Stability and phase-noise analysis

This contribution emphasizes the relevance of Prof. Vittorio Rizzoli’s works on stability and phase-noise analysis and describes how they have impacted more recent investigations. Regarding the stability analysis, in 1985 he developed a frequency-domain formulation that provided unvaluable insight into the way how the perturbed system should be described and analyzed. This formulation enabled the application, for the first time, of the Nyquist criterion to circuits simulated with harmonic balance (HB). In 1994, he derived a HB formulation for phase-noise analysis, which considered both the frequency modulation, associated with the timing noise, and the frequency conversion effects; it provided a complete prediction of the noisy oscillator spectrum at small and large offset frequencies from the carrier. Departing from these relevant contributions, more recent advances in the two topics will be described.