Analysis and Modeling of Super-Regenerative Oscillators With FSCW Signals

Active transponders based on super-regenerative oscillators (SROs) have the advantages of a high gain, low consumption, and a compact implementation. They rely on a switched oscillator excited by a low amplitude frequency-modulated continuous-wave (FMCW) signal, which provides an approximately phase-coherent response. Due to the complexity of their operation mode, involving the start-up transient and a time-varying phase shift, their realistic modeling is demanding. Here, we present an in-depth semianalytical investigation of an SRO transponder excited by a frequency-stepped signal, which includes, for the first time to our knowledge, a thorough analysis of the noise perturbations. The SRO is analyzed with a 2-D envelope-domain formulation, derived from a current function extracted from harmonic balance. As will be shown, the SRO response to the incoming signal can be predicted with two nonlinear functions, corresponding to the amplitude and phase, obtained in a single oscillation interval. We will derive an Ornstein-Uhlenbeck system from which the variance of the SRO amplitude and phase will be determined through a detailed analytical approach. Like the SRO response, the noise behavior can be predicted with functions extracted from a single oscillation pulse, which will relate the noise effects to the unperturbed amplitude and phase at the various oscillation stages. The complete investigation provides insight into the effect of nonlinearity and noise on the detected baseband signal and the estimated distance. It will be applied to an SRO at 2.7 GHz, which has been manufactured and measured.