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This work presents a new formulation to predict the steady state, stability and phase-noise properties of oscillator circuits including either a self-injection network or a two-port feedback network for phase-noise reduction. The additional network contains a slow-wave structure that stabilizes the oscillation signal. Its long delay inherently gives rise to multivalued solutions in some parameter intervals, which should be avoided for a reliable operation. Under a two-port feedback network, the circuit is formulated extracting two outer-tier admittance functions, which depend on the node-voltage amplitudes, phase shift between the two nodes and excitation frequency. Then, the effect of the slow-wave structure is predicted through an analytical formulation of the augmented oscillator, which depends on the numerical oscillator model and the structure admittance matrix. The solution curves are obtained in a straightforward manner by tracing a zero-error contour in the plane defined by the analysis parameter and the oscillation frequency. The impact of the slow-wave structure on the oscillator stability and noise properties is analyzed through a perturbation method, applied to the augmented oscillator. The phase-noise dependence on the group delay is investigated calculating the modulation of the oscillation carrier. The various analysis and design methods have been applied to an oscillator at 2.73 GHz, which has been manufactured and measured, obtaining phase-noise reductions of 13 dB, under a one-port load network, and 18 dB, under a feedback network.

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.