Analysis of stabilization circuits for phase-noise reduction in microwave oscillators

Two configurations for oscillator phase-noise reduction using stabilization circuits have been demonstrated in the literature. One of them is based on the self-injection of the oscillator signal, after it passes through a long delay line or a high-quality-factor resonator. The second one is a stabilization loop, containing a frequency discriminator. In this paper, an in-depth analytical comparison of these two configurations, respectively based on injection locking and phase-locking principles, is presented. Analytical expressions are provided for the variation of the steady-state solution and its phase noise versus the parameters of the feedback network. The expressions are rigorously validated with harmonic balance. Instabilities reported by other authors are investigated through bifurcation analysis. The new expressions enable a good understanding of the amplitude and frequency jumps and sharp phase-noise maxima obtained simulations and measurements versus the feedback parameters. A practical 5-GHz voltage-controlled oscillator has also been implemented, for validation purposes.