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.

Highlights

  • Superregenerative oscillators (SROs) use the exponential growth of an oscillation signal to obtain high gain amplification

  • The oscillation is controlled by a quench signal that periodically switches the oscillator on and off (Fig. 1), by shifting the critical pair of complex-conjugate poles from the left-hand side of the complex plane (LHS) to the right-hand side (RHS) and back to the LHS

  • The input signal provides an initial condition that places the system at a certain level of the initial transient and, in the so-called linear mode, the amplitude of the output pulse is proportional to the amplitude of this input signal [1]

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Summary

INTRODUCTION

Superregenerative oscillators (SROs) use the exponential growth of an oscillation signal to obtain high gain amplification. The analysis presented here will make use of the numerical black-box model proposed in [6], which enables the determination of the SRO response to any arbitrarily modulated input signal. It is based on the calculation of an envelope-domain time-variant transfer function [7], relating the output and input of the SRO, and extracted from circuit-level envelope-transient simulations [8]-[9]. A stochastic analysis will be carried out, taking into account the cyclostationary nature of the autocorrelation function of the output signal This will enable an accurate prediction of the noise power spectral density and a straightforward determination of the signal-to-noise ratio

LTV transfer functions with respect to the noise sources
Stochastic analysis of the SRO output
Signal to noise ratio
APPLICATION TO A FET-BASED SRO
Measurement results
CONCLUSION
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