Two-Scale Envelope-Domain Analysis of Injected Chirped Oscillators

The response of chirped oscillators under the injection of independent signals, for spectrum sensing in cognitive radio, and under self-injection, for radio frequency identification, is analyzed in detail. The investigation is performed by means of a semianalytical formulation, based on a realistic modeling of the free-running oscillator, extracted from harmonic-balance simulations or from experimental measurements, through a new characterization technique. In the new formulation, the oscillator is linearized about a free-running solution that varies with the control voltage. This enables its application to oscillators having a frequency characteristic that deviates from the linear one. In the case of injection by independent signals, the two-scale envelope-domain formulation will enable an efficient handling of the difference between the slow chirp frequency and the beat frequency. The input carriers can be detected from their dynamic synchronization intervals or, at lower input-power levels, from the dynamics of the beat frequency. Noise perturbations are introduced into the formulation, which enables an estimation of the minimum detectable signal. In the case of a self-injected oscillator for radio frequency identification, an insightful formulation is derived to predict the propagation and tag-resonance effects on the instantaneous oscillation frequency. The tag-resonance signature gives rise to a distinct modulation of the oscillation frequency during the chirp period, which can be detected from the variation of the oscillator bias current. The analysis methods are illustrated through their application to a chirped oscillator, operating in the band 2-3 GHz.