stability and bifurcation properties and phase noise. The injection signal stabilizes the system in a large and continuous distance interval, enabling a more robust operation than in autonomous (non-injected) conditions. A coupled system operating at 2.45 GHz has been manufactured and experimentally characterized, obtaining very good agreement between simulations and measurements.

Double Functionality Concurrent Dual-Band Self-Oscillating Mixer

“…As in the single-frequency VCO of [15], two transistor devices are connected to two of the resonator ports. Our goal has been to obtain a demonstrator independent resonance modes at the incommensurate frequencies f1 = 2.4 GHz and f2 = 4.1 GHz; these values enable a comparison of the phase-noise spectral density with previous singlefrequency realizations [32]- [33] using similar components. The resonator design departs from the structure sketched in Fig.…”

Stability and Oscillation Analysis at Circuit Level and Through Semi-Analytical Formulations

“…This section presents a semi-analytical formulation of this interaction, compatible with the use of commercial HB. In this formulation [24], [25], [36], the oscillator is represented with a realistic numerical model, extracted from HB and introduced into an analytical description of the complete system. This has two advantages: it avoids the convergence problems often encountered in HB and provides insight into the dependence of the oscillator solution on the external elements and parameters.…”

“…However, this operation mode often gives rise to multi-valued solutions, virtually impossible to simulate in commercial HB. To cope with this problem, semi-analytical formulations have been introduced [24], [25], [36], which make use of a realistic numerical model of the standalone oscillator, extracted from HB, that is combined with an analytical description of the selfinjection loop. Here a new procedure to determine the stability properties considering the time delay of the signal envelope is presented for the first time.…”

Piecewise Semi-Analytical Formulation for the Analysis of Coupled-Oscillator Systems

“…C OUPLED oscillator systems can be used in several applications like power combination, beam-steering in phased-arrays [1]- [7] or in sensor applications [8]- [10], where the synchronization between the oscillators provides a common time-scale between the nodes of the sensor network. In previous works [11], [12] a semi-analytical formulation (SAF) has been proposed to analyze the behavior of coupled oscillator systems.…”

“…The resulting SAF can be used to model the steady state behavior of the VCO for tuning voltage values in the neighborhood of η 0 . The SAF has been proven to be a powerful technique to model the VCO behavior when operating under free-running conditions [14], synchronized to an external source [12], [14]- [16] or as a part of an array of coupled oscillators, operating both in phased array antenna systems [11]- [13] and in wireless sensor networks [8]- [10]. In the case of coupled oscillators, the SAF is able to predict the coexisting solutions of the array, together with their bifurcation loci.…”