Analysis of Chirped Oscillators Under Injection Signals

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.