Noise Analysis of Super-Regenerative Oscillators in Linear and Nonlinear Modes

A rigorous analysis of noise effects in super-regenerative oscillators (SROs), operating in both linear and nonlinear modes, is presented. For operation in the linear mode, two different analysis methods are presented. One is based on the calculation of linear-time variant (LTV) transfer function with respect to the input signal and the noise sources. The second method is based on a compact semianalytical formulation of the pulsed oscillator under the effect of the quench signal. The compact formulation also enables the analysis of the SRO in the nonlinear mode. It constitutes a fully new mathematical description of SROs, with general applicability, as it is not restricted to a particular oscillator topology. It relies on a numerical nonlinear black-box model of the stand-alone free-running oscillator, extracted from harmonic-balance simulations. This model is introduced into an envelope-domain formulation of the SRO at the fundamental frequency. Both the method based on LTV transfer functions and the semianalytical formulation take into account the cyclostationary nature of the SRO response to the noise sources. In the nonlinear mode, the variances of the amplitude and phase are calculated linearizing the formulation of the pulsed steady-state solution. The particular time variation of the phase variance is explained in detail and related to the onset and extinction of the oscillation in the presence of an RF input signal. The new analysis methods have been validated with both independent circuit-level simulations and measurements.