Abstract

An in-depth investigation of the response of chirped oscillators under injection signals is presented. The study confirms the oscillator capability to detect the input-signal frequencies, demonstrated in former works. To overcome previous analysis limitations, a new formulation is presented, which is able to accurately predict the system dynamics in both locked and unlocked conditions. It describes the chirped oscillator in the envelope domain, where two time scales are used, one associated with the oscillator control voltage and the other associated with the beat frequency. Under sufficient input amplitude, a dynamic synchronization interval is generated about the input-signal frequency. In this interval, the circuit operates at the input frequency, with a phase shift that varies slowly at the rate of the control voltage. The formulation demonstrates the possibility of detecting the input-signal frequency from the dynamics of the beat frequency, which increases the system sensitivity. All the results have been validated with both full circuit-level simulations and measurements.

Highlights

  • The interesting works [1]-[2] successfully investigated the possible application of chirped oscillators under the injection of wireless signals in cognitive radio, for spectrum sensing [3]-[4] and frequency demodulation

  • This conclusion relies on the capability of the chirped oscillator to get locked to an input signal having a frequency comprised within its dynamic oscillation-frequency interval, which is achieved with a certain input-signal power

  • An in-depth investigation of the dynamics of the chirpsignal oscillator under wireless injection is presented. It is based on an envelope-domain, semi-analytical formulation of the injected circuit, using an oscillator model extracted from harmonic balance (HB) [5]-[6]

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Summary

INTRODUCTION

The interesting works [1]-[2] successfully investigated the possible application of chirped oscillators under the injection of wireless signals in cognitive radio, for spectrum sensing [3]-[4] and frequency demodulation This conclusion relies on the capability of the chirped oscillator to get locked to an input signal having a frequency comprised within its dynamic oscillation-frequency interval, which is achieved with a certain input-signal power. The variations of the dynamic oscillation under both locked and unlocked conditions are analyzed using two time scales, one associated with the control voltage of the chirped oscillator, and the other associated with the beat frequency This avoids the computational difficulties of a full envelope-domain formulation [7]-[9], which must cover the slow sawtooth-signal period (on the order of ms) at a small integration time step, accounting for the beat frequency outside the synchronization time interval. The possible system application as a receiver of frequency-modulated signals with carriers within the chirped-oscillator frequency band is investigated, which may, for instance, have interest in sensor networks

FORMULATION OF THE INJECTED CHIRPED OSCILLATOR
OPERATION UNDER UNLOCKED CONDITIONS
CONCLUSIONS
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