Cyclostationary noise analysis of superregenerative oscillators

Abstract

A rigorous analysis of noise effects in super regenerative oscillators (SRO) operating in linear mode is presented. The analysis takes into account the cyclostationary nature of the SRO response to the noise sources, due to the effect of the quench signal. It is based on the determination of an envelope-domain linear-time-variant (LTV) transfer function with respect to each noise source, plus the application of a detailed stochastic analysis of the SRO output. Initially, the autocorrelation of the output signal is calculated, which varies at two different time scales, and is periodic with respect to the quench signal, so it can be expressed in terms of the frequency-dependent harmonic components of the LTV transfer functions. This enables the calculation of the output spectral density, depending on these harmonic components. Once the spectral density is known, the signal-to-noise ratio can be obtained in a straightforward manner. The analysis method has been validated with both independent circuit-level simulations and measurements.

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

“…This procedure is analogous to the one standardly followed in piecewise envelope-transient formulations [19], where it allows coping with the implicit frequency dependence of the passive linear matrixes. Note that unlike other semi-analytical formulations [24], [25], no Taylor-series expansion has been carried out in (16) with respect to either the oscillation amplitude V or the parameter . Instead, a global dependence of both quantities is considered in the nonlinear admittance model ( , , ) YV .…”

“…The aim of this work is to present a generic noise analysis of SROs in both linear and nonlinear modes. In [16], the analysis in linear mode was carried out using linear-time-variant (LTV) transfer functions [17], [18] directly extracted from circuit-level envelope-transient simulations [19], [20]. However, it is not possible to extend this kind of representation to nonlinear mode.…”

“…The paper is organized as follows. Section II provides a summary of the method to calculate the signal-to-noise ratio in linear regime, presented in [16], and relying on the use of LTV transfer functions. Section III describes the new reduced-order envelope-domain formulation of the SRO, valid for linear and nonlinear operation.…”